Network Landscape from a Brownian Particle's Perspective

Details Network Landscape from a Brownian Particle's Perspective Network Landscape from a Brownian Particle's Perspective

2003-02-11

arxiv.org/abs/physics/0302030v1

Physical Review E 67: 041908 (2003)

Physics

Biological Physics

5 pages, 4 color-figures. REVTeX 4 format. To appear in PRE

Scientific paper

10.1103/PhysRevE.67.041908

Given a complex biological or social network, how many clusters should it be decomposed into? We define the distance $d_{i,j}$ from node $i$ to node $j$ as the average number of steps a Brownian particle takes to reach $j$ from $i$. Node $j$ is a global attractor of $i$ if $d_{i,j}\leq d_{i,k}$ for any $k$ of the graph; it is a local attractor of $i$, if $j\in E_i$ (the set of nearest-neighbors of $i$) and $d_{i,j}\leq d_{i,l}$ for any $l\in E_i$. Based on the intuition that each node should have a high probability to be in the same community as its global (local) attractor on the global (local) scale, we present a simple method to uncover a network's community structure. This method is applied to several real networks and some discussion on its possible extensions is made.

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