Introduction to the Modeling and Analysis of Complex Systems

17.2. SHORTEST PATH LENGTH 37717.2 Shortest Path LengthNetwork analysis can measure and characterize various features of network topologiesthat go beyond size and density. Many of the tools used here are actually borrowed fromsocial network analysis developed and used in sociology [60].The first measurement we are going to discuss is the shortest path length from onenode to another node, also called geodesic distance in a graph. If the network is undirected,the distance between two nodes is the same, regardless of which node is thestarting point and which is the end point. But if the network is directed, this is no longerthe case in general.The shortest path length is easily measurable using NetworkX:Code 17.5:>>> g = nx.karate_club_graph()>>> nx.shortest_path_length(g, 16, 25)4The actual path can also be obtained as follows:Code 17.6:>>> nx.shortest_path(g, 16, 25)[16, 5, 0, 31, 25]The output above is a list of nodes on the shortest path from node 16 to node 25. Thiscan be visualized using draw_networkx_edges as follows:Code 17.7: shortest-path.pyfrom pylab import *import networkx as nxg = nx.karate_club_graph()positions = nx.spring_layout(g)path = nx.shortest_path(g, 16, 25)edges = [(path[i], path[i+1]) for i in xrange(len(path) - 1)]nx.draw_networkx_edges(g, positions, edgelist = edges,edge_color = ’r’, width = 10)