Introduction to the Modeling and Analysis of Complex Systems

17.2. SHORTEST PATH LENGTH 379EccentricityDiameterRadiusε(i) = max d(i → j) (17.16)jThis metric is defined for each node and gives the maximal shortest path lengtha node can have with any other node in the network. This tells how far the nodeis to the farthest point in the network.D = maxiε(i) (17.17)This metric gives the maximal eccentricity in the network. Intuitively, it tells ushow far any two nodes can get from one another within the network. Nodeswhose eccentricity is D are called peripheries.R = miniε(i) (17.18)This metric gives the minimal eccentricity in the network. Intuitively, it tells us thesmallest number of steps you will need to reach every node if you can choosean optimal node as a starting point. Nodes whose eccentricity is R are calledcenters.In NetworkX, these metrics can be calculated as follows:Code 17.8:>>> import networkx as nx>>> g = nx.karate_club_graph()>>> nx.average_shortest_path_length(g)2.408199643493761>>> nx.eccentricity(g){0: 3, 1: 3, 2: 3, 3: 3, 4: 4, 5: 4, 6: 4, 7: 4, 8: 3, 9: 4, 10: 4,11: 4, 12: 4, 13: 3, 14: 5, 15: 5, 16: 5, 17: 4, 18: 5, 19: 3, 20: 5,21: 4, 22: 5, 23: 5, 24: 4, 25: 4, 26: 5, 27: 4, 28: 4, 29: 5, 30: 4,31: 3, 32: 4, 33: 4}>>> nx.diameter(g)5>>> nx.periphery(g)