What is a graph?

A graph is a data structure consisting of nodes (vertices) and pointers (edges).  It differs from a linked list and binary tree because each vertex can have more than one or two edges and point to any vertex in the data structure.  The edges can either point in one direction, known as a directed graph, or without specifying a direction (bidirectional), referred to as an undirected graph. 

Graphs can also be weighted, with each edge given a value representing a relationship such as distance between the vertices. 

Although it is common to refer to vertices and edges when discussing graphs, this is largely due to their application in mathematics.  A vertex can also be referred to as a node and an edge as a pointer.