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Recent approaches on elite identification highlighted the important role of{\em intermediaries}, by means of a new definition of the core of a multiplexnetwork, the {\em generalised} $K$-core. This newly introduced core subgraphcrucially incorporates those individuals who, in spite of not being veryconnected, maintain the cohesiveness and plasticity of the core. Interestingly,it has been shown that the performance on elite identification of thegeneralised $K$-core is sensibly better that the standard $K$-core. Here we gofurther: Over a multiplex social system, we isolate the community structure ofthe generalised $K$-core and we identify the weakly connected regions acting asbridges between core communities, ensuring the cohesiveness and connectivity ofthe core region. This gluing region is the {\em Weak core} of the multiplexsystem. We test the suitability of our method on data from the society of420.000 players of the Massive Multiplayer Online Game {\em Pardus}. Resultsshow that the generalised $K$-core displays a clearly identifiable communitystructure and that the weak core gluing the core communities shows very lowconnectivity and clustering. Nonetheless, despite its low connectivity, theweak core forms a unique, cohesive structure. In addition, we find that memberspopulating the weak core have the best scores on social performance, whencompared to the other elements of the generalised $K$-core. The weak coreprovides a new angle on understanding the social structure of elites,highlighting those subgroups of individuals whose role is to glue differentcommunities in the core.

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