  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.
