Entropy Dynamics of Community Alignment in the Italian Parliament   Time-Dependent Network
  Complex institutions are typically characterized by meso-scale structures which are fundamental for the successful coordination of multiple agents. Here we introduce a framework to study the temporal dynamics of the node-community relationship based on the concept of community alignment, a measure derived from the modularity matrix that defines the alignment of a node with respect to the core of its community. The framework is applied to the 16th legislature of the Italian Parliament to study the dynamic relationship in voting behavior between Members of the Parliament (MPs) and their political parties. As a novel contribution, we introduce two entropy-based measures that capture politically interesting dynamics: the group alignment entropy (over a single snapshot), and the node alignment entropy (over multiple snapshots). We show that significant meso-scale changes in the time-dependent network structures can be detected by a combination of the two measures. We observe a steady growth of the group alignment entropy after a major internal conflict in the ruling majority and a different distribution of nodes alignment entropy after the government transition. 
Gabriele Lami and Marco Cristoforetti and Giuseppe Jurman and Cesare   Furlanello and Tommaso Furlanello
cs.SI math.DS physics.soc-ph