Graph basics
Mathematically speaking, a graph G is a data structure consisting of a set of vertices (also called nodes) V, connected to each other by a set of edges E, i.e:
A graph can be equivalently represented as an adjacency matrix A of size (n, n) where n is the number of vertices in the set V. The element A[I, j] of this adjacency matrix represents the edge between vertex i and vertex j. Thus the element A[I, j] = 1 if there is an edge between vertex i and vertex j, and 0 otherwise. In the case of weighted graphs, the edges might have their own weights, and the adjacency matrix will reflect that by setting the edge weight to the element A[i, j]. Edges may be directed or undirected. For example, an edge representing the friendship between a pair of nodes x and y is undirected, since x is friends with y implies that y is friends with x. Conversely, a directed edge can be one in a follower network (social media), where x following y does not imply that y follows x. For...
