README.md

In jdwilson4/NetSurv: Network Surveillance via the Degree Corrected Stochastic Block Model

NetSurv

An R package that implements the model-based network surveillance procedure based on the dynamic degree corrected stochastic block model. Functions in the package can simulate, estimate and generate Shewhart control charts for dynamic sequences of graphs with a structural change.

The key reference for this monitoring method is

• Wilson, J.D., Stevens, N.T., and Woodall, W.H. (2016) Modeling and estimating change in temporal networks via a dynamic degree corrected stochastic block model. arXiv Preprint: http://arxiv.org/abs/1605.04049

Installation

To install NetSurv, use the following commands. Be sure to include the required packages Matrix, Rlab, and devtools from R version 3.1.2 or higher.

#install the latest version of devtools
install.packages("devtools")
library(devtools, quietly = TRUE)

#install and load NetSurv
devtools::install_github("jdwilson4/NetSurv")
library(NetSurv, quietly = TRUE)

#load other required packages
library(Matrix, quietly = TRUE)
library(Rlab, quietly = TRUE)

Description

This package contains four primary functions, which are briefly described below. For a function named function below, type ?function in R to get full documentation.

• DCSBM(): simulate an undirected graph realization from the degree corrected stochastic block random graph model. Edge weights are drawn from a Poisson distribution with specified mean.
• dynamic.DCSBM(): simulate an ordered sequence of undirected graphs from the degree corrected stochastic block random graph model.
• MLE.DCSBM(): estimate the maximum likelihood estimators for P and delta at each time point in a time-varying collection of networks.
• NetSurv(): Shewhart surveillance control chart and plots for a desired collection of statistics

Examples

• Example 1: simulate a single realization of a DCSBM at one time point

?DCSBM
net <- DCSBM(n = 500, k = 2, P = cbind(c(0.10, 0.01), c(0.02, 0.075)),
             sizes = c(200, 300), random.community.assignment = FALSE,
             delta = c(0.2, 0.7), edge.list = FALSE)

image(Matrix(net$Adjacency))

• Example 2: simulate a dynamic DCSBM with 50 time steps and a change at time 25, where the change is a local change in connection propensity in community 1

?dynamic.DCSBM

n <- 100
P.old <- cbind(c(0.10, 0.01), c(0.02, 0.075))
P.new <- cbind(c(0.20, 0.025), c(0.02, 0.075))
P.array <- array(c(replicate(25, P.old), replicate(25, P.new)), dim = c(2, 2, 50))
community.array <- array(rep(c(rep(1, 50), rep(2, 50)), 50), dim = c(100, 1, 50))
delta.array <- array(rep(rep(0.2, 2), 50), dim = c(1, 2, 50))

dynamic.net <- dynamic.DCSBM(n = 100, T = 50, P.array = P.array,
                             community.array = community.array,
                             delta.array = delta.array, edge.list = FALSE)

#View instances of the network before and after the change
image(Matrix(dynamic.net$Adjacency.list[[1]]))
image(Matrix(dynamic.net$Adjacency.list[[30]]))

• Example 3: Estimating MLEs of a dynamic DCSBM

MLEs.example <- MLE.DCSBM(dynamic.net$Adjacency.list, community.array = community.array,
                          T = 50, k = 2)

• Example 4: Generate control charts for maximum likelihood estimators

#Store the statistics in a data frame
statistics.df <- data.frame(Phat_11 = MLEs.example$P.hat.array[1, 1, ], 
                           Phat_12 = MLEs.example$P.hat.array[1, 2, ],
                           Phat_22 = MLEs.example$P.hat.array[2, 2, ],
                           delta_hat = MLEs.example$delta.hat.global)
control.chart <- NetSurv(statistics.df, phase1.length = 20, save.plot = FALSE)
print(control.chart)

Application: Senatorial co-voting Network

Now, we apply the NetSurv methodology on the dynamic networks that describe the co-voting habits of the U.S. Senators over time. See the above reference for more information on the results and description of the data set.

In this application, we assume that community labels correspond to political affiliation of the Senators (Republican vs. Democrat). The data is contained in the NetSurv package and can be loaded directly.

Our surveillance technique reveals periods of (i) political cohesion (Congress 90 - 95), which is associated with the "Rockefeller Republican" era where Republicans swayed left following the ideals of Nelson Rockefeller, and (ii) political polarization (Congress 104 and beyond).

#Load data
data(voting)

#Estimate MLEs using DCSBM. 

MLEs.application <- MLE.DCSBM(voting.network, community.array = political.affiliation, 
                              T = length(voting.network), k = 2)
statistics.application <- data.frame(Phat_11 = MLEs.application$P.hat.array[1, 1, ], 
                                    Phat_12 = MLEs.application$P.hat.array[1, 2, ],
                                    Phat_22 = MLEs.application$P.hat.array[2, 2, ],
                                    delta_hat = MLEs.application$delta.hat.global)

names(statistics.application) = c("Democrat-Democrat", "Republican-Democrat", 
                                  "Republican-Republican", "delta.hat")

control.chart <- NetSurv(statistics.application, phase1.length = 50, xaxis.old = seq(1, 74, 5), 
                         xaxis.new = seq(40, 113, 5), xlab = "Congress", save.plot = FALSE)

Contributors

• James D. Wilson, Assistant Professor of Statistics, University of San Francisco. Developer, contributor, and maintainer.

• Nathaniel T. Stevens, Assistant Professor of Statistics, University of San Francisco. Contributor.

Please send any comments, bugs, or questions to the developer James D. Wilson at [e-mail].

jdwilson4/NetSurv documentation built on May 18, 2019, 11:40 p.m.