  We consider core-periphery structured graphs, which are graphs with a group
of densely and sparsely connected nodes, respectively, referred to as core and
periphery nodes. The so-called core score of a node is related to the
likelihood of it being a core node. In this paper, we focus on learning the
core scores of a graph from its node attributes and connectivity structure. To
this end, we propose two classes of probabilistic graphical models: affine and
nonlinear. First, we describe affine generative models to model the dependence
of node attributes on its core scores, which determine the graph structure.
Next, we discuss nonlinear generative models in which the partial correlations
of node attributes influence the graph structure through latent core scores. We
develop algorithms for inferring the model parameters and core scores of a
graph when both the graph structure and node attributes are available. When
only the node attributes of graphs are available, we jointly learn a
core-periphery structured graph and its core scores. We provide results from
numerical experiments on several synthetic and real-world datasets to
demonstrate the efficacy of the developed models and algorithms.
