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Judul : Struktur Diskrit : Merepresentasikan Graf dalam List dan Matriks
link : Struktur Diskrit : Merepresentasikan Graf dalam List dan Matriks

Struktur Diskrit : Merepresentasikan Graf dalam List dan Matriks

Struktur Diskrit : Merepresentasikan Graf dalam List dan Matriks

Representing Graphs

Adjacency List 

Specify the vertices that are adjacent to each vertex of the graph. 

Adjacency Matrix

Represents graph by a matrix based on the adjacency of vertices

Incidence Matrix 

Represents graph by a matrix based on the incidence of vertices and edges. 

Adjacency List (Undirected Graph)

Specify the vertices that are adjacent to each vertex of the graph 

Adjacency List ( Directed Graph )

List all the vertices that are the terminal vertices of edges starting at each vertex of the graph 

Adjacency Matrices

Suppose that G = (V , E) is a simple graph where |V| = n. Suppose that the vertices of G are listed arbitrarily as v1, v2,..., vn. 

The adjacency matrix A (or AG) of G, with respect to this listing of the vertices, is the n x n zero–one matrix with 1 as its (i, j )th entry when vi and vj are adjacent, and 0 as its (i, j )th entry when they are not adjacent. 

•If its adjacency matrix is A = [aij], then

Adjacency Matrix ( Not Simple Undirected Graph )

Aij is represent by the number of edges that associated to [ai, aj]. A loop at a vertex represent by 1. When multiple edges are present, adjacency matrix is no longer a zero-one matrix. The matrix is symmetric.

Adjacency Matrix ( Directed Graph )

Aij is represent by the number of edges from ai to aj. A loop at a vertex represent by 1. When multiple edges are present, adjacency matrix is no longer a zero-one matrix. The matrix is not symmetric. 

Draw Graph from Adjacency Matrix

An adjacency matrix of a graph is based on the ordering chosen for the vertices.

There are n! different adjacency matrices for a graph with n vertices, because there are n! different ordering of n vertices

EXAMPLE: Draw a graph with the given adjacency matrix

Incidence Matrices

The incidence matrix for undirected graph G with n vertices v1, v2, …, vn, and m edges e1, e2, …, em, is the m × n matrix M = [mij], where

Sumber

Slide Strukdis : Representing Graphs

http://informatika.unpar.ac.id/

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