Package 'streamDAG'

Arcs of a directed graph

Description

This function and its documentation have been lifted from the igraph function E with arguments according to DAG conventions. An arc sequence is a vector containing numeric arc ids, with a special class attribute that allows custom operations: selecting subsets of arcs based on attributes, or graph structure, creating the intersection, union of arcs, etc.

Usage

A(G, P, path)

Arguments

G	Graph object of class igraph. See graph_from_literal.
P	A list of node to select arcs via pairs of nodes. The first and second nodes select the first arc, the third and fourth node select the second arc, etc.
path	A list of nodes, to select arcs along a path. Note that this only works reliably for simple graphs. If the graph has multiple arcs, one of them will be chosen arbitrarily to be included in the arc sequence.

Details

Arc sequences are usually used as function arguments that refer to arcs of a graph.

An arc sequence is tied to the graph it refers to: it really denoted the specific arcs of that graph, and cannot be used together with another graph.

An arc sequence is most often created by the A() function. The result includes arcs in increasing arc id order by default (if none of the P and path arguments are used). An arc sequence can be indexed by a numeric vector, just like a regular R vector.

Value

An arc sequence of the graph.

Author(s)

Gabor Csardi

See Also

See E

Examples

G <- graph_from_literal(a --+ b, c --+ d, d --+ e, b --+ e, e --+ j, j --+ m, f --+ g, g --+ i, 
 h --+ i, i --+ k, k --+ l, l --+ m, m --+ n,  n --+ o)
 
A(G)

---

Raise an adjacency matrix to some power

Description

When applying the definition of matrix multiplication to an adjacency matrix $\mathbf{A}$, the $i,j$ entry in $\mathbf{A}^k$ will give the number of paths in the graph from node $i$ to node $j$ of length $k$.

Usage

A.mult(G, power, text.summary = TRUE)

Arguments

G	Graph object of class igraph. See graph_from_literal.
power	The power to rise the adjacency matrix to.
text.summary	Logical. If TRUE the function returns a summary of the paths of length power. If FALSE. The adjacency matrix raised to power is returned.

Value

Returns either a character vector of paths of a specified length or, if text.summary = TRUE, the adjacency matrix raised to a specified power.

Author(s)

Ken Aho

Examples

kon_full <- streamDAGs("konza_full")
A.mult(kon_full, power = 6)

---

Nodal coordinates for graphs in the AIMS project

Description

Contains spatial coordinates for graph nodes for stream networks in the Aquatic Intermittency effects on Microbiomes in Streams (AIMS) project

Usage

data("AIMS.node.coords")

Format

A data frame with 307 observations on the following 7 variables.

Object.ID

Nodal identifier

lat

Latitude

long

Longitude

site

Stream network name, currently includes: "KZ" = Konza Prairie, "TD" = Talladega, "WH" = Weyerhauser, "PR" = Painted Rock, "JD" = Johnson Draw, "DC" = Dry Creek, and "GJ" = Johnson Draw.

piezo

Logical, indicating whether the location contains a peizometer.

microbial_seasonal_network

Logical, whether the location was sampled as part of AIMS seasonal microbial sampling.

STIC_inferred_PA

Logical, whether surface water presence/absence data were obtained from STIC (Stream Temperature, Intermittency, and Conductivity) sensors at the location.

New_in_2023

Logical, referring to sites at Johnson Draw added in 2023.

---

Obtain arc stream activity outcomes based on bounding nodes

Description

Given nodal water presence absence data $\in \{0,1\}$ for a graph, G, the function calculates arc water presence probabilities using particular rules (see approaches in Details).

Usage

arc.pa.from.nodes(G, node.pa, approach = "aho", na.rm = TRUE)

Arguments

G	Graph object of class igraph. See graph_from_literal.
node.pa	A data frame or matrix of nodal presence absence data with column names corresponding to node names in G.
approach	One of "aho", "dstream", or "ustream" (see Details).
na.rm	For approach = "aho", one of TRUE or FALSE indicating whether NA values should be stripped before calculating means. Ignored for other appraches.

Details

The approach argument currently supports three alternatives "aho", "dstream" and "ustream". Let $x_{k}$ represent the $k$th arc with bounding nodes $u$ and $v$.

Under approach = "aho" there are three possibilities: $x_{k} = 1.0$ if both $u$ and $v$ are wet, $x_{k} = 0$ if both $u$ and $v$ are dry, and $x_{k} = 0.5$ if only one of $u$ or $v$ is wet.

Under approach = "dstream", $x_{k} = 1.0$ if $v$ is wet, and $x_{k} = 0$ if $v$ is dry.

Conversely, if approach = "ustream", $x_{k} = 1.0$ if u is wet, and $x_{k} = 0$ if u is dry.

Value

Returns a matrix whose entries are estimated probabilities of success (e.g. surface water presence) based on the rules given in Aho et al. (2023). Matrix columns specify arcs and rows typically represent time series observations.

Author(s)

Ken Aho

References

Aho, K., Derryberry, D., Godsey, S. E., Ramos, R., Warix, S., Zipper, S. (2023) The communication distance of non-perennial streams. EarthArXiv https://eartharxiv.org/repository/view/4907/

Examples

murphy_spring <- graph_from_literal(IN_N --+ M1984 --+ M1909, IN_S --+ M1993,  
M1993 --+ M1951 --+ M1909 --+ M1799 --+ M1719 --+ M1653 --+ M1572 --+ M1452, 
M1452 --+ M1377 --+ M1254 --+ M1166 --+ M1121 --+ M1036 --+ M918 --+ M823, 
M823 --+ M759 --+ M716 --+ M624 --+ M523 --+ M454 --+ M380 --+ M233 --+ M153, 
M153 --+ M91 --+ OUT)

data(mur_node_pres_abs)
pa <- mur_node_pres_abs[400:405,][,-1]
arc.pa.from.nodes(murphy_spring, pa)
arc.pa.from.nodes(murphy_spring, pa, "dstream")

---

Assortativity

Description

Calculates graph assortativity

Usage

assort(G, mode = "in.out")

Arguments

G	Graph object of class igraph. See graph_from_literal.
mode	One of "in.in", "in.out", "out.out", "out.in", or "all".

Details

The definitive measure of graph assortativity is the Pearson correlation coefficient of the degree of pairs of adjacent nodes (Newman, 2002). Let $\overrightarrow{u_iv_i}$ define nodes and directionality of the ith arc, $i=1,2,3,\ldots,m$, let $\gamma,\tau\in{-,+}$ index the degree type: $-=in, +=out$, and let $\left(u_i^\gamma,v_i^\tau\right)$, be the $\gamma-$ and $\tau-$degree of the ith arc. Then, the general form of assortativity index is:

$r\left(\gamma,\tau\right)=m^{-1}\frac{\sum_{i= 1}^m (u_i^\gamma-\bar{u}^\gamma)(v^\tau_i-\bar{v}^\tau)}{s^\gamma s^\tau}$

where $\bar{u}^\gamma$ and $\bar{v}^\gamma$ are the arithmetic means of the $u_i^\gamma$s and $v_i^\tau$s, and $s^\gamma$ and $s^\tau$ are the population standard deviations of the $u_i^\gamma$s and $v_i^\tau$s. Under this framework, there are four possible forms to $r\left(\gamma,\tau\right)$ (Foster et al., 2010). These are: $r\left(+,-\right), r\left(-,+\right), r\left(-,-\right)$, and $r\left(+,+\right)$.

Value

Assortativity coefficeint outcome(s)

Author(s)

Ken Aho, Gabor Csardi wrote degree

References

Newman, M. E. (2002). Assortative mixing in networks. Physical Review Letters, 89(20), 208701.

Foster, J. G., Foster, D. V., Grassberger, P., & Paczuski, M. (2010). Edge direction and the structure of networks. Proceedings of the National Academy of Sciences, 107(24), 10815-10820.

Examples

network_a <- graph_from_literal(a --+ b, c --+ d, d --+ e, b --+ e, e --+ j, 
j --+ m, f --+ g, g --+ i, h --+ i, i --+ k, k --+ l, l --+ m, m --+ n,  
n --+ o)
assort(network_a)

---

Botter and Durighetto Bernoulli stream length

Description

A simple function for calculating the dot product of a vector of stream arc lengths and a corresponding vector of either binary (stream presence or absence) outcomes, probabilities of stream presence or inverse probabilites of stream presence.

Usage

bern.length(lengths, pa, mode = "local")

Arguments

lengths	A numeric vector of stream arc lengths
pa	A numeric vector of either binary (stream presence or absence) outcomes, probabilities of stream presence or inverse probabilites of stream presence. A vector outcome in lengths should correspond to an outcome for the same arc in pa.
mode	One of "local" of "global"

Value

When pa is a vector of binary (stream presence or absence) data, the function provides a measure of instantaneous stream length (in the units used in lengths). When pa is a vector of probabilities of stream presence, the function provides average stream length (in units used in lengths). When pa is a vector of inverse probabilites of stream presence, the function provides average communication distance (in units used in lengths).

Author(s)

Ken Aho

References

Botter, G., & Durighetto, N. (2020). The stream length duration curve: A tool for characterizing the time variability of the flowing stream length. Water Resources Research, 56(8), e2020WR027282.

Examples

lengths <- rexp(10, 10)
pa <- rbinom(10, 11, 0.4)
bern.length(lengths, pa)

---

Posterior Beta and Inverse-beta summaries

Description

Calculates summaries for beta and inverse-beta posteriors given prior probabilities for success, binary data and prior weight specification. Summaries include beta and inverse beta posterior means and variances and stream length and communication distance summaries given that stream length is provided for intermittent stream segments.

Usage

beta.posterior(p.prior, dat, length = NULL, w = 0.5)

Arguments

p.prior	Prior probability for success for the beta prior. The beta prior for the probability of success (e.g., stream presence) for kth outcome (e.g., stream segment) is defined as: $\theta_k \sim BETA(\alpha, \beta = t \alpha)$, where $\frac{1}{1+t} = p_{prior}$. This results in: $E(\theta_k) = p_{prior}$.
dat	An $n \times s$ matrix of binary outcomes, where n is the number of observations (e.g., stream observations over time) and s is the number experimental units observed, (e.g., stream segments).
length	An optional $n \times 1$ vector containing stream segement lengths to allow calculation of mean stream Bernoulli stream length and mean communication distance.
w	Weight for the prior distribution compared to the actual data (generally a proportion).

Details

As our Bayesian framework we assume a conjugate beta prior $\theta_k \sim BETA(\alpha, \beta)$ and binomial likelihood $\boldsymbol{x}_k \mid \theta_k \sim BIN(n, \theta_k)$ resulting in the posterior $\theta_k \mid \boldsymbol{x}_k \sim BETA(\alpha + \sum \boldsymbol{x}_k, \beta + n - \sum \boldsymbol{x}_k)$.

Value

Returns a list with components:

alpha	The $\alpha$ shape parameters for the beta and inverse beta posteriors.
beta	The $\beta$ shape parameters for the beta and inverse beta posteriors.
mean	The means of the beta posteriors.
var	The variances of the beta posteriors.
mean.inv	The means of the inverse-beta posteriors.
var.inv	The variances of the inverse-beta posteriors.
Com.dist	If length is supplied, the mean communication distances of the network.
Length	If length is supplied, the mean stream length of the network.
x	The observed number of Bernoulli successes over n trials observed in dat.

Author(s)

Ken Aho

See Also

dinvbeta.

---

Bivariate Bernoulli Distribution

Description

Densities (probabilities) of a bivariate Bernoulli distribution, $Y_1,Y_2$.

Usage

biv.bern(p11, p10, p01, p00, y1, y2)

Arguments

p11	The probability that $y_1,y_2 = 1,1$.
p10	The probability that $y_1,y_2 = 1,0$.
p01	The probability that $y_1,y_2 = 0,1$.
p00	The probability that $y_1,y_2 = 0,0$.
y1	Outcome for $Y_1$.
y2	Outcome for $Y_2$.

Value

Densities (probability) of the joint Bernoulli distribution.

Author(s)

Ken Aho

Examples

biv.bern(0.25,0.25,0.25,0.25,1,0)
biv.bern(0.1,0.4,0.3,0.2,1,0)

---

Stream segment presence absence data for Dry Cr. Idaho

Description

Stream segment presence absence data for Dry Cr. Idaho (outlet coordinates: 43.71839$^\circ$N, 116.13747$^\circ$W). Arc outcomes determined from STIC (Stream Temperature, Intermittency, and Conductivity) sensors at bounding nodes.

Usage

data("dc_arc_pres_abs")

Format

A data frame with 46187 observations on the following 29 variables.

datetime

a POSIXlt

‘⁠DC10-->C1⁠’

a numeric vector

‘⁠C1-->DC12⁠’

a numeric vector

‘⁠DC11-->C1⁠’

a numeric vector

‘⁠DC12-->C2⁠’

a numeric vector

‘⁠C2-->DC15⁠’

a numeric vector

‘⁠DC13-->C2⁠’

a numeric vector

‘⁠DC15-->C3⁠’

a numeric vector

‘⁠C3-->DC16⁠’

a numeric vector

‘⁠DC14-->C3⁠’

a numeric vector

‘⁠DC16-->C4⁠’

a numeric vector

‘⁠C4-->DC19⁠’

a numeric vector

‘⁠DC17-->C5⁠’

a numeric vector

‘⁠C5-->C4⁠’

a numeric vector

‘⁠DC18-->C5⁠’

a numeric vector

‘⁠DC19-->C6⁠’

a numeric vector

‘⁠C6-->DC4⁠’

a numeric vector

‘⁠DC20-->C6⁠’

a numeric vector

‘⁠DC4-->C7⁠’

a numeric vector

‘⁠C7-->DC5⁠’

a numeric vector

‘⁠DC1-->DC2⁠’

a numeric vector

‘⁠DC2-->DC3⁠’

a numeric vector

‘⁠DC3-->C7⁠’

a numeric vector

‘⁠DC5-->C8⁠’

a numeric vector

‘⁠C8-->DC6⁠’

a numeric vector

‘⁠DC9-->C9⁠’

a numeric vector

‘⁠C9-->DC7⁠’

a numeric vector

‘⁠DC8-->C9⁠’

a numeric vector

‘⁠DC7-->C8⁠’

a numeric vector

Source

Maggie Kraft

---

Lengths of Dry Creek stream (arc) segments

Description

Lengths of stream (arc) segments from Dry Creek Idaho (outlet coordinates: 43.71839$^\circ$N, 116.13747$^\circ$W).

Usage

data("dc_lengths")

Format

A data frame with 28 observations on the following 2 variables.

Arcs

Arc names, arrows directionally connect nodes.

Lengths

Stream segment (arc) length in kilometers.

Source

Maggie Kraft

---

Stream node presence absence data for Dry Cr. Idaho

Description

Stream node surface water presence absence at Dry Creek ID (outlet coordinates: 43.71839$^\circ$N, 116.13747$^\circ$W). Outcomes based on STIC (Stream Temperature, Intermittency, and Conductivity) sensor and piezometer responses, resulting in binary observations for 36 nodes at 15 minutes intervals, over four years.

Usage

data("dc_node_pres_abs")

Format

A data frame with 86958 observations on the following 37 variables.

datetime

a POSIXlt object

DC10

a numeric vector

C1

a numeric vector

DC11

a numeric vector

DPZ07

a numeric vector

DPZ06

a numeric vector

DC12

a numeric vector

C2

a numeric vector

DC13

a numeric vector

DC15

a numeric vector

C3

a numeric vector

DC14

a numeric vector

DC16

a numeric vector

DPZ05

a numeric vector

C4

a numeric vector

DC17

a numeric vector

C5

a numeric vector

DC18

a numeric vector

DC19

a numeric vector

C6

a numeric vector

DC20

a numeric vector

DC4

a numeric vector

C7

a numeric vector

DC1

a numeric vector

DC2

a numeric vector

DC3

a numeric vector

DC5

a numeric vector

DPZ02

a numeric vector

C8

a numeric vector

DPZ04

a numeric vector

DPZ03

a numeric vector

DC9

a numeric vector

C9

a numeric vector

DC8

a numeric vector

DC7

a numeric vector

DC6

a numeric vector

DSS01

a numeric vector

Source

Maggie Kraft

---

Potential degree distributions

Description

Calculates degree distribution probability density. By default calculates an uncorrelated (random) density for a given degree.

Usage

degree.dists(d, exp.lambda = 3/2, normalize = TRUE)

Arguments

d	degree
exp.lambda	if not NULL, allows specification of chaotic exp.lambda < 3/2 and correlated stochastic processes exp.lambda < 3/2.
normalize	ensures that sum of demsities = 1

Details

In general $f(d) = \exp(-\lambda d)$ where $d$ is the degree. For random degree distributions, $\lambda = \log(3/2)$.

Value

Returns a density plot for a degree.

Author(s)

Ken Aho

See Also

degree.distribution, plot_degree.dist.

---

Delete arcs based on presence absence data

Description

Create a new graph after deleting stream graph arcs based on presence/absence data, e.g., data based on outcomes from STIC (Stream Temperature, Intermittency, and Conductivity) loggers.

Usage

delete.arcs.pa(G, pa)

Arguments

G	A graph object of class "igraph", see graph_from_literal
pa	A vector of binary = 0,1 values indicating the absence or presence of arcs from E(G).

Value

Returns a igraph graph object missing the arcs indicated with 0 in pa.

Author(s)

Ken Aho, Gabor Csardi wrote delete.edges

Examples

G <- graph_from_literal(a--+b--+c--+d--+e)
delete.arcs.pa(G, c(0,0,1,1))

---

Delete nodes based on presence absence data

Description

Create a new graph after deleting stream graph nodes based on presence/absence data, e.g., data based on outcomes from STIC (Stream Temperature, Intermittency, and Conductivity) loggers.

Usage

delete.nodes.pa(G, pa, na.response = "none")

Arguments

G	A graph object of class "igraph", see graph_from_literal
pa	A vector of binary = 0,1 values indicating the absence or presence of nodes from V(G). Adding a names attribute to pa allows checking of the correspondence of the order of node names in G and pa.
na.response	One of "none", "treat.as.0", or "treat.as.1" (see Details).

Details

A perennial problem with STIC (Stream Temperature, Intermittency, and Conductivity) sensors is the presence of missing data. If na.response = "none" and NAs exist then the waring message "NAs in data need to be addressed. NAs converted 0." is printed. One can also choose na.response = "treat.as.0" or na.response = "treat.as.1" which converts NAs to zeroes or ones. Clearly, none of these draconian approaches is optimal. Thus, if NAs occur, an attribute is added to the output graph object returned by the function, which lists the nodes with missing data. This attribute can be obtained with out$NA.vertices where out <- delete.nodes.pa(...), see Examples below. An alternative is to use a classification algorithm for imputation e.g., STIC.RFimpute, which uses missForest::missForest.

Value

Returns a igraph graph object, missing the nodes indicated with 0 in pa.

Author(s)

Ken Aho, Gabor Csardi wrote delete.vertices

Examples

G <- graph_from_literal(a--+b--+c--+d--+e)
delete.nodes.pa(G, c(0,0,1,1,1)) 
# delete.nodes.pa(G, c(0,0,NA,1,1)) # gives warning and converts NA to 0 
d <- delete.nodes.pa(G, c(0,0,NA,1,1), "treat.as.0")
d
d$NA.vertices

---

Inverse Beta Distribution

Description

Calculates density (dinvbeta), lower-tailed probability (pinvbeta) and obtains random outcomes (rinvbeta) for an inverse beta distribution

Usage

dinvbeta(x, alpha, beta)
pinvbeta(x, alpha, beta)
rinvbeta(n, alpha, beta)

Arguments

x	Quantile vector or scalar at which to evaluate density or probability.
alpha	Alpha parameter
beta	Beta parameter
n	Number of random outcomes to be generated.

Value

Returns density, probability, and random outcomes for an inverse beta distribution.

Author(s)

Ken Aho and Dwayne Derryberry

See Also

See Also dbeta.

Examples

dinvbeta(1,1,1)
pinvbeta(1,1,1)
rinvbeta(1,1,1)

---

Local and global efficiency

Description

Efficiency is the reciprocal of internodal distance. Thus, the efficiency beween nodes i and j is defined as $e_{i,j} = \frac{1}{d_{i,j}}$ where $d_{i,j}$ denotes the distance between nodes i and j for all $i \neq j$.

Usage

efficiency.matrix(G, mode = "in")

avg.efficiency(G, mode = "in")

global.efficiency(G, mode = "in")

Arguments

G	Graph object of class "igraph". See graph_from_literal.
mode	One of "in" or "out". The former considers in-path efficiencies, whereas the latter considers out-paths.

Details

The function efficiency.matrix calculates an efficiency matrix whose elements correspond to elements in the graph distance matrix. The function avg.efficiency calculates average efficiencies of nodes to all other nodes, thus providing a local measure of graph connectedness. The function global.efficiency calculates the mean of the of all pairwise efficiencies, thus providing a global measure of graph connectedness. For all three functions, reciprocals of infinite distances are taken to be zero.

Value

The function efficiency.matrix returns a reciprocal distance matrix for nodes in G. The function avg.efficiency treats efficiency as a local measure, and thus returns a vector whose entries are average efficiencies for each node. The function global.efficiency returns a scalar (the mean of the reciprocal distance matrix).

Author(s)

Ken Aho. Gabor Csardi wrote the function distances in igraph.

References

Ek, B., VerSchneider, C., & Narayan, D. A. (2015). Global efficiency of graphs. AKCE International Journal of Graphs and Combinatorics, 12(1), 1-13.

Examples

kon_full <- streamDAGs("konza_full")
efficiency.matrix(kon_full)
avg.efficiency(kon_full)
global.efficiency(kon_full)

---

Loads AIMS dataset associated with a particular AIMS graph

Description

The function creates a list of associated dataframes for particular AIMS graph objects. Currently these include one of more of $coords $arc.length $node.pa.

Usage

get.AIMS.data(graph = "mur_full", supress.message = FALSE)

Arguments

graph	A character string defining one of the AIMS graphs codified in streamDAGs.
supress.message	Logical. Supress message detailing objects created by function.

Details

The function radically simplifies code gymnastics required to obtain datasets associated AIMS graphs (see, for instance, Detaails in streamDAGs).

Value

Returns a list containg up to three dataframes:

coords	Spatial coordinates and other information from AIMS.node.coords.
arc.length	Lengths of network, generally in km.
node.pa	Presence(1)/absence(0) of surface water at the node.

Author(s)

Ken Aho

See Also

streamDAGs

Examples

jd <- get.AIMS.data("jd_full", TRUE)
head(jd$coords)
head(jd$arc.length)
head(jd$node.pa)

---

Coordinates of nodes at Gibson Jack Creek, Idaho for a 2016 survey

Description

Latitudes and Longitudes of nodes established at Gibson Jack in 2016. Datum: WGS 84.

Usage

data("gj_coords16")

Format

A data frame with 124 observations on the following 3 variables.

Object.ID

Node name

lat

Latitude

long

Longitude

---

Lengths of Gibson Jack stream (arc) segments

Description

Lengths of stream (arc) segments from the Gibson Jack watershed in southeast Idaho (outlet coordinates: 42.767180$^\circ$N, 112.480240$^\circ$W). The dataframe gj_lengths contains arc lengths for a network including STICs, but excluding piezometers. The dataframe gj_lengths_piezo_full contains arc lengths for a network that includes both STICs and piezometers.

Usage

data("gj_lengths")

Format

A data frame with 28 observations jd_lengths or 35 observations jd_lengths_piezo_full on the following 2 variables.

Arcs

Arc names, arrows directionally connect nodes.

Lengths

Stream segment (arc) length in kilometers.

Source

Maggie Kraft

---

Stream node presence absence data for Gibson Jack Idaho

Description

Stream node surface water presence absence data from Gibson Jack, Idaho (outlet coordinates: 42.767180$^\circ$N, 112.480240$^\circ$W). Outcomes based on STIC (Stream Temperature, Intermittency, and Conductivity) sensors, resulting in binary observations for 29 nodes at 15 minutes intervals over three years.

Usage

data("gj_node_pres_abs")

Format

A data frame with 55109 observations on the following 36 variables.

datetime

a POSIXlt vector

GJ16

a numeric vector

GJ14

a numeric vector

C2

a numeric vector

C3

a numeric vector

C4

a numeric vector

GJ11

a numeric vector

GJ13

a numeric vector

GJ12

a numeric vector

GJ19

a numeric vector

GJ20

a numeric vector

GJ18

a numeric vector

GJ17

a numeric vector

C5

a numeric vector

GJ10

a numeric vector

GJ9

a numeric vector

C6

a numeric vector

GJ23

a numeric vector

GJ22

a numeric vector

C1

a numeric vector

C7

a numeric vector

GJ25

a numeric vector

GJ21

a numeric vector

GJ8

a numeric vector

GJ7

a numeric vector

GJ3

a numeric vector

C8

a numeric vector

GJ6

a numeric vector

GJ5

a numeric vector

GJ4

a numeric vector

GPZ02

a numeric vector

GPZ03

a numeric vector

GPZ04

a numeric vector

GPZ05

a numeric vector

GPZ06

a numeric vector

GPZ07

a numeric vector

GSS01

a numeric vector

Source

Maggie Kraft

---

Stream node presence absence data for Gibson Jack Cr. Idaho, for a 2016 survey

Description

Streamflow presence and absence data for each node location collected by manual observation November 6, 2016, May 6, 2017, and August 14, 2017. Note, a longer dataset 2021-2023, gathered by the AIMS team at fewer points, is available for Gibson Jack under the name gj_node_pres_abs.

Usage

data("gj_node_pres_abs16")

Format

A data frame with 3 observations on the following 125 variables.

Date

a character vector

GJ_ST1_0600

a numeric vector

GJ_ST1_0400

a numeric vector

GJ_ST1_0200

a numeric vector

GJ_ST1_0000

a numeric vector

GJ_SF_2800

a numeric vector

GJ_SF_2600

a numeric vector

GJ_SF_2400

a numeric vector

GJ_SF_2200

a numeric vector

GJ_SF_2000

a numeric vector

GJ_SF_1800

a numeric vector

GJ_SF_1600

a numeric vector

GJ_SF_1400

a numeric vector

GJ_SF_1200

a numeric vector

GJ_SF_1000

a numeric vector

GJ_SF_0800

a numeric vector

GJ_SF_0600

a numeric vector

GJ_SF_0400

a numeric vector

GJ_SF_0200

a numeric vector

GJ_SF_0000

a numeric vector

GJ_NT1_WF_FH

a numeric vector

GJ_NT1_WF_000

a numeric vector

GJ_NT1_0800

a numeric vector

GJ_NT1_0600

a numeric vector

GJ_NT1_0400

a numeric vector

GJ_NT1_0200

a numeric vector

GJ_NT1_0000

a numeric vector

GJ_NT2_1600

a numeric vector

GJ_NT2_1400

a numeric vector

GJ_NT2_1200

a numeric vector

GJ_NT2_1000

a numeric vector

GJ_NT2_0800

a numeric vector

GJ_NT2_0600

a numeric vector

GJ_NT2_0400

a numeric vector

GJ_NT2_0200

a numeric vector

GJ_NT2_0000

a numeric vector

GJ_NT3_0200

a numeric vector

GJ_NT3_0000

a numeric vector

GJ_NT4_0600

a numeric vector

GJ_NT4_0400

a numeric vector

GJ_NT4_0200

a numeric vector

GJ_NT4_0000

a numeric vector

GJ_NF_3800

a numeric vector

GJ_NF_3750

a numeric vector

GJ_NF_3600

a numeric vector

GJ_NF_3400

a numeric vector

GJ_NF_3200

a numeric vector

GJ_NF_3000_CU

a numeric vector

GJ_NF_3000_CD

a numeric vector

GJ_NF_2800_CU

a numeric vector

GJ_NF_2800_CD

a numeric vector

GJ_NF_2600

a numeric vector

GJ_NF_2400_CU

a numeric vector

GJ_NF_2400_CD

a numeric vector

GJ_NF_2200

a numeric vector

GJ_NF_2000

a numeric vector

GJ_NF_1800

a numeric vector

GJ_NF_1600

a numeric vector

GJ_NF_1400

a numeric vector

GJ_NF_1200

a numeric vector

GJ_NF_1060_CU

a numeric vector

GJ_NF_1060_CD

a numeric vector

GJ_NF_1000

a numeric vector

GJ_NF_0800

a numeric vector

GJ_NF_0600

a numeric vector

GJ_NF_0400

a numeric vector

GJ_NF_0200

a numeric vector

GJ_NF_0000

a numeric vector

GJ_MT2_0900

a numeric vector

GJ_MT2_0800

a numeric vector

GJ_MT2_0600

a numeric vector

GJ_MT2_0400

a numeric vector

GJ_MT2_0200

a numeric vector

GJ_MT2_0000

a numeric vector

GJ_MT1_1650

a numeric vector

GJ_MT1_1600

a numeric vector

GJ_MT1_1550

a numeric vector

GJ_MT1_1500

a numeric vector

GJ_MT1_1450

a numeric vector

GJ_MT1_1400

a numeric vector

GJ_MT1_1350

a numeric vector

GJ_MT1_1300

a numeric vector

GJ_MT1_1250

a numeric vector

GJ_MT1_1200

a numeric vector

GJ_MT1_1150

a numeric vector

GJ_MT1_1100

a numeric vector

GJ_MT1_1050

a numeric vector

GJ_MT1_1000

a numeric vector

GJ_MT1_0950

a numeric vector

GJ_MT1_0900

a numeric vector

GJ_MT1_0850

a numeric vector

GJ_MT1_0800

a numeric vector

GJ_MT1_0750

a numeric vector

GJ_MT1_0700

a numeric vector

GJ_MT1_0650

a numeric vector

GJ_MT1_0600

a numeric vector

GJ_MT1_0550

a numeric vector

GJ_MT1_0500

a numeric vector

GJ_MT1_0450

a numeric vector

GJ_MT1_0400

a numeric vector

GJ_MT1_0350

a numeric vector

GJ_MT1_0300

a numeric vector

GJ_MT1_0250

a numeric vector

GJ_MT1_0200

a numeric vector

GJ_MT1_0150

a numeric vector

GJ_MT1_0100

a numeric vector

GJ_MT1_0050

a numeric vector

GJ_MT1_0000

a numeric vector

GJ_MS_3000

a numeric vector

GJ_MS_2800

a numeric vector

GJ_MS_2600

a numeric vector

GJ_MS_2400

a numeric vector

GJ_MS_2200

a numeric vector

GJ_MS_2000

a numeric vector

GJ_MS_1800_CU

a numeric vector

GJ_MS_1800_CD

a numeric vector

GJ_MS_1600

a numeric vector

GJ_MS_1400

a numeric vector

GJ_MS_1200

a numeric vector

GJ_MS_1000

a numeric vector

GJ_MS_0800

a numeric vector

GJ_MS_0600

a numeric vector

GJ_MS_0400

a numeric vector

GJ_MS_0200

a numeric vector

GJ_MS_0000

a numeric vector

---

Global Summary

Description

This function calculates useful DAG global summaries including size, diameter, number of paths to sink, mean path length, mean alpha centrality, mean PageRank centrality, graph centralization, Strahler order, Shreve order, the Randic index, the first Zagreb Index, the second Zagreb index, atom-bond connectivity, the geometric-arithmatic index, the harmonic index, the Harary index, global efficiency, the assortativity correlation (+, -), and the assortativity correlation (+, +).

Usage

global.summary(G, which = "all", sink, mode = "in", inf.paths = FALSE)

Arguments

G	graph object of class "igraph". See graph_from_literal.
which	Which metric to use. Currently one of "all", "size", "diameter", "graph.order", "n.sources", "n.paths.to.sink", "sink.path.len.summary", "deg.summary", "avg.alpha.cent", "shreve.num", "strahler.num", "fst.zagreb", "scd.zagreb", "ABC", "harary", "global.efficiency", "assort.in.out", "assort.in.in".
sink	sink node from graph object G.
mode	Type of degree used. One of "in" or "out".
inf.paths	logical, consider infinite paths?

Details

Simple global graph measures of complexivity and/or connectivity of a stream DAG include size, diameter, and number of paths to a sink. The size is equal to the number of arcs in the stream network. The diameter equals the length of the longest path, i.e., the height of the sink, and in eccentricity of the sink. The number of paths to the sink is equivalent to the number of nodes from which the sink node is reachable, which will be $n-1$ for a fully active stream. For more information on $I(D)$ metrics see I.D. Links describing other metrics are provided below.

Value

Returns a vector of global graph measures for G.

Author(s)

Ken Aho, Gabor Csardi wrote alpha_centrality and other underlying functions.

References

Kunkler, S. J., LaMar, M. D., Kincaid, R. K., & Phillips, D. (2013). Algorithm and complexity for a network assortativity measure. arXiv Preprint arXiv:1307.0905.

Das, K. C., Gutman, I., & Furtula, B. (2011). On atom-bond connectivity index. Chemical Physics Letters, 511(4-6), 452-454.

Li, X., & Shi, Y. (2008). A survey on the randic index. MATCH Commun. Math. Comput. Chem, 59(1), 127-156.

See Also

alpha_centrality, I.D, spath.lengths, n.sources, stream.order, harary

Examples

network_a <- graph_from_literal(a --+ b, c --+ d, d --+ e, b --+ e, 
e --+ j, j --+ m, f --+ g, g --+ i, h --+ i, i --+ k, k --+ l, 
l --+ m, m --+ n,  n --+ o)

global.summary(network_a, sink ="o")

---

Harary Index

Description

Computes the Harary global metric for a stream DAG.

Usage

harary(G)

Arguments

G	Graph object of class igraph. See graph_from_literal.

Details

The Harary index is computed as:

$\frac{1}{2}\sum_i^m\sum_j^m (RD)_{ij}$

where $(RD)_{ij}$ is the reciprocal of the $ij$th element of the graph distance matrix. Reciprocals of infinite values in the distance matrix are taken to be zero. Users should be aware that the graph object G is assumed to be DAG, and that distances are based on in-paths.

Value

Returns a scalar: the global Harary index.

Author(s)

Ken Aho, Gabor Csardi wote distances

References

Plavsic, D., Nikolic, S., Trinajstic, N., & Mihalic, Z. (1993). On the Harary index for the characterization of chemical graphs. Journal of Mathematical Chemistry, 12(1), 235-250.

Examples

harary(streamDAGs("konza_full"))

---

Generalized DAG indices

Description

Calculates global generalized topopological indices for a digraph

Usage

I.D(G, mode = "gen.rand", alpha = -1/2, mult = FALSE, degrees = "out.in")

Arguments

G	Graph object of class. See graph_from_literal.
mode	One of "gen.rand","gen.sum.con", "ABC", "GA", "harm", "aug.rand".
alpha	Exponent value for forms of omega with alpha exponent.
mult	Logical if TRUE use experimental multiplicative measures.
degrees	Degree designations for the arc $\vec{uv}$. One of "out.in", "out.out", "in.out", "in.in". See Details below. The default designation, "out.in", is strongly reccomended for stream DAGs.

Details

For an arc $a={\overrightarrow{uv}}$, $a \in A$, we denote the out degree of $u$ as $d_u^+$, and the in degree of $v$ as $d_v^-$. Now let $I(D)$ represent a generalized topopological index for a digraph, $D$ (cf. Deng et al., 2021) that depends on $d_u^+$ and $d_v^-$:

$I(D)=1/2 \sum_{uv \in A}\omega(d_u^+,d_v^-)$

Six basic configurations for $I(D)$ can be recognized:

1. If $\omega(x,y)=(xy)^\alpha$, for $\alpha \neq 0$, then $I(D)$ is the general directed Randic index (Kincaid et al., 2016) for $D$. Specific variants include the Randic index $(\alpha =-1/2)$, the second Zagreb index $(\alpha =1)$ and the second modified Zagreb index $(\alpha =-1)$ (Anthony & Marr, 2021).

2. If $\omega(x,y)=(x+y)^\alpha$, then $I(D)$ is the general sum-connectivity index for D (Deng et al., 2021). Further, if $\omega(x,y)=2(x+y)^\alpha$, then $I(D)$ is the sum connectivity (Zhou & Trinajstic, 2009), and the directed first Zagreb index (Anthony & Marr, 2021) for $\alpha =-1/2$ and $\alpha=1$, respectively .

3. If $\omega(x,y)=\sqrt{((x+y-2)/xy)}$, then $I(D)$ is the atom bond connectivity of D (Estrada et al., 1998).

4. If $\omega(x,y)=\sqrt{xy}/(1/2(x+y))$, then $I(D)$ is the geometric-arithmetic index for $D$ (Vukicevic & Furtula, 2009).

5. If $\omega(x,y)=2/(x+y)$, then $I(D)$ is the harmonic index of $D$ (Favaron et al., 1993).

6. If $\omega(x,y)=\left(\frac{xy}{x+y-2}\right)^3$, then $I(D)$ is the augmented Randic index of $D$ (Furtula et al. 2010). This index is not reccomended for stream DAGs as it will contained undefined terms for any network with unbranched paths.

More options are possible under the generalization of Kincaid (1996). Specifically, for an arc $a=\vec{uv},a\in A$, let $\gamma,\tau\in-,+$ index the degree type: $-= in, +=out$. Then, four combinations of $d_u^\gamma, d_v^\tau$ can occur, resulting in four different versions of each $I(D)$ metric described above. These combinations are: $d_u^+,d_v^-$ (as shown above), $d_u^+,d_v^+$, $d_u^-,d_v^-$, and $d_u^-,d_v^+$. The default $d_u^+,d_v^-$ is strongly reccomended for stream DAGs over other variants.

Value

Index values for a DAG

Author(s)

Ken Aho, Gabor Csardi wrote degree

References

Anthony, B. M., & Marr, A. M. (2021). Directed zagreb indices. Graphs and Combinatorial Optimization: From Theory to Applications: CTW 2020 Proceedings, 181-193.

Deng, H., Yang, J., Tang, Z., Yang, J., & You, M. (2021). On the vertex-degree based invariants of digraphs. arXiv Preprint arXiv:2104.14742.

Estrada, E., Torres, L., Rodriguez, L., & Gutman, I. (1998). An atom-bond connectivity index: Modelling the enthalpy of formation of alkanes. NISCAIR-CSIR, India.

Favaron, O., Maheo, M., & Sacle, J.-F. (1993). Some eigenvalue properties in graphs (conjectures of graffitii). Discrete Mathematics, 111(1-3), 197-220.

Furtula, B., Graovac, A., & Vukicevic, D. (2010). Augmented Zagreb index. Journal of Mathematical Chemistry, 48(2), 370-380.

Kincaid, R. K., Kunkler, S. J., Lamar, M. D., & Phillips, D. J. (2016). Algorithms and complexity results for finding graphs with extremal Randic index. Networks, 67(4), 338-347.

Vukicevic, D., & Furtula, B. (2009). Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges. Journal of Mathematical Chemistry, 46(4), 1369-1376.

Zhou, B., & Trinajstic, N. (2009). On a novel connectivity index. Journal of Mathematical Chemistry, 46(4), 1252-1270.

See Also

degree

Examples

network_a <- graph_from_literal(a --+ b, c --+ d, d --+ e, b --+ e, 
e --+ j, j --+ m, f --+ g, g --+ i, h --+ i, i --+ k, k --+ l, 
l --+ m, m --+ n,  n --+ o)
I.D(network_a)

---

Integral connectivity scale length (ICSL)

Description

Integral connectivity scale lengths (ICSL, Western et al. 2013) is the average distance between wet locations using either (1) Euclidean distance or (2) topographically-defined hydrologic distance, e.g., instream hydrologic distance, subsurface distance (Ali and Roy 2009) and outlet distance, in which connected saturated paths must reach the catchment outlet.

Usage

ICSL(G, coords = NULL, names = NULL, lengths = NULL, 
dist.matrix = NULL, show.dist = FALSE)

Arguments

G	A graph object of class "igraph", see graph_from_literal
coords	Spatial coordinates to allow computation of nodal Euclidean distances
names	Nodal names
lengths	Stream arc lengths or hydrologic arc lengths
show.dist	Logical. Show distance matrix?
dist.matrix	An optional distance matrix, potentially providing non-Euclidean node distances (e.g., node subsurface distance, etc.). Distance matrix Labels in dist.matrix must be analogous to those used in G. Note that dimensions in dist.matrix can be larger than the number of nodes in G if, for instance, dist.matrix represents distances of the complete wetted network and G is a subgraph of the complete wetted network after drying.

Details

Computes either: 1) the average Euclidean distance of connected nodal locations as defined in G, if coords are provided, 2) if dist.matrix is provided, the average nodal distances of a distance matrix provided in dist.matrix for nodes that remain in G, or 3) the instream distances of connected nodal locations if stream lenghts are provided in lengths. For 3), the length vector will need to be trimmed as arcs disappear within intermittent streams (see Examples).

Value

Returns a global distance scalar. See Details.

Author(s)

Ken Aho, Gabor Csardi wrote underlying functions distances and E

References

Ali, G. A., & Roy, A. G. (2010). Shopping for hydrologically representative connectivity metrics in a humid temperate forested catchment. Water Resources Research, 46(12).

Western, A. W., Bloschl, G., & Grayson, R. B. (2001). Toward capturing hydrologically significant connectivity in spatial patterns. Water Resources Research, 37(1), 83-97.

See Also

distances

Examples

murphy_spring <- graph_from_literal(IN_N --+ M1984 --+ M1909, IN_S --+ M1993,  
M1993 --+ M1951 --+ M1909 --+ M1799 --+ M1719 --+ M1653 --+ M1572 --+ M1452, 
M1452 --+ M1377 --+ M1254 --+ M1166 --+ M1121 --+ M1036 --+ M918 --+ M823, 
M823 --+ M759 --+ M716 --+ M624 --+ M523 --+ M454 --+ M380 --+ M233 --+ M153, 
M153 --+ M91 --+ OUT)

#---- ICSL based on nodal Euclidean distances ----#
data(mur_coords)
ICSL(murphy_spring, coords = mur_coords[,2:3], names = mur_coords[,1])

#---- ICSL based on in-stream length data ----#
data(mur_lengths)
ICSL(murphy_spring, lengths = mur_lengths[,2], names = mur_coords[,1])

# or, simply
ms <- murphy_spring
E(ms)$weight <- mur_lengths[,2]
ICSL(ms)

# Arcs 1 and 3 dry
B <- graph_from_literal(IN_N, M1984, IN_S --+ M1993 --+ M1951 --+ M1909, 
M1909 --+ M1799 --+ M1719 --+ M1653 --+ M1572 --+ M1452 --+ M1377 --+ M1254,
M1254 --+ M1166 --+ M1121 --+ M1036 --+ M918 --+ M823 --+ M759 --+ M716, 
M716 --+ M624 --+ M523 --+ M454 --+ M380 --+ M233 --+ M153 --+ M91 --+ OUT)
ICSL(B, lengths = mur_lengths[,2][-c(1,3)], show.dist = TRUE)

---

Improved Closeness Centrality

Description

Calculates improved closeness centrality of individual nodes in a DAG.

Usage

imp.closeness(G)

Arguments

G	Graph object of class "igraph", see See graph_from_literal.

Details

Improved closeness centrality (Beauchamp, 1965) was developed for weakly connected or disconnected digraphs. The measure is based on the reciprocal of nodal shortest path distances from the jth node to the kth node, $1/\delta_{j,k}$. For the jth node this is:

$H_j=(n-1) \sum_{j \neq k} 1/\delta_{j,k}$

where, for disconnected nodes, the reciprocal distance $1/\infty$ is taken to be zero.

Value

Improved closeness centrality of a node

Author(s)

Ken Aho, Gabor Csardi wrote distances

References

Beauchamp, M. A. (1965). An improved index of centrality. Behavioral Science, 10(2), 161-163.

See Also

distances

Examples

network_a <- graph_from_literal(a --+ b, c --+ d, d --+ e, b --+ e, 
e --+ j, j --+ m, f --+ g, g --+ i, h --+ i, i --+ k, k --+ l, 
l --+ m, m --+ n,  n --+ o)
imp.closeness(network_a)

---

Detects and defines islands in a streamDAG

Description

The function was written primarilly to recognize DAG islands to allow correct implementation of the function stream.order and is still early in its development.

Usage

isle(G)

Arguments

G	Graph object of class igraph. See graph_from_literal.

Details

The function currently allows detection of simple island structures (those that don't contain sub-islands). One of the output objects from the function is a new graph object with island nodes into a single node(s).

Value

Output consists of the following:

test	Logical indicating whether or not G contains islands.
island	List of islands with their nodal components
input.id	Neighboring node(s) directly upstream from island(s).
output.id	Neighboring node(s) directly downstream from island(s).
new.graph	New graph object created from G in which nodes constituing islands a combined into a single node
island.names	Names of island nodes created in new output graph (that combines nodes constituing islands into a single node). Follows the naming system "i-1", "i-2", etc.
splits	The number of islands detected.

Author(s)

Ken Aho

See Also

stream.order, delete.vertices, add.vertices, add.edges

Examples

G <- graph_from_literal(a --+ c --+ e, b --+ d --+ e --+ f --+ p, g --+ i --+ j --+ m, 
i --+ k --+ m, m --+ n --+ o --+ p, h --+ l --+ n, p --+ q --+ r)
plot(G)
isle(G)

---

Lengths of Johnson Draw stream (arc) segments

Description

Lengths of stream (arc) segments from Johnson Draw in southwest Idaho (outlet coordinates: 43.12256$^\circ$N, 116.77630$^\circ$W). The dataframe jd_lengths contains segment lengths in the absence of piezos [nodes are currently defined by STIC (Stream Temperature, Intermittency, and Conductivity) locations only] and thus correspond to the network in streamDAGs("jd_full"). The dataframe jd_lengths_full contains segment lengths for node designated by both STICs and piezos. A corresponding network that includes piezos is depicted by streamDAGs("jd_piezo_full"). The dataframe jd_lengths_2023 contains segment lengths for node designated by both STICs, piezos and additional STC sites established in 2023. A correspding network can be obtained with streamDAGs("jd_piezo_full_2023").

Usage

data("jd_lengths")

Format

A data frame with observations on the following 2 variables.

Arcs

Arc names, arrows directionally connect nodes.

Lengths

Lengths in in km.

Source

Arya Legg, Maggie Kraft

---

Stream node presence absence data for Johnson Draw Idaho

Description

Stream node surface water presence absence data from 2022-2023 for the Johnson Draw watershed in southwest Idaho (outlet coordinates: 43.12256$^\circ$N, 116.77630$^\circ$W). Outcomes are based on STIC sensors and piezometers, resulting in binary observations for 35 nodes (28 STICs and 7 piezometers) at 15 minutes intervals over three years. JD21, JD22, JD23, JD25, JD26, JD27, JD28 were added in 2023 for the AIMS experiment.

Usage

data("jd_node_pres_abs")

Format

A data frame with 51653 observations on the following 36 variables.

datetime

a POSIXlt

JD5

a numeric vector

JD6

a numeric vector

JD7

a numeric vector

C1

a numeric vector

JD10

a numeric vector

JD9

a numeric vector

JD8

a numeric vector

JD11

a numeric vector

JD12

a numeric vector

JD13

a numeric vector

C2

a numeric vector

JD16

a numeric vector

JD17

a numeric vector

JD18

a numeric vector

JD19

a numeric vector

JD20

a numeric vector

JD4

a numeric vector

JD3

a numeric vector

JD2

a numeric vector

JD1

a numeric vector

JD15

a numeric vector

JD14

a numeric vector

JSS01

a numeric vector

JPZ02

a numeric vector

JPZ03

a numeric vector

JPZ04

a numeric vector

JPZ05

a numeric vector

JPZ06

a numeric vector

JPZ07

a numeric vector

JD21

a numeric vector

JD22

a numeric vector

JD23

a numeric vector

JD25

a numeric vector

JD26

a numeric vector

JD27

a numeric vector

JD28

a numeric vector

Source

Maggie Kraft

---

Coordinates of nodes in the Konza Praire dataset

Description

Coordinates (in Lat/Long) of nodes established at the Konza Prairie stream network.

Usage

data("kon_coords")

Format

A data frame with 46 observations on the following 3 variables.

Object.ID

Node name

lat

Latitude

long

Longitude

---

Lengths of Murphy Cr. stream (arc) segments

Description

Lengths of Murphy Cr. stream (arc) segments

Usage

data("kon_lengths")

Format

A data frame with 45 observations on the following 2 variables.

Arcs

Arc names, arrows directionally connect nodes.

Lengths

Lengths in meters

Source

Rob Ramos

---

local (nodal) summaries of a DAG

Description

Obtains local (nodal) summaries from a DAG

Usage

local.summary(G, metric = "all", mode = "in")

Arguments

G	Graph of class "igraph". See graph_from_literal
metric	One of "all", "alpha.cent", "imp.closeness", "n.paths", "n.nodes", "page.rank", "path.len.summary", "path.deg.summary", "size.intact.in". Partial matches allowed.
mode	One of "in" or "out"

Value

Nodes are returned with values measuring the indegree, alpha centrality, PageRank centrality, improved closeness centrality, betweenness centrality, upstream network length, and upstream in-path length mean, variance, max (i.e., in-eccentricity), skew, kurtosis, and mean efficiency.

Author(s)

Ken Aho, Gabor Csardi wrote degree, page_rank and alpha_centrality functions.

See Also

degree, alpha_centrality, page_rank, betweenness, imp.closeness, skew, kurt

Examples

network_a <- graph_from_literal(a --+ b, c --+ d, d --+ e, b --+ e, 
e --+ j, j --+ m, f --+ g, g --+ i, h --+ i, i --+ k, k --+ l, 
l --+ m, m --+ n,  n --+ o)
local.summary(network_a)

---

Stream segment presence absence data for Murphy Cr. Idaho

Description

Simulated multivariate Benroulli outcomes for 27 stream segments, based on their observed marginal probabilities for steam presence and covariance structures. "M"-labelling for nodes indicates "meters above outlet".

Usage

data("mur_arc_pres_abs")

Format

A data frame with 1000 observations on the following 27 variables.

‘⁠IN_N-->M1984⁠’

a numeric vector

‘⁠M1984-->M1909⁠’

a numeric vector

‘⁠M1909-->M1799⁠’

a numeric vector

‘⁠IN_S-->M1993⁠’

a numeric vector

‘⁠M1993-->M1951⁠’

a numeric vector

‘⁠M1951-->M1909⁠’

a numeric vector

‘⁠M1799-->M1719⁠’

a numeric vector

‘⁠M1719-->M1653⁠’

a numeric vector

‘⁠M1653-->M1572⁠’

a numeric vector

‘⁠M1572-->M1452⁠’

a numeric vector

‘⁠M1452-->M1377⁠’

a numeric vector

‘⁠M1377-->M1254⁠’

a numeric vector

‘⁠M1254-->M1166⁠’

a numeric vector

‘⁠M1166-->M1121⁠’

a numeric vector

‘⁠M1121-->M1036⁠’

a numeric vector

‘⁠M1036-->M918⁠’

a numeric vector

‘⁠M918-->M823⁠’

a numeric vector

‘⁠M823-->M759⁠’

a numeric vector

‘⁠M759-->M716⁠’

a numeric vector

‘⁠M716-->M624⁠’

a numeric vector

‘⁠M624-->M523⁠’

a numeric vector

‘⁠M523-->M454⁠’

a numeric vector

‘⁠M454-->M380⁠’

a numeric vector

‘⁠M380-->M233⁠’

a numeric vector

‘⁠M233-->M153⁠’

a numeric vector

‘⁠M153-->M91⁠’

a numeric vector

‘⁠M91-->OUT⁠’

a numeric vector

---

Coordinates of nodes at Murphy Ck. Idaho

Description

UTM coordinates (Zone 11T) and Latitudes and Longitudes of nodes established at Murphy Cr. Idaho. Datum: WGS 84.

Usage

data("mur_coords")

Format

A data frame with 28 observations on the following 5 variables.

Object.ID

Node name

E

UTM Easting

N

UTM Northing

lat

Latitude

long

Longitude

---

Lengths of Murphy Cr. stream (arc) segments

Description

Lengths of Murphy Cr. stream (arc) segments

Usage

data("mur_lengths")

Format

A data frame with 27 observations on the following 2 variables.

Arcs

Arc names, arrows directionally connect nodes.

Lengths

Stream segment (arc) length in meters.

Source

Warix, S. R., Godsey, S. E., Lohse, K. A., & Hale, R. L. (2021). Influence of groundwater and topography on stream drying in semi-arid headwater streams. Hydrological Processes, 35(5), e14185.

---

Stream node presence absence data for Murphy Cr. Idaho

Description

A subset of stream node presence absence data from Warix et al. (2019) resulting in binary observations for 28 nodes at 2.5 hr intervals.

Usage

data("mur_node_pres_abs")

Format

A data frame with 1163 observations on the following 29 variables.

Datetime

a character vector

IN_N

a numeric vector

M1984

a numeric vector

M1909

a numeric vector

IN_S

a numeric vector

M1993

a numeric vector

M1951

a numeric vector

M1799

a numeric vector

M1719

a numeric vector

M1653

a numeric vector

M1572

a numeric vector

M1452

a numeric vector

M1377

a numeric vector

M1254

a numeric vector

M1166

a numeric vector

M1121

a numeric vector

M1036

a numeric vector

M918

a numeric vector

M823

a numeric vector

M759

a numeric vector

M716

a numeric vector

M624

a numeric vector

M523

a numeric vector

M454

a numeric vector

M380

a numeric vector

M233

a numeric vector

M153

a numeric vector

M91

a numeric vector

OUT

a numeric vector

References

Warix, S. R., Godsey, S. E., Lohse, K. A., & Hale, R. L. (2021). Influence of groundwater and topography on stream drying in semi-arid headwater streams. Hydrological Processes, 35(5), e14185.

---

Simulated seasonal arc presence absence data for Murphy Cr

Description

A data frame with one hundred multivariate Bernoulli simulated outcomes representing spring, summer and fall.

Usage

data("mur_seasons_arc_pa")

Format

A data frame with 300 observations on the following 28 variables.

‘⁠IN_N -> M1984⁠’

a numeric vector

‘⁠M1984 -> M1909⁠’

a numeric vector

‘⁠M1909 -> M1799⁠’

a numeric vector

‘⁠IN_S -> M1993⁠’

a numeric vector

‘⁠M1993 -> M1951⁠’

a numeric vector

‘⁠M1951 -> M1909⁠’

a numeric vector

‘⁠M1799 -> M1719⁠’

a numeric vector

‘⁠M1719 -> M1653⁠’

a numeric vector

‘⁠M1653 -> M1572⁠’

a numeric vector

‘⁠M1572 -> M1452⁠’

a numeric vector

‘⁠M1452 -> M1377⁠’

a numeric vector

‘⁠M1377 -> M1254⁠’

a numeric vector

‘⁠M1254 -> M1166⁠’

a numeric vector

‘⁠M1166 -> M1121⁠’

a numeric vector

‘⁠M1121 -> M1036⁠’

a numeric vector

‘⁠M1036 -> M918⁠’

a numeric vector

‘⁠M918 -> M823⁠’

a numeric vector

‘⁠M823 -> M759⁠’

a numeric vector

‘⁠M759 -> M716⁠’

a numeric vector

‘⁠M716 -> M624⁠’

a numeric vector

‘⁠M624 -> M523⁠’

a numeric vector

‘⁠M523 -> M454⁠’

a numeric vector

‘⁠M454 -> M380⁠’

a numeric vector

‘⁠M380 -> M233⁠’

a numeric vector

‘⁠M233 -> M153⁠’

a numeric vector

‘⁠M153 -> M91⁠’

a numeric vector

‘⁠M91 -> OUT⁠’

a numeric vector

Season

A categorical variable with three levels: "spring" (6/3/2019 - 7/13/2019), "summer" (7/13/2019 - 8/23/2019) and "fall" (8/23/2019 - 10/2/2019)

---

Identify source and sink nodes

Description

Identify the number of sources and the source nodes. Sources are assumed to be linked to the sink.

Usage

n.sources(G, sink = NULL)
sources(G, sink = NULL)

Arguments

G	A graph object of class "igraph", see graph_from_literal
sink	The name of the sink node.

Value

Returns a character vector listing streamDAG source nodes (those linked to the sink with indegree 0).

Author(s)

Ken Aho, Gabor Csardi wrote degree

Examples

sources(streamDAGs("konza_full"), sink = "SFM01_1")

---

Path Lengths

Description

Obtains all shortest in paths to a sink

Usage

path.lengths.sink(G, sink = NULL, inf.paths = TRUE)

Arguments

G	Graph object of class "igraph", see: graph_from_literal.
sink	sink node from G.
inf.paths	Logical, consider infinite paths?

Value

Length of path to a sink

Author(s)

Ken Aho, Gabor Csardi wrote distances

Examples

murphy_spring <- graph_from_literal(IN_N --+ M1984 --+ M1909, IN_S --+ M1993, 
M1993 --+ M1951 --+ M1909 --+ M1799 --+ M1719 --+ M1653 --+ M1572 --+ M1452,
M1452--+ M1377 --+ M1254 --+ M1166 --+ M1121 --+ M1036 --+ M918 --+ M823, 
M823 --+ M759 --+ M716 --+ M624 --+ M523 --+ M454 --+ M380 --+ M233 --+ M153,
M153 --+ M91 --+ OUT)

path.lengths.sink(murphy_spring, sink = "OUT")

# with stream lengths as weights
data(mur_lengths)

E(murphy_spring)$weights <- mur_lengths[,2]
path.lengths.sink(murphy_spring, "OUT")

---

Path Visibilities

Description

Functions detect and summarize visibilities of path nodes from one or several source nodes to an sink. Specifically, the function The function path.visibility determines path visibilities from single source node to a single sink. multi.path.visibility Generates tables of path visibilities and visibility summaries for multiple source nodes to a single sink.

Ordering of nodes, vitally important to the calculation of visibility is currently obtained by identifying paths from each source node to the sink. The sum of node distances in each path are then sorted decreasingly to define an initial order for calculating visibilities. It is currently assumed that the user will manually handle disconnected paths via the source argument of visibility functions. Use of source nodes disconnected to the sink will result in the message: "only use source nodes connected to sink". Because of this situation disconnected graphs will be handled by a function in development single.node.visibility.

Usage

path.visibility(G, degree = "in", source = NULL, sink = NULL, weights = NULL)

multi.path.visibility(G, degree = "in", source = NULL, sink = NULL, 
weights = NULL, autoprint = TRUE)

Arguments

G	Graph of class "igraph". See graph_from_literal
degree	One of "out" for outdegree, "in" for indegree or "all" for the sum of the two.
source	A starting node for a path. The function multi.path.visibility allows multiple starting nodes.
sink	An ending node for a path.
weights	If !null, refers to a $1 \times n$ data.frame of weights, with the data.frame name attribute in weights corresponding to node names in G.
autoprint	Logical. Should table summary of nodal visibilities be automatically printed or made ?

Details

Following Lacasa et al. (2008), let $t_a$ represent the occurrance number of the $a$th node in a time series or stream path, and let $y_a$ represent a data outcome from the $a$th node. Nodes $a$ and $b$ will have visibility if all other data, $y_c$, between $a$ and $b$ fufill:

$y_c < y_b + (y_a - y_b)\frac{t_b - t_c}{t_b - t_a}.$

Value

The function path.visibility returns a symmetric matrix whose upper triangle denotes nodal co-visibilities. The lower triangle is left empty for efficiency. Reading down a column in the upper triangle shows upstream visibilites to and from a node, while reading across rows shows downstream visibilities.

The function multi.path.visibility returns a list containing the three objects. The first is printed and the latter two are invisible by default.

visibility.summary	The printed result is a matrix of path visibity counts for a node, with respect to upstream (to), downstream (from), and combined directions (both).
complete.matrix	Analogous, to path.visibility, this result attempts to synthesize visibilities within source-to-sink paths for all requested sources into a single matrix.
all.matrices	A list containing path.visibility summary matrices for each source-to-sink path.

Output is summarized based on a deduced ordering of nodes from sources to sin. The ordering is based on nodal path lengths.

Author(s)

Ken Aho, Gabor Csardi wrote degree and shortest_paths.

References

Lacasa, L., Luque, B., Ballesteros, F., Luque, J., & Nuno, J. C. (2008). From time series to complex networks: The visibility graph. Proceedings of the National Academy of Sciences, 105(13), 4972-4975.

See Also

degree, shortest_paths

Examples

A <- graph_from_literal(a --+ b, c --+ d, d --+ e, b --+ e, 
e --+ j, j --+ m, f --+ g, g --+ i, h --+ i, i --+ k, k --+ l, 
l --+ m, m --+ n,  n --+ o)

path.visibility(A, source = "a", sink = "o")
  
multi.path.visibility(A, source = c("a","c","f","h"), 
sink = "o")

# From Lacasa et al. (2008)

B <- graph_from_literal(a --+ b --+ c --+ d --+ e --+ f --+ g)
weights <- data.frame(matrix(nrow = 1, data = c(0.87, 0.49, 0.36, 0.83, 0.87, 0.49, 0.36))) 
names(weights) = letters[1:7]
path.visibility(B, source = "a", sink = "g", weights = weights)

---

Plot degree distributions

Description

Plots bserved degree distribution against models for uncorrelated random, chaotic and correlated random processes.

Usage

plot_degree.dist(G, mode = "all", exp.lambda = c(1.1, 3/2, 2), leg.loc = "topright")

Arguments

G	Graph object of class "igraph". See graph_from_literal
mode	Character string, one of "out" for out-degree, "in" for in-degree or "all" for the sum of the two. For undirected graphs this argument is ignored.
exp.lambda	log.lamda = if not NULL, allows specification of chaotic exp.lambda < 3/2 and correlated stochastic processes exp.lambda < 3/2
leg.loc	placement of legend,

Value

Plots processes for observed versus distributions under random or chaotic degrees.

Author(s)

Ken Aho

See Also

degree.dists, degree.distribution

Examples

network_a <- graph_from_literal(a --+ b, c --+ d, d --+ e, b --+ e, 
e --+ j, j --+ m, f --+ g, g --+ i, h --+ i, i --+ k, k --+ l, 
l --+ m, m --+ n,  n --+ o)
plot_degree.dist(network_a)

---

Bounds for the correlation of two (or more) Benrnoulli random variables

Description

Replaces impossible correlations (values too small or too large) with minimum and maximum correlations, respectively.

Usage

min_r(p1, p2)
max_r(p1, p2)
R.bounds(p, R, pad = 0.001)

Arguments

p1	Probability of success for first random variable
p2	Probability of success for second random variable
p	Vector of marginal probabilities for multivariate Bernoulli random variables, for R.bounds.
R	Raw correlation matrix for random variables
pad	Padding (in correlation units) to adjust the returned correlation matrix with respect extremal values.

Details

The functions r.min and r.max define minimum and maximimum possible correlations. The function R.bounds replaces impossibly large or small values with maximally large or small values repectively.

Value

Functions return a scalar defining minimum or maximimum possible correlations. See Aho et al. (2023).

Author(s)

Ken Aho

References

Aho, K., Derryberry, D., Godsey, S. E., Ramos, R., Warix, S., Zipper, S. (2023) The communication distance of non-perennial streams. EarthArXiv https://eartharxiv.org/repository/view/4907/

Examples

min_r(0.6, 0.9)
max_r(0.1, 0.2)

x1 <- rep(c(1,0),5)
x2 <- c(rep(1,7), rep(0,3))
x3 <- c(rep(1,3), rep(0,7))
R <- cor(cbind(x1, x2, x3))
R.bounds(c(0.5, 0.7, 1), R)

---

Size of the intact network above an arc

Description

The function measures the “size” of the intact network or sub-network (either number of upstream nodes, or user defined defined length, e.g., m, km) with respect to network arcs.

Usage

size.intact.to.arc(G, arc.node = "in")

Arguments

G	Graph object of class "igraph", see: graph_from_literal.
arc.node	One of "in" or "out", indicating whether the upstream network or sub-network will be defined with respect to input nodes of directional arcs (arc.node = "in") or output (end) nodes of arcs (arc.node = "out"). The former (default) option is reccomended (see Details).

Details

For an unweighted graph, the upstream network “size” equates to the number of nodes in the intact network or sub-network upstream of an arc. For a graph whose arcs are weighted with actual stream segment lengths (see Examples), this will be the length (in measured units of length given in the weights) of the intact network or sub-network upstream of the arc. The argument arc.node allows upstream network size to be calculated with respect to either the upstream ("in") nodes of arcs or the downstream ("out") nodes of arcs. This designation will be applied to define the end (outlet) of the network or sub-network. Thus, option "out" may produce unexpectedly large results when these downstream "out" nodes of arcs occur at confluences.

Value

Output is a numeric vector whose length will be equal to the number of arcs in G.

Author(s)

Ken Aho, Gabor Csardi wrote distances

See Also

local.summary

Examples

mur <- streamDAGs("mur_full")
data(mur_lengths)
E(mur)$weight <- mur_lengths[,2]
size.intact.to.arc(mur) # upstream network sizes are in meters

---

Size of intact network that feeds into the sink or a particular node

Description

The length of the subgraph network that ends (feeds into) a particular node, e.g., the sink. For a weighted graph, the sum of the weights of the subgraph are given. Thus, if weights are stream lengths the function will give the stream length of the portion of the intact stream network that feeds into a particular node.

Usage

size.intact.to.sink(G, sink = NULL)

size.intact.to.node(G, node = NULL)

Arguments

G	A graph object of class "igraph", see graph_from_literal
sink	The sink node of G.
node	A node of interest. If node = "all", the index will be computed for all nodes.

Value

Returns the size of the graph or subgraph whose downstream end (outlet) is a node of interest.

Author(s)

Ken Aho, Gabor Csardi wrote several important function components including subgraph.

Examples

# Murphy Cr. disconnected network, no arc from M1799 to M1719!

G <- graph_from_literal(IN_N --+ M1984 --+ M1909, IN_S --+ M1993 --+ M1951, 
M1951 --+ M1909 --+ M1799, M1719 --+ M1653 --+ M1572 --+ M1452 --+ M1377, 
M1377 --+ M1254 --+ M1166 --+ M1121 --+ M1036 --+ M918 --+ M823 --+ M759, 
M759 --+ M716 --+ M624 --+ M523 --+ M454 --+ M380 --+ M233 --+ M153 --+ M91, 
M91 --+ OUT)

data(mur_coords) # coordinate data
spatial.plot(G, mur_coords[,2], mur_coords[,3], names =  mur_coords[,1])

data(mur_lengths) # segment length data 

lengths_new <- mur_lengths[-7,] # Drop M1799 -> M1719 arc length
E(G)$weight <- lengths_new[,2] # units are in meters
size.intact.to.node(G, node = "all") 
size.intact.to.sink(G, sink = "OUT") # same as output below:
size.intact.to.node(G, node = "OUT")

---

Shortest path lengths and number of paths

Description

The function spath.lengths calculates path lengths from all possible nodes to or from a designated node, i.e., the shortest in-paths and out-paths repsectively. Weighted path length are possible, including weighted path lengths based on field-observed instream arc lengths (see Examples). This results in "actual" path lengths in observed units. The function n.tot.paths calculates the total number of paths beginning or ending at all nodes in a graph, based on exponention of the the adjacency matrix.

Usage

spath.lengths(G, node = NULL, mode = "in", ignore.inf = TRUE)

n.tot.paths(G, mode = "in", sink = NULL)

Arguments

G	Graph of class "igraph". See graph_from_literal
node	Designated node.
mode	One of "in" or "out". The former gives in-paths, whereas the latter gives out-paths.
ignore.inf	Logical. Whether infinite distances are to be ignored. By default ignore.inf = TRUE, allowing impossible upstream distances to be ignored in stream DAGs.
sink	Name of sink node.

Value

Lengths of paths to a node of interest.

Author(s)

Ken Aho , Gabor Csardi wrote distances

Examples

data(mur_lengths)
mur <- streamDAGs("mur_full")
n.tot.paths(mur)

spath.lengths(mur, "M1653")
E(mur)$weight <- mur_lengths[,2] # weighted (actual in-stream lengths in meters)
spath.lengths(mur, "M1653")

---

Spatial plot of an igraph object or stream shapefile

Description

Makes a spatial plot of a igraph object or stream shapefile, given nodal coordinates and node IDs.

Usage

spatial.plot(G, x, y, names = NULL, 
                         plot = TRUE,
                         col = "lightblue", 
                         cex.text = .4, cex = 1,
                         arrow.col = "lightblue", arrow.lwd = 1, 
                         plot.bg = "white", pch = 21, 
                         pt.bg = "orange", grid.lwd = 2, 
                         plot.dry = FALSE,
                         col.dry = gray(.7),
                         cex.dry = 1, pch.dry = 19, 
                         arrow.col.dry = gray(.7), arrow.lwd.dry = 1,
                         cnw = NULL, xlim = NULL, ylim = NULL, 
                         arrow.warn = TRUE, ...)


spatial.plot.sf(x, y, names, shapefile = NULL, cex = 1, arrow.col = "lightblue", 
                arrow.lwd = 1, pch = 21, pt.bg = "orange")

Arguments

G	Graph object, see graph_from_literal.
x	X-coordinates of nodes.
y	Y-coordinates of nodes.
names	Names of nodes, must use the same names as G and correspond to the order of coordinates in x and y.
plot	Logical. Create plot?
shapefile	Shapefile object brought in using library sf
col	point symbol color.
cex.text	Character expansion for node labels in plot; cex.text = 0 suppresses labels.
cex	Chahracter expnansion of point symbols.
arrow.col	Color of plot arrows.
arrow.lwd	Arrow line width.
plot.bg	Background color of plot.
pch	Plotting character.
pt.bg	Background color for plotting character.
grid.lwd	Grid line width; grid.lwd = 0 suppresses grid.
plot.dry	Logical. Should “dry” nodes, i.e., nodes in names (and x and y) that are not also in G be plotted?
col.dry	Color of “dry” nodes in plot.
cex.dry	Symbol sizer of “dry” nodes in plot.
pch.dry	Plotting character (symbol) of “dry” nodes in plot.
arrow.col.dry	Arrow color for "dry" arcs. Dry arrow rendering requires cnw designation (see Examples).
arrow.lwd.dry	Arrow line width for "dry" arcs. Dry arrow rendering requires cnw designation (see Examples).
cnw	Complete network spatial.plot object.
xlim	A numeric vector of length 2, giving the lower and upper y-axis limits.
ylim	A numeric vector of length 2, giving the lower and upper x-axis limits.
arrow.warn	Logical. The function arrows omits arrowheads (with a warning) for any arrow of length less than 1/1000 inch. To elimiate this warning (which may occur for nearby nodes) specify arrow.warn = FALSE.
...	Other arguments to plot

Details

The function spatial.plot makes a plot of a stream DAG, showing arc flow directions to and from spatial node locations. The function can also be used to identify node and arc arrow coordinates for plotting (see Examples). The function spatial.plot.sf can create a spatially explicit graph from a stream shapefile with the stream outlay under a ggplot framework (see Examples). The function spatial.plot can be used to distinguish dry and wet nodes and arcs) (see Examples).

Value

A plot and an invisible list containing the x and y coordinates of nodes: the objects $x and $y, respectively, and the x and y coordinates of start and end points of arc arrows:the objects $x0, $y0, $x1, and $y1, respectively.

Author(s)

Ken Aho

Examples

G <- graph_from_literal(IN_N --+ M1984 --+ M1909, IN_S --+ M1993, 
M1993 --+ M1951 --+ M1909 --+ M1799 --+ M1719 --+ M1653 --+ M1572 --+ M1452,
M1452--+ M1377 --+ M1254 --+ M1166 --+ M1121 --+ M1036 --+ M918 --+ M823, 
M823 --+ M759 --+ M716 --+ M624 --+ M523 --+ M454 --+ M380 --+ M233 --+ M153,
M153 --+ M91 --+ OUT)

data(mur_coords)

x <- mur_coords[,2]
y <- mur_coords[,3]
names <- mur_coords[,1]
spatial.plot(G, x, y, names)

# using shapefiles


library(ggplot2); library(sf); library(ggrepel)
mur_sf <- st_read(system.file("shape/Murphy_Creek.shp", package="streamDAG"))
g1 <- spatial.plot.sf(x, y, names, shapefile = mur_sf)

# modify ggplot
g1 + theme_classic()


#-- Distinguishing wet and dry arcs and nodes --#

data(mur_node_pres_abs) # STIC H2O presence/absence
npa <- mur_node_pres_abs[650,][,-1] # STC data from 8/9/2019 22:30 
G1 <- delete.nodes.pa(G, npa) # delete nodes based STIC data

# Example 1 (only show wet nodes and arcs with associated wet nodes)
spatial.plot(G1, x, y, names)

# Example 2 (show wet nodes and arcs with associated wet nodes, and dry nodes)
spatial.plot(G1, x, y, names, plot.dry = TRUE)

# Example 3 (show wet nodes and arcs wet node arcs, and underlying network)
entire <- spatial.plot(G, x, y, names, plot = FALSE)
spatial.plot(G1, x, y, names, plot.dry = TRUE, cnw = entire)


#-- Animation: drying of Johnson Draw drainage --#

jd_graph <- streamDAGs("jd_full")
data(AIMS.node.coords)
jd_coords <- AIMS.node.coords[AIMS.node.coords$site == "JD",]
jd_coords <- jd_coords[jd_coords$STIC_inferred_PA,] 
data(jd_node_pres_abs)

# Drop 2023 sites 
jd_pa <- jd_node_pres_abs[,-c( 22, 23, 24, 25, 26, 27, 
28, 31, 32, 33, 34, 35, 36, 37)]

pb = txtProgressBar(min = 1, max = 250, initial = 1, style = 3) 
times <- round(seq(1,50322, length = 250),0)

for(i in 1:250){
  dev.flush()
  jd_sub <- delete.nodes.pa(jd_graph, 
                            jd_pa[times[i],][-1],
                            na.response = "treat.as.1")
  spatial.plot(jd_sub, 
               x = jd_coords[,3], 
               y = jd_coords[,2], 
               names = jd_coords[,1], 
               ylim = c(43.122, 43.129), 
               xlim = c(-116.8, -116.775), 
               plot.dry = TRUE, main = jd_node_pres_abs[,1][times[i]], 
               xlab = "Longitude", ylab = "Latitude")
  dev.hold()
  Sys.sleep(.05)
  setTxtProgressBar(pb, i)
  }

---