What is a graph?

A linear graph (simply a graph) G(V,E) consists of a set of objects V={v1,v2……} called vertices, and another set E={e1,e2……..} whose elements are called edges, such that each edge  is identified with an unordered pair(vi,vj) of vertices. The vertices vi, vj associated with each edge ek are called end vertices of ek.

Definition also permits an edge to be associated with a vertex   pair (vi,vi) such an edge having the same vertex as both its end vertices is called self loop. V2 is having self loop.
The definition also permits more than one edge associated with a given pair of vertices, such edges are called parallel edges. Such as e4 and e5 of the following graph.

A graph that has neither self loop nor parallel edges is called a simple graph.

A graph is also called a linear complex, a 1-complex, or a one-dimensional complex. A vertex is also called as a node, a junction, a point, 0-cell, or a 0-simplex. Other term used for an edge is a branch, a line, an element, a 1-cell, and a 1-simplex. But we generally use graph, vertex, and edges.

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