Related papers: Maximal-entropy random walks in complex networks w…
The aim of this paper is to check feasibility of using the maximal-entropy random walk in algorithms finding communities in complex networks. A number of such algorithms exploit an ordinary or a biased random walk for this purpose. Their…
Random walks are fundamental tools for analyzing complex networked systems, including social networks, biological systems, and communication infrastructures. While classical random walks focus on pairwise interactions, many real-world…
The concept of entropy rate for a dynamical process on a graph is introduced. We study diffusion processes where the node degrees are used as a local information by the random walkers. We describe analitically and numerically how the degree…
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…
Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the…
We define a new class of random walk processes which maximize entropy. This maximal entropy random walk is equivalent to generic random walk if it takes place on a regular lattice, but it is not if the underlying lattice is irregular. In…
Stochastic processes under resetting at random times have attracted a lot of attention in recent years and served as illustrations of nontrivial and interesting static and dynamic features of stochastic dynamics. In this paper, we aim to…
This article introduces a model for interacting vertex-reinforced random walks, each taking values on a complete sub-graph of a locally finite undirected graph. The transition probability for a walk to a given vertex depends on the…
Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…
Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…
In this paper analogies between different (dis)similarity matrices are derived. These matrices, which are connected to path enumeration and random walks, are used in community detection methods or in computation of centrality measures for…
We study the problem of finding the maximum of a function defined on the nodes of a connected graph. The goal is to identify a node where the function obtains its maximum. We focus on local iterative algorithms, which traverse the nodes of…
Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…
A simple strategy to explore a network is to use a random-walk where the walker jumps from one node to an adjacent node at random. It is known that biasing the random jump, the walker can explore every walk of the same length with equal…
The Maximal Entropy Random Walk (MERW) is a natural process on a finite graph, introduced a few years ago with motivations from theoretical physics. The construction of this process relies on Perron-Frobenius theory for adjacency matrices.…
Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the…
Efficient techniques to navigate networks with local information are fundamental to sample large-scale online social systems and to retrieve resources in peer-to-peer systems. Biased random walks, i.e. walks whose motion is biased on…
We define the probability structure of a continuous-time time-homogeneous Markov jump process, on a finite graph, that represents the continuous-time counterpart of the so-called Ruelle-Bowen discrete-time random walk. It constitutes the…
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…
The random walk with choice is a well known variation to the random walk that first selects a subset of $d$ neighbours nodes and then decides to move to the node which maximizes the value of a certain metric; this metric captures the number…