The $\lambda$-core vertices of a graph correspond to the non-zero entries some eigenvector $\lambda$ for universal adjacency matrix $\mathbf{U}$ graph. We define partition vertex set $V$ based on and its neighbourhoods at distance $r$, give number results relating structure this partition. For such partitions, we also an entropic measure information content graph, related every distinct eigenva...

Despite the central role of self-assembled groups in animal and human societies, statistical tools to explain their composition are limited. The authors introduce a framework for cross-sectional observations with exclusive membership illuminate social organizational mechanisms that bring people together. Drawing from stochastic models networks partitions, proposed introduces an exponential fami...