## Adjacency list representation, Data Structure & Algorithms

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An Adjacency list representation of Graph G = {V, E} contains an array of adjacency lists mentioned by adj of V list. For each of the vertex u?V, adj[u] contains all vertices adjacent to u in the graph G.

Consider the graph of Figure. Figure: A Graph

Given is the adjacency list representation of graph of above Figure:

adj  = {2, 3, 5}

adj  = {1, 4, 5}

adj  = {2, 3, 5}

adj  = {1, 3, 4}

An adjacency matrix representation of a Graph G=(V, E) is a matrix

The adjacency matrix for the graph of Figure is following:

 1 2 3 4 5 1 0 1 1 0 1 2 1 0 0 1 1 3 1 0 0 1 1 4 0 1 1 0 1 5 1 0 1 1 0

Observe that the matrix is symmetric along the main diagonal. If we described the adjacency matrix as A and the transpose as AT , then for undirected graph G as above, A = AT.

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