Related papers: Further Results on Random Walk Labelings

It is well known that almost all graphs are canonizable by a simple combinatorial routine known as color refinement, also referred to as the 1-dimensional Weisfeiler-Leman algorithm. With high probability, this method assigns a unique label…

We present an algorithm to grow a graph with scale-free structure of {\it in-} and {\it out-links} and variable wiring diagram in the class of the world-wide Web. We then explore the graph by intentional random walks using local…

For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinatorial characterization of graphs that have flexible labelings.…

Random walks on graphs can be slow. To speed them up, imagine that at each step instead of choosing the neighbor at random, there is a small probability $\varepsilon>0$ that we can choose it. We show that in this case, at least for graphs…

Consider a collaborative dynamic of $k$ independent random walks on a finite connected graph $G$. We are interested in the size of the set of vertices visited by at least one walker and study how the number of walkers relates to the…

Estimating characteristics of large graphs via sampling is a vital part of the study of complex networks. Current sampling methods such as (independent) random vertex and random walks are useful but have drawbacks. Random vertex sampling…

Graph embedding has recently gained momentum in the research community, in particular after the introduction of random walk and neural network based approaches. However, most of the embedding approaches focus on representing the local…

We study tree-indexed random walks as introduced by Benjamini, H\"aggstr\"om, and Mossel, i.e. labelings of a tree for which adjacent vertices have labels differing by 1. It is a conjecture of those authors that the distribution of the…

Focusing on coupling between edges, we generalize the relationship between the normalized graph Laplacian and random walks on graphs by devising an appropriate normalization for the Hodge Laplacian -- the generalization of the graph…

We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…

We study a generalization of strongly regular graphs. We call a graph strongly walk-regular if there is an $\ell >1$ such that the number of walks of length $\ell$ from a vertex to another vertex depends only on whether the two vertices are…

A simple and connected $n$-vertex graph has a prime vertex labeling if the vertices can be injectively labeled with the integers $1, 2, 3,\ldots, n$, such that adjacent vertices have relatively prime labels. We will present previously…

Using random walks for sampling has proven advantageous in assessing the characteristics of large and unknown social networks. Several algorithms based on random walks have been introduced in recent years. In the practical application of…

Motivated by a problem arising from pharmaceutical science [B. Baeumer et al., Discr. Contin. Dyn. Sys. B 12], we study random walks on the contact graph of a bidisperse random sphere packing. For a random walk on the unweighted graph that…

The combinatorial properties of double vertex graphs has been widely studied since the 90's. However only very few results are know about the independence number of such graphs. In this paper we obtain the independence numbers of the double…

Random walks have been intensively studied on regular and complex networks, which are used to represent pairwise interactions. Nonetheless, recent works have demonstrated that many real-world processes are better captured by higher-order…

We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…

For $\lambda>0$, we define a $\lambda$-damped random walk to be a random walk that is started from a random vertex of a graph and stopped at each step with probability $\frac{\lambda}{1+\lambda}$, otherwise continued with probability…

We study a discrete time self interacting random process on graphs, which we call Greedy Random Walk. The walker is located initially at some vertex. As time evolves, each vertex maintains the set of adjacent edges touching it that have not…

The involution walk is the random walk on $S_n$ generated by involutions with a binomially distributed with parameter $1-p$ number of $2$-cycles. This is a parallelization of the transposition walk. The involution walk is shown in this…