Structural Node Importance Beyond Classical Centrality: A Comparative Study of Entropy-Based k-Hop Measures

Abstract

This paper investigates whether entropy-based k-hop metrics capture aspects of structural node importance that are not emphasized by classical centrality measures. We compare degree and eigenvector centrality with two entropy-based measures, Entropy-Weighted Redundancy (EWR) and Normalized Entropy Density (NED), on three real-world Twitter-derived networks with different sizes and connectivity patterns. Unlike conventional centrality measures, EWR and NED characterize node importance through the informational diversity and redundancy of the induced k-hop neighborhood. The results show that entropy-based rankings differ substantially from classical rankings and highlight structurally distinctive nodes whose local environments exhibit different structural properties. Furthermore, the observed rankings depend on both the underlying network topology and the neighborhood radius. Overall, the study demonstrates that entropy-based k-hop analysis provides a complementary perspective on structural node importance and motivates further comparative evaluation on other classes of networks.