Date of Publication

8-15-2023

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics with Specialization in Computer Applications

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics Department

Thesis Advisor

John Vincent S. Morales

Defense Panel Chair

Rafael Reno S. Cantuba

Defense Panel Member

Rigor B. Ponsones

Abstract/Summary

A graph is viewed as a combinatorial representation of existing relations among objects where we call the objects vertices and the relations edges. The importance of a vertex in a graph or vertex centrality can be measured according to the number of neighbours of a vertex (degree), how close one vertex is to the other (closeness), the frequency of a certain vertex being passed by other vertices (betweenness), or how one vertex has influenced by the vertex’s connections (eigenvector). In 2012, Qi et. al. proposed a new centrality measurement known as the Laplacian centrality, which measures the centrality based on how the vertex has affected the whole network or graph after its deletion. In this paper, we give an exposition focusing on the proposed measurement that will benefit future researchers by the provision of additional details on the established results of the said new centrality measure. The main results of Qi et. al. are illustrated using sample social networks found on a network repository. Using Python, we compute the Laplacian energy and Laplacian centrality in our sample social networks.

Abstract Format

html

Language

English

Format

Electronic

Keywords

Laplacian matrices

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Embargo Period

8-15-2023

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