The forest matrix of a graph, particularly its diagonal elements, has far-reaching implications
in network science and machine learning. The state-of-the-art algorithms for the diagonal of …

Effective resistance (ER) is a fundamental metric for measuring node similarities in a graph,
and it finds applications in various domains including graph clustering, recommendation …

For an undirected graph, its Kemeny's constant is defined as the mean hitting time of random
walks from one vertex to another chosen randomly according to the stationary distribution …

In this paper, we study a problem of index maintenance on evolving graphs for effective
resistance computation. Unlike an existing matrices-based index, we show that the index …

We study resistance eccentricity, a fundamental metric in network science for measuring the
structural significance of a node. For a node in a graph, the resistance eccentricity is its …

The pseudo-inverse of a graph Laplacian matrix, denoted as $ L^\dagger $, finds extensive
application in various graph analysis tasks. Notable examples include the calculation of …

The resistance diameter of a graph is the maximum resistance distance among all pairs of
nodes in the graph, which has found various applications in many scenarios. However …

The purpose of this thesis is to provide new methods for estimating rare event probabilities
for Piecewise Deterministic Markov Processes (PDMPs). This very general class of …