#### Session

Computer Science and Communication Engineering

#### Description

In this paper we will focus mainly on some basic concepts and definitions regarding incidence matrices and some examples of their application in graph theory. To give their clearest definition of the incidence matrix, we will first give the meaning of the incidence structure, then through it to define the incidence matrix. The structure of incidence is called the ordered triplet S=(P,B,I), where P∩B=ϕ, I⊆P×B and P,B while, are two non-empty sets and I a relation in between them, such that I⊂P×B. We call the elements of P community dots and we will mark them in lower case letters of, and we will call B the elements of the community blocks or lines and we will mark them in uppercase letters. Like any double bond, between two finite sets the incidence I bond of a finite structure S=(P,B,I) has the bond matrix, which we call the incidence matrix. The incidence matrix A represents a reflection of P×B→0,1, that is (p,X)⟶1, if p I X and (p,X)⟶0, if and is denoted A=aijvxb. If G is a graph with n vertices, m edges and without self-loops. The incidence matrix A of G is an n×m matrix A=(aij) whose n rows correspond to the n vertices and the m columns correspond to m edges such that

A=aij={1, if jth edge mj is incident on the ith vertex 0, otherwise

Incidence matrices have a great application in many fields of science such as:

telecommunications, coding theory, graph theory, etc.

#### Keywords:

Matrices, incidence, graph, rank, submatrices, cycle, Cut-SetMatrixCNN, Traffic Sign Recognition, Neural Networks, Artificial Intelligence, Data Mining, Image Classification.

Zhilbert Tafa

Xhafer Krasniqi

Edmond Hajrizi

#### ISBN

978-9951-550-47-5

1

10

#### Location

UBT Kampus, Lipjan

#### Start Date

30-10-2021 1:30 PM

#### End Date

30-10-2021 4:15 PM

#### DOI

10.33107/ubt-ic.2021.382

#### Share

COinS

Oct 30th, 1:30 PM Oct 30th, 4:15 PM

Incidence matrix and some of its applications in graph theory

UBT Kampus, Lipjan

In this paper we will focus mainly on some basic concepts and definitions regarding incidence matrices and some examples of their application in graph theory. To give their clearest definition of the incidence matrix, we will first give the meaning of the incidence structure, then through it to define the incidence matrix. The structure of incidence is called the ordered triplet S=(P,B,I), where P∩B=ϕ, I⊆P×B and P,B while, are two non-empty sets and I a relation in between them, such that I⊂P×B. We call the elements of P community dots and we will mark them in lower case letters of, and we will call B the elements of the community blocks or lines and we will mark them in uppercase letters. Like any double bond, between two finite sets the incidence I bond of a finite structure S=(P,B,I) has the bond matrix, which we call the incidence matrix. The incidence matrix A represents a reflection of P×B→0,1, that is (p,X)⟶1, if p I X and (p,X)⟶0, if and is denoted A=aijvxb. If G is a graph with n vertices, m edges and without self-loops. The incidence matrix A of G is an n×m matrix A=(aij) whose n rows correspond to the n vertices and the m columns correspond to m edges such that

A=aij={1, if jth edge mj is incident on the ith vertex 0, otherwise

Incidence matrices have a great application in many fields of science such as:

telecommunications, coding theory, graph theory, etc.