Graph Representation
Graph is a mathematical structure and finds its applications in many areas of interest in which problems need to be solved using computer. Thus this mathematical structure must be represented in some kind of data structure. Three such representations are commonly used. These are Adjacent Matrix, Adjacency list representation and Multi-list representation.
Adjacency Matrix
The adjacency matrix A for a graph G= (V, E) with n vertices is an n*n matrix of bits such that
Aij=1, if there is an edge from v I to v j
And a ij= o, if there is no such edge.
We can also write it as
A (I, j) 1 if and only if edge (v ij v j) is in E.g.
O otherwise
Adjacency List Representation
In this representation we store a graph as a linked structure. We store all the vertices in a list the vertices in a list and then for each vertex we have a linked list of its adjacent vertices.
djacency list representation of the undirected graph of Fig 9.9 is given in Fig 9.13. the adjacency list representation needs a list of all of its nodes i.e.
And for each node a linked list of its adjacent nodes.
An undirected graph of order N with E edges requires N entries in the directory and Z x E linked list entries that each loop reduces the number of linked list entries by one.
Adjacency list representation of the directed graph
A directed graph of order N with E edges requires N entries in the directory and E. linked list entries.
Multi-list Representation
In the Multi- list representation of graph structures; these are two parts, a directory of Node information and a set of linked list of edge information. There is one entry in the node directory for each node of the graph. The directory entry for node I points to a linked adjacency list for node i. each record of the linked list area appears on two adjacency lists: one for the node at each end of the represented edge.
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