Scale-free property of local-world networks and their community structures

Abstract

The scale-free property and community structures of complex networks formed by local events have been studied theoretically, numerically, and empirically. We showed analytically and numerically that the degree distribution function P (k) of the local-world evolving network exhibits a crossover from an exponential to power-law form by increasing the local-world size M . For M much larger than the crossover local-world size M co , the distribution function P (k) has a power-law form for any degree k(≫ 1). Below M co , however, P (k) obeys a power law for 1 ≪ k ≪ k co and decays exponentially for k ≫ k co . The crossover size M co and the crossover degree k co have been also elucidated. In addition, we constructed the drug prescription network (DPN) as a real local-world network, in which the local-world subsets are definitely specified, to reveal how the local-world nature affects properties of real-world networks. We found that the community structure of the DPN strongly correlates with the local worlds.

Growing local likelihood network: Emergence of communities

“…Moreover, many real-world networks exhibit clusters and communities, but it is unclear how a simple growth algorithm can explain this. Furuya and Yakubo [18] discuss the community structure on localevolving scale-free network, but only via the BA method. In this paper, we will show the novel properties that the networks generated via this likelihood method exhibit, in particular, strong community modularity.…”