Introduction to the Modeling and Analysis of Complex Systems

15.6. GENERATING RANDOM GRAPHS 321sions where you want to have a randomly generated network. Here are some examplesof NetworkX’s built-in functions that can generate random graph samples:Code 15.21: random-graphs.pyfrom pylab import *import networkx as nxsubplot(2, 2, 1)nx.draw(nx.gnm_random_graph(10, 20))title(’random graph with\n10 nodes, 20 edges’)subplot(2, 2, 2)nx.draw(nx.gnp_random_graph(20, 0.1))title(’random graph with\n 20 nodes, 10% edge probability’)subplot(2, 2, 3)nx.draw(nx.random_regular_graph(3, 10))title(’random regular graph with\n10 nodes of degree 3’)subplot(2, 2, 4)nx.draw(nx.random_degree_sequence_graph([3,3,3,3,4,4,4,4,5,5]))title(’random graph with\n degree sequence\n[3,3,3,3,4,4,4,4,5,5]’)show()The output is shown in Fig. 15.10. The first example, gnm_random_graph(n, m), simplygenerates a random graph made of n nodes and m edges. The second example,gnp_random_graph(n, p), generates a random graph made of n nodes, where eachnode pair is connected to each other with probability p. These two types of randomgraphs are called Erdős-Rényi random graphs after two Hungarian mathematicians PaulErdős and Alfréd Rényi who studied random graphs in the 1950s [63]. The third example,random_regular_graph(k, n), generates a random regular graph made of n nodes thatall have the same degree k. The fourth example, random_degree_sequence_graph(list),generates a random graph whose nodes have degrees specified in list. In this particularexample, four nodes have degree 3, four nodes have degree 4, and two nodes have degree5. Note that this function may not be able to generate a graph within a given numberof trials (which is set to 10 by default). You can increase the number of trials by specifyingthe tries option in the function, e.g., tries = 100.