Relationship between the behaviour of entropy, the conductance and the coefficient of clustering of networks using symbolic dynamics

Abstract

The past recent years have seen a large increase in the study of complex networks. This interest has undoubtedly been triggered by the introduction of systems that allowed an exponential growth in the availability of data on large networks in the real world. The theory of dynamical networks is a com- bination of graph theory and nonlinear dynamics. We analyse a joint action of these different perspectives by methods of symbolic dynamics and thermodynamic formalism. The characterization of the geometry and topology of complex networks and the principles that govern their dynamical behavior became a subject of great importance to scientists of various disciplines. The entropy as a fundamental invariant of the dynamic system, and as a measure of structural and dynamic properties of the networks gained signi cant importance. For this characterization, we will use the concept of network entropy introduced for Demetrius et al. Our goal is to understand what the relationship between the behavior of entropy, the conductance and the coef cient of clustering when there is the formation of clusters by the considered system.