Graph definitions
An undirected graph G = (V, E) consists of a set V of nodes and a set E of edges, E ⊆ V × V. An edge e = (i, j) connects two nodes i and j, e ∈ E. The neighbors N(i) of node i are defined to be the set of directly connected nodes of node i. The degree d(i) of a node i is the number of the edges connected to node i. A path is defined as a sequence of nodes (i1,..., ik) such that from each of its nodes there is an edge to the successor node. The length of a path is the number of nodes in its node sequence. A shortest path between two nodes, i and j, is a minimal length path between them. The distance between two nodes, i and j, is the length of its shortest path.