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.
Session Chair
Zhilbert Tafa
Session Co-Chair
Xhafer Krasniqi
Proceedings Editor
Edmond Hajrizi
ISBN
978-9951-550-47-5
First Page
1
Last Page
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
Recommended Citation
Leka, Hizer and Kabashi, Faton, "Incidence matrix and some of its applications in graph theory" (2021). UBT International Conference. 399.
https://knowledgecenter.ubt-uni.net/conference/2021UBTIC/all-events/399
Included in
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.