» 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
