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 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 ofR(u) andR(v), otherwise. We study a notion of planarity, called Clique Planarity, for intersection-link representations of graphs in which the dense subgraphs are cliques. Submitted: November 2016 Reviewed: April 2017 Revised: May 2017 Accepted: June 2017 Final: June 2017 Published: July 2017 Article type: regular paper Communicated by: W. S. Evans This article reports on work supported by the U.S. Defense Advanced Research Projects Agency (DARPA) under agreement no. AFRL FA8750-15-2-0092. The views expressed are those of the authors and do not reflect the official policy or position of the Department of Defense or the U.S. Government. This research was also partially supported by MIUR project “MODE”, by H2020-MSCA-RISE project N. 734922 “CONNECT”, and by DFG