First return times on sparse random graphs
O Evnin, W Horinouchi - arXiv preprint arXiv:2408.10530, 2024 - arxiv.org
We consider random walks in the form of nearest-neighbor hopping on Erdos-Renyi random
graphs of finite fixed mean degree c as the number of vertices N tends to infinity. In this …
graphs of finite fixed mean degree c as the number of vertices N tends to infinity. In this …
Random matrices with row constraints and eigenvalue distributions of graph Laplacians
P Akara-pipattana, O Evnin - Journal of Physics A: Mathematical …, 2023 - iopscience.iop.org
Symmetric matrices with zero row sums occur in many theoretical settings and in real-life
applications. When the offdiagonal elements of such matrices are iid random variables and …
applications. When the offdiagonal elements of such matrices are iid random variables and …
Hammerstein equations for sparse random matrices
P Akara-pipattana, O Evnin - arXiv preprint arXiv:2410.00355, 2024 - arxiv.org
Finding eigenvalue distributions for a number of sparse random matrix ensembles can be
reduced to solving nonlinear integral equations of the Hammerstein type. While a systematic …
reduced to solving nonlinear integral equations of the Hammerstein type. While a systematic …
Distribution of shortest path lengths on trees of a given size in subcritical Erdős-Rényi networks
In the subcritical regime Erdős-Rényi (ER) networks consist of finite tree components, which
are nonextensive in the network size. The distribution of shortest path lengths (DSPL) of …
are nonextensive in the network size. The distribution of shortest path lengths (DSPL) of …
An empirical comparison of connectivity-based distances on a graph and their computational scalability
P Miasnikof, AY Shestopaloff, L Pitsoulis… - Journal of Complex …, 2022 - academic.oup.com
In this study, we compare distance measures with respect to their ability to capture vertex
community structure and the scalability of their computation. Our goal is to find a distance …
community structure and the scalability of their computation. Our goal is to find a distance …
Statistical field theory of random graphs with prescribed degrees
P Akara-pipattana, O Evnin - arXiv preprint arXiv:2410.11191, 2024 - arxiv.org
Statistical field theory methods have been very successful with a number of random graph
and random matrix problems, but it is challenging to apply these methods to graphs with …
and random matrix problems, but it is challenging to apply these methods to graphs with …
A Gaussian integral that counts regular graphs
O Evnin, W Horinouchi - arXiv preprint arXiv:2403.04242, 2024 - arxiv.org
In a recent article J. Phys. Compl. 4 (2023) 035005, Kawamoto evoked statistical physics
methods for the problem of counting graphs with a prescribed degree sequence. This …
methods for the problem of counting graphs with a prescribed degree sequence. This …
Graph clustering with Boltzmann machines
P Miasnikof, M Bagherbeik, A Sheikholeslami - Discrete Applied …, 2024 - Elsevier
Graph clustering is the process of labeling nodes so that nodes sharing common labels form
densely connected subgraphs with sparser connections to the remaining vertices. Because …
densely connected subgraphs with sparser connections to the remaining vertices. Because …