Scaling of Nestedness in Complex Networks

Nestedness characterizes the linkage pattern of networked systems, indicating the likelihood that a node is linked to the neighbors of the nodes with larger degrees than it. Networks of mutualistic relationship between distinct groups of species in ecological communities exhibit such nestedness, which is known to support the network's robustness. Despite such importance, the quantitative characteristics of nestedness are little understood. Here, we take a graph-theoretic approach to derive the scaling properties of nestedness in various model networks. Our results show how the heterogeneous connectivity patterns enhance nestedness. Also, we find that the nestedness of bipartite networks depends sensitively on the fraction of different types of nodes, causing nestedness to scale differently for nodes of different types.