# Graph Theory

**Topics:**Graph theory, Graph, Glossary of graph theory

**Pages:**4 (819 words)

**Published:**December 11, 2010

Graphs

Graph:- A graph consists of a nonempty set of points or vertices, and a set of edges that link together the vertices. A simple real world example of a graph would be your house and the corner store. Where the house and the store are the vertices and the road between them is the edge connecting the two vertices.

Or a graph is a network consisting of vertices (or nodes) and edges (V,E) Simple Graph

A graph can take on many forms: directed or undirected.

Directed Graph:- A directed graph is one in which the direction of any given edge is defined. Or A graph with directed edges = directed graph (digraph)

Directed edges = arcs

Directed Graph

Undirected Graph:- An undirected graph is one in which the direction of any given edge is not defined. Conversely, in an undirected graph you can move in both directions between vertices. Or a graph with undirected edges is called undirected graph. Undirected graph Mixed Graph:- A graph is one in which contains both directed and undirected edges.

Mixed Graph

Null Graph: - A null graph is one that contains only isolated vertices (example no edges). Null Graph

Connected graph:- All vertices are directly or indirectly connected with each other (otherwise we have a graph, consisting of at least two sub graphs).

Connected Graph

Complete graph:- Each vertex is directly connected with every other vertex. Or a simple graph in which every pair of vertices is adjacent.

Complete Graph

Weighted Graph:- The edges can...

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