  Nestedness characterizes the linkage pattern of networked systems, indicating
the likelihood that a node is linked to the nodes linked to 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 robustness. Despite such importance, quantitative
characteristics of nestedness is little understood. Here we take
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 depend sensitively on the fraction of different types of nodes,
causing nestedness to scale differently for nodes of different types.
