Spectral measures of bipartivity in complex networks

Abstract

We introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network. Spectral graph theory is used to quantify how close to bipartite a network is and the extent to which individual nodes and edges contribute to the global network bipartivity. It is shown that the bipartivity characterizes the network structure and can be related to the efficiency of semantic or communication networks, trophic interactions in food webs, construction principles in metabolic networks, or communities in social networks.

Bipartite network projection and personal recommendation

“…Recently, a large amount of attention is addressed to analyzing [8,20,25,26,27] and modeling [28,29,30] bipartite network. However, for the convenience of directly showing the relations among a particular set of nodes, the bipartite network is usually compressed by one-mode projecting.…”

Estrada and L-Estrada Indices of Edge-Independent Random Graphs

“…The Estrada index as a graph-spectrum-based invariant has found its widespread applicability in chemistry (such as the degree of folding of long-chain polymeric molecules [4,5], extended atomic branching [6], and the Shannon entropy descriptor [7][8][9]) and complex networks, see e.g., [10][11][12][13][14]. Various quantitative estimates of the Estrada index have been reported, see e.g., [15][16][17][18][19][20].…”

Understanding how both the partitions of a bipartite network affect its one-mode projection

“…The latter arise from an underlying wordsentence bipartite network. Therefore, for several real-world complex systems as described in [3,4,5,6], understanding the underlying bipartite process turns out to be extremely important.…”