arXiv subjects

Yingyue Ke

Publications and source records attributed to Yingyue Ke.

3 recordsLinked to original sources

arXiv2025

The Laplacian matrix of weighted threshold graphs

Threshold graphs are generated from one node by repeatedly adding a node that links to all existing nodes or adding a node without links. In the weighted threshold graph, we add a new node in step $i$, which is linked to all existing nodes by a link of weight $w_i$. In this work, we consider the set ${\cal A}_N$ that contains all Laplacian matrices of weighted threshold graphs of order $N$. We show that ${\cal A}_N$ forms a commutative algebra. Using this, we find a common basis of eigenvectors for the matrices in ${\cal A}_N$. It follows that the eigenvalues of each matrix in ${\cal A}_N$ can be represented as a linear transformation of the link weights. In addition, we prove that, if there are just three or fewer different weights, two weighted threshold graphs with the same Laplacian spectrum must be isomorphic.

math.CO↗

arXiv2025

Some Laplacian eigenvalues can be computed by matrix perturbation

Based on matrix perturbation theory, closed-form analytic expansions are studied for a Laplacian eigenvalue of an undirected, possibly weighted graph, which is close to a unique degree in that graph. An approximation is presented to provide an analytic estimate of a Laplacian eigenvalue and complements bounds on Laplacian eigenvalues in spectral graph theory. Then, we apply the Euler summation and numerically analyze how the structure of graphs influences the convergence of the corresponding Euler series. Moreover, we obtain the explicit form of the perturbation Taylor series and its Euler series of almost regular graphs in which only one node has a unique degree and all remaining nodes have the same degree. We find that the Euler series possesses a superior convergence range than the perturbation Taylor series for almost regular graphs.

math.SP↗

arXiv2022

The Impact of Vaccination Behavior on Disease Spreading Based on Complex Networks

Vaccination is an effective way to prevent and control the occurrence and epidemic of infectious diseases. However, many factors influence whether the residents decide to get vaccinated or not, such as the efficacy and side effects while individuals hope to obtain immunity through vaccination. In this paper, the public attitude toward vaccination is investigated, especially how it is influenced by the public estimation of vaccines efficacy and reliance on their neighbors' vaccination behavior. We find that improving people's trust in the vaccination greatly benefits increasing the vaccination rate and accelerating the vaccination process. Counterintuitively, if the individual's attitude towards vaccination is more reliant on his neighbors' vaccination behavior, more individuals will get vaccinated, and the vaccination process will speed up. Besides, individuals are more willing to get vaccinated if they have more neighbors.

physics.soc-ph↗