We introduce a network growth model based on complete redirection: a new node randomly selects an existing target node, but attaches to a random neighbor of this target. For undirected networks, this simple growth rule generates unusual, highly modular networks. Individual network realizations typically contain multiple macrohubs—nodes whose degree scales linearly with the number of nodes N. The size of the network “nucleus”—the set of nodes of degree greater than one—grows sublinearly with N and thus constitutes a vanishingly small fraction of the network. The network therefore consists almost entirely of leaves (nodes of degree one) as N→∞.
Emergent Network Modularity
P. L. Krapivsky, S. Redner