Related papers: Centrality measures and thermodynamic formalism fo…

Eigenvector centrality is a common measure of the importance of nodes in a network. Here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to…

Identifying central entities and interactions is a fundamental problem in network science. While well-studied for graphs (pairwise relations), many biological and social systems exhibit higher-order interactions best modeled by hypergraphs.…

Knowledge graphs play a central role for linking different data which leads to multiple layers. Thus, they are widely used in big data integration, especially for connecting data from different domains. Few studies have investigated the…

Various quantum-walk based algorithms have been proposed to analyse and rank the centrality of graph vertices. However, issues arise when working with directed graphs --- the resulting non-Hermitian Hamiltonian leads to non-unitary…

We provide a framework for determining the centralities of agents in a broad family of random networks. Current understanding of network centrality is largely restricted to deterministic settings, but practitioners frequently use random…

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…

Identifying important nodes for disease spreading is a central topic in network epidemiology. We investigate how well the position of a node, characterized by standard network measures, can predict its epidemiological importance in any…

In many studies, it is common to use binary (i.e., unweighted) edges to examine networks of entities that are either adjacent or not adjacent. Researchers have generalized such binary networks to incorporate edge weights, which allow one to…

Researchers have designed many algorithms to measure the distances between graph nodes, such as average hitting times of random walks, cosine distances from DeepWalk, personalized PageRank, etc. Successful although these algorithms are,…

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…

A city can be topologically represented as a connectivity graph, consisting of nodes representing individual spaces and links if the corresponding spaces are intersected. It turns out in the space syntax literature that some defined…

Network representation learning (NRL) technique has been successfully adopted in various data mining and machine learning applications. Random walk based NRL is one popular paradigm, which uses a set of random walks to capture the network…

Experts from several disciplines have been widely using centrality measures for analyzing large as well as complex networks. These measures rank nodes/edges in networks by quantifying a notion of the importance of nodes/edges. Ranking aids…

We study the mean traversal time for a class of random walks on Newman-Watts small-world networks, in which steps around the edge of the network occur with a transition rate F that is different from the rate f for steps across small-world…

In this article we introduce an entropy-based, scale-dependent centrality that is evaluated as the Shannon entropy of the distribution at time t of a continuous-time random walk. It ranks nodes as a function of the time t, which acts as a…

PageRank, the prestige measure for Web pages used by Google, is the stationary probability of a peculiar random walk on directed graphs, which interpolates between a pure random walk and a process where all nodes have the same probability…

We uncover a new relation between Closeness centrality and the Condorcet principle. We define a Condorcet winner in a graph as a node that compared to any other node is closer to more nodes. In other words, if we assume that nodes vote on a…

Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the…

The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world…

We review various features of the statistics of random paths on graphs. The relationship between path statistics and Quantum Mechanics (QM) leads to two canonical ways of defining random walk on a graph, which have different statistics and…