2012/04/28 by E. Weinan, Weinan, E., Jianfeng Lu +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Physical sciences #Methodology (stat.ME) #Molecular Networks (q-bio.MN) #Physics and Society (physics.soc-ph) #Social and Information Networks (cs.SI) #cs.SI #physics.soc-ph #q-bio.MN #stat.ME
paper · pdf · doi:10.48550/arxiv.1204.6376
arxiv created 2012/04/28 · arxiv updated 2012/05/01
Topological landscape is introduced for networks with functions defined on the nodes. By extending the notion of gradient flows to the network setting, critical nodes of different indices are defined. This leads to a concise and hierarchical representation of the network. Persistent homology from computational topology is used to design efficient algorithms for performing such analysis. Applications to some examples in social and biological networks are demonstrated, which show that critical nodes carry important information about structures and dynamics of such networks.