Graph Data Structures Java Program

Graphs, vertices and edges

A graph is a collection of nodes called vertices, and the connections between them, called edges.

Undirected and directed graphs

When the edges in a graph have a direction, the graph is called a directed graph or digraph, and the edges are called directed edges or arcs. Here, I shall be exclusively concerned with directed graphs, and so when I refer to an edge, I mean a directed edge. This is not a limitation, since an undirected graph can easily be implemented as a directed graph by adding edges between connected vertices in both directions.
A representation can often be simplified if it is only being used for undirected graphs, and I'll mention in passing how this can be achieved.

Neighbours and adjacency

A vertex that is the end-point of an edge is called a neighbour of the vertex that is its starting-point. The first vertex is said to be adjacent to the second.

An example

The following diagram shows a graph with 5 vertices and 7 edges. The edges between A and D and B and C are pairs that make a bidirectional connection, represented here by a double-headed arrow.


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