A little graph theory
Graph theory is a branch of mathematics that deals with mathematical objects known as graphs. Here, a graph does not have the everyday meaning that we are more used to talking about, in the sense of a diagram or plot with an x and y axis. In graph theory, a graph consists of two sets. The first is a set of vertices, which are also referred to as nodes. We typically use integers to label and enumerate the vertices. The second set consists of edges between these vertices.
Thus, a graph is nothing more than a description of some points and the connections between them. The connections can have a direction so that an edge goes from the source or tail vertex to the target or head vertex. In this case, we have a directed graph. Alternatively, the edges can have no direction, so that the graph is undirected.
A common way to describe a graph is via the adjacency matrix. If we have V vertices in the graph, an adjacency matrix is a V×V matrix whose entries are 0 if the vertex represented...
