Introduction to the Modeling and Analysis of Complex Systems

17.4. CLUSTERING 387while the numerator is the number of such triplets where j is also connectedto k. This essentially captures the same aspect of the network as the averageclustering coefficient, i.e., how locally clustered the network is, but the transitivitycan be calculated on directed networks too. It also treats each triangle moreevenly, unlike the average clustering coefficient that tends to underestimate thecontribution of triplets that involve highly connected nodes.Again, calculating these clustering metrics is very easy in NetworkX:Code 17.11:>>> import networkx as nx>>> g = nx.karate_club_graph()>>> nx.clustering(g){0: 0.15, 1: 0.3333333333333333, 2: 0.24444444444444444, 3:0.6666666666666666, 4: 0.6666666666666666, 5: 0.5, 6: 0.5, 7: 1.0,8: 0.5, 9: 0.0, 10: 0.6666666666666666, 11: 0.0, 12: 1.0, 13: 0.6,14: 1.0, 15: 1.0, 16: 1.0, 17: 1.0, 18: 1.0, 19: 0.3333333333333333,20: 1.0, 21: 1.0, 22: 1.0, 23: 0.4, 24: 0.3333333333333333, 25:0.3333333333333333, 26: 1.0, 27: 0.16666666666666666, 28:0.3333333333333333, 29: 0.6666666666666666, 30: 0.5, 31: 0.2, 32:0.19696969696969696, 33: 0.11029411764705882}>>> nx.average_clustering(g)0.5706384782076823>>> nx.transitivity(g)0.2556818181818182Exercise 17.9 Generate (1) an Erdős-Rényi random network, (2) a Watts-Strogatz small-world network, and (3) a Barabási-Albert scale-free network of comparablesize and density, and compare them with regard to how locally clusteredthey are.The clustering coefficient was first introduced by Watts and Strogatz [56], where theyshowed that their small-world networks tend to have very high clustering compared totheir random counterparts. The following code replicates their computational experiment,varying the rewiring probability p:Code 17.12: small-world-experiment.py