Random Graphs 4: Small-World and Scale-Free Networks

Here we are concerned with modeling some salient properties observed in many real networks (social, technological, biological). The first property is compactness, i.e., of small distances between nodes. The second property is transitivity or clustering, i.e., the presence of many 3-cycles (triangles) in the network. The third property is a scale-free degree distribution, i.e., the degree sequence follows a power law.