Introduction to the Modeling and Analysis of Complex Systems

Chapter 17Dynamical Networks II: Analysis ofNetwork Topologies17.1 Network Size, Density, and PercolationNetworks can be analyzed in several different ways. One way is to analyze their structuralfeatures, such as size, density, topology, and statistical properties.Let me first begin with the most basic structural properties, i.e., the size and densityof a network. These properties are conceptually similar to the mass and composition ofmatter—they just tell us how much stuff is in it, but they don’t tell us anything about howthe matter is organized internally. Nonetheless, they are still the most fundamental characteristics,which are particularly important when you want to compare multiple networks.You should compare properties of two networks of the same size and density, just likechemists who compare properties of gold and copper of the same mass.The size of a network is characterized by the numbers of nodes and edges in it.NetworkX’s Graph objects have functions dedicated for measuring those properties:Code 17.1:>>> g = nx.karate_club_graph()>>> g.number_of_nodes()34>>> g.number_of_edges()78371