## » Vertex:

A **vertex **(also called a node or a point) is a basic unit in a graph. It represents an object in the system that is being modeled.

## » Edge:

An **edge **(also called a link or a line) is a connection between two vertices in a graph. It represents a relationship between the two objects that the vertices represent.

## » Adjacent vertices:

Two vertices are adjacent if they are connected by an edge.

## » Degree of a vertex:

The degree of a vertex is the number of edges that are connected to it.

• **Even and Odd Vertex** − If the degree of a vertex is even, the vertex is called an even vertex and if the degree of a vertex is odd, the vertex is called an odd vertex.

• **Degree of a Graph **− The degree of a graph is the largest vertex degree of that graph. For the above graph the degree of the graph is 3.

• **The Handshaking Lemma** − In a graph, the sum of all the degrees of all the vertices is equal to twice the number of edges.

## » Path:

A **path **is a sequence of vertices that are connected by edges, where no vertex is repeated.

## » Cycle:

A **cycle **is a path that starts and ends at the same vertex.

## » Connected graph:

A **connected graph **is a graph in which every pair of vertices is connected by a path.

## » Weighted graph:

A **weighted graph **is a graph in which each edge has a weight associated with it. The weight can represent the distance between the two vertices, the cost of traveling between