Related papers: Gaussian Networks Generated by Random Walks
Gaussian fields $(g_x)$ on $\mathbb{Z}_q^d$ are constructed from a class of reversible long range random walks $(X_t)_{t\in \mathbb{N}}$ on $\mathbb{Z}_q^d$ in arXiv:2510.22554. The construction is from taking the covariance function of…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
In a landscape composed of N randomly distributed sites in Euclidean space, a walker (``tourist'') goes to the nearest one that has not been visited in the last \tau steps. This procedure leads to trajectories composed of a transient part…
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…
Performing random walks in networks is a fundamental primitive that has found numerous applications in communication networks such as token management, load balancing, network topology discovery and construction, search, and peer-to-peer…
We present the analytical and numerical results of a random walk on the family of small-world graphs. The average access time shows a crossover from the regular to random behavior with increasing distance from the starting point of the…
In this paper we introduce a new model of random spanning trees that we call choice spanning trees, constructed from so-called choice random walks. These are random walks for which each step is chosen from a subset of random options,…
Mechanistic models can provide an intuitive and interpretable explanation of network growth by specifying a set of generative rules. These rules can be defined by domain knowledge about real-world mechanisms governing network growth or may…
Message-passing graph neural networks (GNNs) excel at capturing local relationships but struggle with long-range dependencies in graphs. In contrast, graph transformers (GTs) enable global information exchange but often oversimplify the…
We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of…
Node-level random walk has been widely used to improve Graph Neural Networks. However, there is limited attention to random walk on edge and, more generally, on $k$-simplices. This paper systematically analyzes how random walk on different…
In many complex systems, for the activity f(i) of the constituents or nodes i, a power-law relationship was discovered between the standard deviation sigma(i) and the average strength of the activity: sigma(i) ~ <f(i)>^alpha; universal…
We propose local-biased random walks on general networks where a Markovian walker can choose between different types of biases in each node to define transitions to its neighbors depending on their degrees. For this ergodic dynamics, we…
We present our recent work on stochastic particle systems on complex networks. As a noninteracting system we first consider the diffusive motion of a random walker on heterogeneous complex networks. We find that the random walker is…
Representing networks in a low dimensional latent space is a crucial task with many interesting applications in graph learning problems, such as link prediction and node classification. A widely applied network representation learning…
We derive an efficient method to perform clustering of nodes in Gaussian graphical models directly from sample data. Nodes are clustered based on the similarity of their network neighborhoods, with edge weights defined by partial…
We apply random matrix theory to complex networks. We show that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks, namely scale-free, small-world and random networks follow…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Many widely used network centralities are based on counting walks that meet specific criteria. This paper introduces a systematic framework for walk enumeration using generating functions. We introduce a first-passage decomposition that…