Graph terminologies :

Adjacent vertices: Two vertices a & b are said to be adjacent if there is an edge connecting a & b. For instance, in given Figure, vertices 5 & 4 are adjacent.

Path: A path is described as a sequence of distinct vertices, wherein each vertex is adjacent to the next. For instance, the path from 1 to 4 can be described as a sequence of adjacent vertices (1,5), (5,4).

A path, p, of length, k, through a graph is a sequence of associated vertices:

p = 0,v₁,...,v_k>

Cycle: A graph contains cycles if there is path of non-zero length by the graph, p = 0,v₁,...,v_k> such that v₀ = v_k.

Edge weight : It is the cost connected with edge.

Loop: this is an edge of the form (v,v).

Path length : this is the number of edges onto the path.

Simple path : this is the set of all different vertices onto a path (except possibly first and last).