A Fractional (q,q′) Non-Extensive Information Dimension for Complex Networks

Abstract

This article introduces a new fractional approach to the concept of information dimensions in complex networks based on the (q,q′)-entropy proposed in the literature. The q parameter measures how far the number of sub-systems (for a given size ε) is from the mean number of overall sizes, whereas q′ (the interaction index) measures when the interactions between sub-systems are greater (q′>1), lesser (q′<1), or equal to the interactions into these sub-systems. Computation of the proposed information dimension is carried out on several real-world and synthetic complex networks. The results for the proposed information dimension are compared with those from the classic information dimension based on Shannon entropy. The obtained results support the conjecture that the fractional (q,q′)-information dimension captures the complexity of the topology of the network better than the information dimension.