|
|||||
 |
|
|
|
|
|
|
|
On the epidemic
threshold of a network
Vadym Cherniavskyi, Gabriel Dennis and S. R. Kingan |
|
Vol. 18 (2025), No. 2, 283–296
|
Abstract |
|
We present an approach to vertex centrality that measures the impact of a vertex in a graph by removing it and considering the subgraph . Various parameters can be calculated for and compared with the corresponding parameters for to obtain a ranking of the vertices. The parameter examined in this paper is the largest eigenvalue of the adjacency matrix of the graph. Previous work demonstrates the tight relationship between this invariant, the birth and death rates of a contagion spreading on the graph, and the trajectory of the contagion over time. We begin by conducting a simulation to examine the validity of this claim. Subsequently, we introduce a new centrality measure that we call the spread centrality. The spread centrality of a vertex in a graph is the difference between the largest eigenvalues of and . In some, but not all, cases the vertex rankings given by spread centrality and eigenvector centrality are correlated; we provide examples of both. |
Keywords
graph theory, centrality measures, epidemic modeling,
epidemic threshold, eigenvalues
|
Mathematical Subject Classification
Primary: 05C50
|
Milestones
Received: 27 May 2023
Revised: 23 January 2024
Accepted: 25 January 2024
Published: 26 February 2025
Communicated by Ronald Gould
|
Authors |
| Vadym Cherniavskyi | |
| Department of Mathematics Brooklyn College, CUNY Brooklyn, NY United States |
|
| Gabriel Dennis | |
| Department of Mathematics Brooklyn College, CUNY Brooklyn, NY United States |
|
| S. R. Kingan | |
| Department of Mathematics Brooklyn College, CUNY Brooklyn, NY United States |
Department of Mathematics Graduate Center, CUNY New York, NY United States |
| © 2025 MSP (Mathematical Sciences Publishers). |
