The weak core and the structure of elites in social multiplex networks

TL;DR

This paper introduces the concept of the weak core in multiplex social networks, revealing its role in connecting elite communities and its association with high social performance, based on analysis of online game data.

Contribution

It extends the generalized K-core concept by identifying the weak core as a cohesive bridge between elite communities in multiplex networks.

Findings

Weak core has low connectivity and clustering but forms a cohesive structure.

Members of the weak core exhibit the highest social performance scores.

Generalized K-core reveals clear community structure in social networks.

Abstract

Recent approaches on elite identification highlighted the important role of {\em intermediaries}, by means of a new definition of the core of a multiplex network, the {\em generalised} $K$-core. This newly introduced core subgraph crucially incorporates those individuals who, in spite of not being very connected, maintain the cohesiveness and plasticity of the core. Interestingly, it has been shown that the performance on elite identification of the generalised $K$-core is sensibly better that the standard $K$-core. Here we go further: Over a multiplex social system, we isolate the community structure of the generalised $K$-core and we identify the weakly connected regions acting as bridges between core communities, ensuring the cohesiveness and connectivity of the core region. This gluing region is the {\em Weak core} of the multiplex system. We test the suitability of our method on data from the society of 420.000 players of the Massive Multiplayer Online Game {\em Pardus}. Results show that the generalised $K$-core displays a clearly identifiable community structure and that the weak core gluing the core communities shows very low connectivity and clustering. Nonetheless, despite its low connectivity, the weak core forms a unique, cohesive structure. In addition, we find that members populating the weak core have the best scores on social performance, when compared to the other elements of the generalised $K$-core. The weak core provides a new angle on understanding the social structure of elites, highlighting those subgroups of individuals whose role is to glue different communities in the core.