Analyzing the Correlation of Classical and Community-aware Centrality Measures in Complex Networks

International audienceIdentifying influential nodes in social networks is a fundamental issue. Indeed, it has many applications, such as inhibiting epidemic spreading, accelerating information diffusion, preventing terrorist attacks, and much more. Classically, centrality measures quantify the node's importance based on various topological properties of the network, such as Degree and Betweenness. Nonetheless, these measures are agnostic of the community structure, although it is a ubiquitous characteristic encountered in many real-world networks. To overcome this drawback, there is a growing trend to design so-called community-aware centrality measures. Although several works investigate the relationship between various classical centrality measures [1-3], the interplay between classical and community-aware centrality measures is still unexplored. This work presents an extensive investigation aimed at a better understanding of the relationship between community-aware centrality measures, classical centrality measures, and network topology. Artificial and real-world networks are used in the experiments. The Kendall's Tau correlation quantifies the interaction between ten classical and twenty-eight community-aware centrality measures. The community-aware centrality measures are divided into three groups. The first group's ten measures are based on the intra-community links of a node (local measures). The second group's twelve measures are based on the inter-community links of a node (global measures). Finally, the six measures of the third group consider both types of links (mixed measures). The LFR algorithm generates artificial networks with controlled properties. Indeed, the community structure strength (µ), the exponent of the degree distribution (γ), and the community size distribution (θ) can be specified. The experiments show that the community structure strength is the main feature governing the correlation between classical and community-aware centrality measures. The heatmap on the left of Figure 1 represents the correlation in an artificial network with a strong community structure. The global community-aware centrality measures exhibit a low correlation with classical centrality measures, while local communityaware centrality measures show a high correlation. The results are inverted when the network has a weak community structure. Differences are more subtle for mixed community-aware measures. One can also notice that results are relatively insensitive to variation of the degree and community size distributions' exponents. Fifty real-world networks originating from various domains are also investigated. Linear regression is performed considering six macroscopic