A graph is a non-linear data structure that can be looked at as a collection of vertices (or nodes) potentially connected by line segments named edges.

Graph common terminology :
Directed vs Undirected
An Undirected Graph is a graph where each edge is undirected or bi-directional. This means that the undirected graph does not move in any direction.
A Directed Graph also called a Digraph is a graph where every edge is directed. Unlike an undirected graph, a Digraph has direction. Each node is directed at another node with a specific requirement of what node should be referenced next.
Complete vs Connected vs Disconnected

There are many different types of graphs. This depends on how connected the graphs are to other node/vertices.
Graph Representation We represent graphs through: