A simple graph is a graph that does not have more than one edge between any two vertices and no edge starts and ends at the same vertex. In other words a simple graph is a graph without loops and multiple edges. Two vertices are said to be adjacent if there is an edge (arc) connecting them.

A line graph is a graphical display of information that changes continuously over time. A line graph may also be referred to as a line chart. Within a line graph, there are points connecting the data to show a continuous change. The lines in a line graph can descend and ascend based on the data.

A graph is a common data structure that consists of a finite set of nodes (or vertices) and a set of edges connecting them. For example, a single user in Facebook can be represented as a node (vertex) while their connection with others can be represented as an edge between nodes.

An undirected graph is graph, i.e., a set of objects (called vertices or nodes) that are connected together, where all the edges are bidirectional. An undirected graph is sometimes called an undirected network. In contrast, a graph where the edges point in a direction is called a directed graph.

Graphs are used to define the flow of computation. Graphs are used to represent networks of communication. Graphs are used to represent data organization. Graph transformation systems work on rule-based in-memory manipulation of graphs.

Every complete graph is also a simple graph. However, between any two distinct vertices of a complete graph, there is always exactly one edge; between any two distinct vertices of a simple graph, there is always at most one edge.

A complete graph is a graph in which each pair of graph vertices is connected by an edge. The complete graph with graph vertices is denoted and has (the triangular numbers) undirected edges, where. is a binomial coefficient. In older literature, complete graphs are sometimes called universal graphs.

An original-graph G is a pair (V, E) where V is finite non empty set of vertices and E is a set of original edges. A simple general-graph is a general-graph with no loops, no inverse loop and no multiple edges. Definition 9. A multiple general-graph is a general-graph allows multiple edges.

Regular Graph: A simple graph is said to be regular if all vertices of a graph G are of equal degree. It is also called Weighted Graph. Digraph Graph: A graph G = (V, E) with a mapping f such that every edge maps onto some ordered pair of vertices (Vi, Vj) is called Digraph. It is also called Directed Graph.

If edges in your graph have weights then your graph is said to be a weighted graph, if the edges do not have weights, the graph is said to be unweighted. A weight is a numerical value attached to each individual edge.

For searching in graphs, there are two different methods. The Breadth First Search and the Depth First searching techniques.

A graph with a finite number of nodes and edges. If it has nodes and has no multiple edges or graph loops (i.e., it is simple), it is a subgraph of the complete graph . A graph which is not finite is called infinite. If every node has finite degree, the graph is called locally finite.

In graph theory, a cycle in a graph is a non-empty trail in which the only repeated vertices are the first and last vertices. A directed cycle in a directed graph is a non-empty directed trail in which the only repeated vertices are the first and last vertices. A graph without cycles is called an acyclic graph.

In the mathematical discipline of graph theory, a wheel graph is a graph formed by connecting a single universal vertex to all vertices of a cycle. A wheel graph with n vertices can also be defined as the 1-skeleton of an (n-1)-gonal pyramid.

A weighted graph is a graph in which each branch is given a numerical weight. A weighted graph is therefore a special type of labeled graph in which the labels are numbers (which are usually taken to be positive).