## ----include = FALSE---------------------------------------------------------- knitr::opts_chunk$set( collapse = TRUE, comment = "#>" ) ## ----setup-------------------------------------------------------------------- library(graphonmix) library(ggplot2) library(igraph) requireNamespace("gridExtra", quietly = TRUE) ## ----------------------------------------------------------------------------- g1 <- make_star(4,mode = "undirected") g1 <- add_vertices(g1, 1) g1 <- add_edges(g1,c(4,5)) lg1 <- make_line_graph(g1) oldpar <- par(mfrow = c(1,2)) plot(g1, vertex.label = NA, edge.label = c(1,2,3,4), main = "Graph G") plot(lg1, vertex.label = c(1,2,3,4), vertex.size = 20, main = "Line graph L(G)") par(oldpar) ## ----------------------------------------------------------------------------- st <- make_star(10, mode = "undirected") lgr_st <- make_line_graph(st) oldpar <- par(mfrow = c(1,2)) plot(st, vertex.label = NA, main = "Star graph G") plot(lgr_st, vertex.label = NA, main = "Line graph L(G) of a star") par(oldpar) ## ----------------------------------------------------------------------------- stardensity <- gnpdensity <- rep(0, 20) for(i in 1:20){ n <- i*100 gr1 <- sample_gnp(n, p = 0.1) gnpdensity[i] <- edge_density(gr1) gr2 <- make_star(n, mode = "undirected") stardensity[i] <- edge_density(gr2) } gnpdensity stardensity ## ----------------------------------------------------------------------------- gr <- make_star(10, mode = "undirected") emp <- empirical_graphon(gr) plot_graphon(emp) + coord_fixed() ## ----------------------------------------------------------------------------- gr <- make_star(20, mode = "undirected") emp <- empirical_graphon(gr) g1 <- plot_graphon(emp) + coord_fixed() + ggtitle('n = 10') gr <- make_star(100, mode = "undirected") emp <- empirical_graphon(gr) g2 <- plot_graphon(emp) + coord_fixed() + ggtitle('n = 100') gr <- make_star(200, mode = "undirected") emp <- empirical_graphon(gr) g3 <- plot_graphon(emp) + coord_fixed() + ggtitle('n = 200') gridExtra::grid.arrange(g1, g2, g3, nrow = 1) ## ----------------------------------------------------------------------------- gr1 <- make_star(10, mode = "undirected") gr <- gr1 %du% gr1 lgr <- make_line_graph(gr) emp <- empirical_graphon(lgr) g1 <- plot_graphon(emp) + coord_fixed() + ggtitle('n = 20') gr1 <- make_star(50, mode = "undirected") gr <- gr1 %du% gr1 lgr <- make_line_graph(gr) emp <- empirical_graphon(lgr) g2 <- plot_graphon(emp) + coord_fixed() + ggtitle('n = 100') gr1 <- make_star(100, mode = "undirected") gr <- gr1 %du% gr1 lgr <- make_line_graph(gr) emp <- empirical_graphon(lgr) g3 <- plot_graphon(emp) + coord_fixed() + ggtitle('n = 200') gridExtra::grid.arrange(g1, g2, g3, nrow = 1) ## ----------------------------------------------------------------------------- wts <- c(0.5, 0.3, 0.2) U <- line_graphon(wts) gr <- sample_graphon(U, n = 100) plot(gr, vertex.size = 1, edge.color = "lightgray", # Light colored edges vertex.label = NA, vertex.color = "lightblue" ) ## ----------------------------------------------------------------------------- grsp <- generate_star_union(wts, n = 100) plot(grsp, edge.curved = 0.3, vertex.size = 1, edge.color = "lightgray", # Light colored edges vertex.label = NA, vertex.color = "lightblue" )