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Graph Data Structure

 

Graph: A graph is a non-linear data structure consisting of nodes and edges.The nodes are sometimes also referred to as vertices and the edges are lines and arcs that connect any two nodes in the graph.


A graph consists of a finite set of vertices(or nodes) and a set of edges which connect a pair of nodes.


Graphs are used to solve many real-life problems. Graphs are used to represent networks. The networks may include paths in a city or telephone network or circuit network. Graphs are also used in social networks like linkedIn, Facebook.


A graph can be defined as a group of vertices and edges that are used to connect these vertices. A graph G can be defined as an ordered set of G(V,E) where V(G) represents the set of vertices and E(G) represents the set of edges which are used to connect these vertices.


Directed and Undirected Graph 


A graph can be directed or undirected.


In an undirected graph, edges are not associated with the directions with them. If an edge exists between vertex A and B then the vertices can be traversed from B to A as well as A to B.



In a directed graph, edges form an ordered pair. Edges represent a specific path from some vertex A to another vertex B. Node A is called initial Node while node B is called terminal node.



Loop


An edge that is associated with the similar endpoints can be called a Loop.


Adjacent Nodes


If two nodes U and V are connected via an edge e, then the nodes U and V are called as neighbours or adjacent nodes.


Connected Graph


A connected graph  is the one in which some path exists between every two vertices(U,V) in V. There are no isolated nodes in the connected graph.


Complete Graph


A complete graph is the one in which every node is connected with all other nodes. A complete graph contains n(n-1)/2 edges where n is the number of nodes in the graph.


Weighted Graph


In a weighted graph, each edge is assigned with some data such as length or weight. The weight of an edge e can be given as w(e) which must be a positive(+) value indicating the cost of traversing the edge.



Degree of the Node


A degree of a node is the number of edges that are connected with that node. A node with degree 0 is called an isolated node.

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