No abstract

The problem of community detection is relevant in many disciplines of science and modularity optimization is the widely accepted method for this purpose. It has recently been shown that this approach presents a resolution limit by which it is not possible to detect communities with sizes smaller than a threshold which depends on the network size. Moreover, it might happen that the communities resulting from such an approach do not satisfy the usual qualitative definition of commune, i.e., nodes in a commune are more connected among themselves than to nodes outside the commune. In this article we introduce a new method for community detection in complex networks.We define new merit factors based on the weak and strong community definitions formulated by Radicchi et al (Proc. Nat. Acad. Sci. USA 101, 2658-2663) and we show that this local definitions avoid the resolution limit problem found in the modularity optimization approach.

Activity-driven modeling has been recently proposed as an alternative growth mechanism for time varying networks, displaying power-law degree distribution in time-aggregated representation.This approach assumes memoryless agents developing random connections, thus leading to random networks that fail to reproduce two-nodes degree correlations and the high clustering coefficient widely observed in real social networks. In this work we introduce these missing topological features by accounting for memory effects on the dynamic evolution of time-aggregated networks. To this end, we propose an activity-driven network growth model including a triadicclosure step as main connectivity mechanism. We show that this simple mechanism provides some of the fundamental topological features expected for real social networks. We derive analytical results and perform extensive numerical simulations in regimes with and without population growth. Finally, we present two cases of study, one comprising face-to-face encounters in a closed gathering, while the other one from an online social friendship network.