A detailed characterization of complex networks using Information Theory

Abstract

Understanding the structure and the dynamics of networks is of paramount importance for manyscientific fields that rely on network science. Complex network theory provides a variety of features thathelp in the evaluation of network behavior. However, such analysis can be confusing and misleading asthere are many intrinsic properties for each network metric. Alternatively, Information Theory methodshave gained the spotlight because of their ability to create a quantitative and robust characterizationof such networks. In this work, we use two Information Theory quantifiers, namely Network Entropyand Network Fisher Information Measure, to analyzing those networks. Our approach detects nontrivialcharacteristics of complex networks such as the transition present in the Watts-Strogatz modelfrom k-ring to random graphs; the phase transition from a disconnected to an almost surely connectednetwork when we increase the linking probability of Erdős-Rényi model; distinct phases of scale-freenetworks when considering a non-linear preferential attachment, fitness, and aging features alongsidethe configuration model with a pure power-law degree distribution. Finally, we analyze the numericalresults for real networks, contrasting our findings with traditional complex network methods. Inconclusion, we present an efficient method that ignites the debate on network characterization.