Visualization of Genetic Networks: Edge Crossing Minimization of a Graph Drawing with Vertex Pairs

Inference of genetic networks from expression profile data is still one of the challenging works in the field of the microarray informatics. A good visualization tool would provide us a great insight into the interactions among the genes in the inferred networks. Here, we focus on the time series data of expression profiles, and discuss the method to draw a two-layered graph representing the causality among the genes. We assume that the causality among the genes is given. For a two-layered graph, layers corresponds to time steps t and t+1, respectively. Each vertex in a layer corresponds to a gene. The causality between a pair of genes is expressed as an edge from a vertex in the layer for time t to a vertex in the layer for time t + 1. There is a restriction for drawing two-layered graphs for genetic networks that the same gene should occupy the same positions in the two layers. In drawing a visually understandable graph on a plane, readability, i.e., aesthetic criteria, is indispensable. Minimizing the edge crossings is the most popular aesthetic criterion [1] and we employ it to obtain a drawing to read easily. In general, the problem to minimize the edge crossings of a graph is called the minimum crossing number problem. There have been many studies on the problem, especially for a two-layered graph [2, 4, 5, 6]. However, there is no study for drawing a two-layered graph under the restriction described above. Here we deal with the problem to find a drawing under the restriction with the minimum number of edge crossing.