Supplementary Material for Searching for repetitions in biological networks: methods, resources and tools

The graph in Figure S1 is undirected, since the edges have no orientation. If it is necessary to specify the orientation of edges, then the graph is directed and this is graphically represented by inserting arrows on the edges, having (x, y) to denote a strictly ordered pair, such that x corresponds to the tail and y to the head of the arrow. The degree of a vertex is the number of edges that connect to it (e.g., A in Figure S1 has degree equal to 3). A path in a graph is a sequence of vertices such that wi is in V and (wi, wi+1) is in E for 1≤ i≤ n-1 (e.g., ). If w1 =wn, the path is a cicle. A graph without cicles is acyclic. A tree is an acyclic graph that is also connected, that is, each of its nodes is linked to at least another node. The adjacency matrix of a graph G is a binary matrix M where both rows and columns are associated to the nodes of G, such that M[i, j]=1 if the nodes i and j are linked by an edge, M[i, j]=0 otherwise. We finally recall the notions of bipartite graph, that is a graph whose vertices can be divided into two disjoint sets A and B such that every edge connects a vertex in A to one in B (see Figure S2).