A Game Theory Inspired Approach to Stable Core Decomposition on Weighted Networks

Meso-scale structural analysis, like core decomposition has uncovered groups of nodes that play important roles in the underlying complex systems. The existing core decomposition approaches generally focus on node properties like degree and strength. The node centric approaches can only capture a limited information about the local neighborhood topology. In the present work, we propose a group density based core analysis approach that overcome the drawbacks of the node centric approaches. The proposed algorithmic approach focuses on weight density, cohesiveness, and stability of a substructure. The method also assigns an unique score to every node that rank the nodes based on their degree of core-ness. To determine the correctness of the proposed method, we propose a synthetic benchmark with planted core structure. A performance test on the null model is carried out using a weighted lattice without core structures. We further test the stability of the approach against random noise. The experimental results prove the superiority of our algorithm over the state-of-the-arts. We finally analyze the core structures of several popular weighted network models and real life weighted networks. The experimental results reveal important node ranking and hierarchical organization of the complex networks, which give us better insight about the underlying systems.