//The degree matrix is the number of neighbors of the count vertices, only fill in the diagonal.
//The adjacency matrix is whether there is a relationship between two vertices, so the data in the matrix is either 0 or 1.
// Laplacian matrix is adjacency matrix - degree matrix.
Table of contents
degree matrix
adjacency matrix
The relationship between degree matrix and adjacency matrix
identity matrix
Degree matrix (degree matrix)
The degree matrix is a diagonal matrix, and the elements on the diagonal are the degrees of each vertex, and the degree of a vertex represents the number of variables associated with the vertex.
In an undirected graph, the degree of the vertex (that is, the number of edges connected to the vertex)
in the directed graph, the degree of the vertex vi is divided into the out-degree and in-degree of the vertex vi, that is, the number of directed edges going out from the vertex vi and the number of directed edges entering vertex vi.
The degree matrix corresponding to the above figure is:
Adjacency matrix (adjaceny matrix)
The adjacency matrix represents the relationship between vertices, and is an n-order square matrix (n is the number of vertices)
Adjacency matrix is divided into directed adjacency matrix and undirected adjacency matrix. An undirected adjacency matrix is a symmetric matrix, while the adjacency matrix of a directed graph is not necessarily symmetric.
The formula for the adjacency matrix is as follows:
If the following figure is given:
The corresponding adjacency matrix is:
The relationship between the degree matrix and the adjacency matrix
, where D is the degree matrix and S is the adjacency matrix.
The identity matrix (identity matrix)
The identity matrix is a square matrix, and the elements on the diagonal (called the main diagonal) from the upper left corner to the lower right corner are all 1. All other values are 0.
Features:
Any matrix multiplied by the identity matrix is equal to itself
express:
Notation:
————————————————
Copyright Statement: This article is the original article of CSDN blogger "Xunluo Tingzi Xiaotingzi", following the CC 4.0 BY-SA copyright agreement, please attach the original text for reprinting Source link and this statement.
Original link: https://blog.csdn.net/weixin_41862755/article/details/123412438