Semi-Local Integration Measure for Directed Graphs

Abstract

Directed and weighted graphs can be used for many real-world applications to model and analyse the quality and structure of communication within the system, the distribution and flow of information, and various resources, dependencies, resilience, etc. On social media platforms, for example, highly networked members, so-called influencers, disseminate information, opinions and trends to their followers, who in turn increase the popularity of the influencers through likes and comments. Both types of interaction have a major influence on discussions and activities in the social network. To identify the nodes with the highest integration and interconnectivity within the neighbourhood subnetwork, we introduce the Directed Semi-Local Integration (DSLI) centrality measure for directed and weighted graphs. This centrality measure evaluates the integration of nodes assessed by the presence of connection, the strength of links, the organisation and optimisation of inbound and outbound interconnectivity, and the redundancy in the local subnetwork, and provides a stronger differentiation of the importance of nodes than standard centrality measures. Thus, DSLI has the potential to be used for analysing the degree of integration for the uptake and dissemination of resources in complex networks in many different contexts.