Energy Models for Drawing Signed Graphs

Graph drawing is the pictorial representation of graphs in a multi-dimensional space. Energy models are the prevalent approach to graph drawing. In this paper, we propose energy models for drawing signed unidirectional graphs where edges are labeled either as positive (attractive) or as negative (repulsive). The existent energy models do not discriminate against edge sign. Hence, they do not lend themselves to drawing signed graphs. We suggest a general equation for signed energy models by proposing a dual energy model for graphs containing uniquely negative edges, and combining it linearly with the primary model. We then concentrate on revealing the community structure of social network graphs (sociograms) where edge sign represents the state of relationship between two individuals. In this goal, Signed LinLog model is built based on LinLog model whose clustering properties for unsigned graphs is already known. The properties of Signed LinLog model are outlined analytically, and its synthetic and real layouts are presented