  In online communications, patterns of conduct of individual actors and use of
emotions in the process can lead to a complex social graph exhibiting
multilayered structure and mesoscopic communities. Using simplicial complexes
representation of graphs, we investigate in-depth topology of online social
network which is based on MySpace dialogs. The network exhibits original
community structure. In addition, we simulate emotion spreading in this network
that enables to identify two emotion-propagating layers. The analysis resulting
in three structure vectors quantifies the graph's architecture at different
topology levels. Notably, structures emerging through shared links, triangles
and tetrahedral faces, frequently occur and range from tree-like to maximal
5-cliques and their respective complexes. On the other hand, the structures
which spread only negative or only positive emotion messages appear to have
much simpler topology consisting of links and triangles. Furthermore, we
introduce the node's structure vector which represents the number of simplices
at each topology level in which the node resides. The total number of such
simplices determines what we define as the node's topological dimension. The
presented results suggest that the node's topological dimension provides a
suitable measure of the social capital which measures the agent's ability to
act as a broker in compact communities, the so called Simmelian brokerage. We
also generalize the results to a wider class of computer-generated networks.
Investigating components of the node's vector over network layers reveals that
same nodes develop different socio-emotional relations and that the influential
nodes build social capital by combining their connections in different layers.
