The topological relationship between the large-scale attributes and local interaction patterns of complex networks

Details The topological relationship between the large-scale attributes and local interaction patterns of complex networks The topological relationship between the large-scale attributes and local interaction patterns of complex networks

2004-08-19

arxiv.org/abs/cond-mat/0408431v2

PNAS 101, 17945 (2004)

Physics

Condensed Matter

Disordered Systems and Neural Networks

paper

Scientific paper

10.1073/pnas.0406024101

Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the underlying reasons for the variable quantity of different subgraph types, their propensity to form clusters, and their relationship with the networks' global organization remain poorly understood. Here we show that a network's large-scale topological organization and its local subgraph structure mutually define and predict each other, as confirmed by direct measurements in five well studied cellular networks. We also demonstrate the inherent existence of two distinct classes of subgraphs, and show that, in contrast to the low-density type II subgraphs, the highly abundant type I subgraphs cannot exist in isolation but must naturally aggregate into subgraph clusters. The identified topological framework may have important implications for our understanding of the origin and function of subgraphs in all complex networks.

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