Intersection-Link Representations of Graphs

We consider drawings of graphs that contain dense subgraphs. We introduce intersection-link representations for such graphs, in which each vertex u is represented by a geometric object R(u) and in which each edge (u, v) is represented by the intersection between R(u) and R(v) if it belongs to a dense subgraph or by a curve connecting the boundaries of R(u) and R(v) otherwise. We study a notion of planarity, called Clique Planarity, for intersection-link representations of graphs in which the dense subgraphs are cliques