Graph Theoretical Approaches to Delineate Dynamics of Biological Processes

Graphs are used in Computational Biology to model the relati onships between biological entities. For example, experimentally determine d protein interactions are commonly represented by a graph, the so-called protein interaction network , where proteins are nodes and every pair of interacting proteins is connected by an edge. Even though such a representation may not capture all the com plexity of protein interactions in underlying biological processes, the study of th e topological properties of these networks has become an important tool in searching for general principles that govern the organization of molecular networks. For example , it was observed that in protein interaction networks some types of small-size subn etworks are much more abundant than would be expected by chance [53]. The discover y f these overrepresented subnetworks or network motifshas led to investigation of their information processing properties [64] and network evolution mechanis ms that could account for their emergence [52]. Usage of graph theoretical tools is no t limited to the study of protein interaction networks, graphs are also used to mod el metabolic networks (processes), gene co-expression, gene co-regulation, phy logenies, etc. In general, graphs are not required to have any type of regula rity. This makes them very flexible combinatorial objects, which are able to repre sent complex and diverse relationships. In practice, however, graphs that model rea l world phenomena often belong to families of graphs with a special structure, which can be exploited to gain