Familial groups in social networks

Many structural definitions for social community have been proposed in attempt to characterize and further understand the structure of social relationships. Algorithms using quantitative concepts such as centrality measures, spectral methods and other clustering measures have been used to compute social communities. While these methods have had much success in extracting meaningful subgroups in social and biological (and other) networks, they do not necessarily reveal the defining structure of social attraction.We propose a new definition here for social community with a very clear and simple graph-theoretic structure which can also be realized as a new clique-relaxation. This structure evolved from Freeman's definition of social community, and this definition is further supported by long-standing sociometric principles such as Granovetter's weak-tie hypothesis or Faust's and others’ studies on how global structure can be inferred from a complete understanding of local structures (although our definition goes beyond dyadic and triadic configurations). We provide computational results that show our simply-stated structural definition reveals communities that correspond almost identically to, and sometimes are better than, the widely used centrality-based methods.We name these new communities familial groups, inspired by the network structures resulting from inheritance or blood-line relations. These structures form naturally in hierarchical arrangements such as in corporate settings. Using results from graph theory, our structural definition for familial groups also immediately implies a ranking of the individuals within the group, easily identifying leaders and subcommunities.

• We give a new simple definition for community using graph-theoretic concepts.
• Properties of familial groups (FGs) are consistent with sociological principles.
• FGs are structurally characterized by family-tree relationships.
• We model the related algorithmic problems and find their complexity.
• Computational results show that FGs yield meaningful communities.