Related papers: Random Walk Fundamental Tensor and Its Application…

We derive an approximate but explicit formula for the Mean First Passage Time of a random walker between a source and a target node of a directed and weighted network. The formula does not require any matrix inversion, and it takes as only…

Tensor networks, a class of variational quantum many-body wave functions have attracted considerable research interest across many disciplines, including classical machine learning. Recently, Aizpurua et al. demonstrated explainable anomaly…

Neural network models are one of the most successful approaches to machine learning, enjoying an enormous amount of development and research over recent years and finding concrete real-world applications in almost any conceivable area of…

Multiplex networks are receiving increasing interests because they allow to model relationships between networked agents on several layers simultaneously. In this supplementary material for the paper "Navigability of interconnected networks…

Biomolecular networks, such as protein-protein interactions, gene-gene associations, and cell-cell interactions, offer valuable insights into the complex organization of biological systems. These networks are key to understanding cellular…

Identification of influential nodes is an important step in understanding and controlling the dynamics of information, traffic and spreading processes in networks. As a result, a number of centrality measures have been proposed and used…

Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the…

Most real complex networks -- such as protein interactions, social contacts, the internet -- are only partially known and available to us. While the process of exploring such networks in many cases resembles a random walk, it becomes a key…

In network embedding, random walks play a fundamental role in preserving network structures. However, random walk based embedding methods have two limitations. First, random walk methods are fragile when the sampling frequency or the number…

By applying network analysis techniques to large input-output system, we identify key sectors in the local/regional economy. We overcome the limitations of traditional measures of centrality by using random-walk based measures, as an…

Recurrent Neural Networks (RNNs) are very successful at solving challenging problems with sequential data. However, this observed efficiency is not yet entirely explained by theory. It is known that a certain class of multiplicative RNNs…

Graphs are useful structures that can model several important real-world problems. Recently, learning graphs have drawn considerable attention, leading to the proposal of new methods for learning these data structures. One of these studies…

Network embedding algorithms are able to learn latent feature representations of nodes, transforming networks into lower dimensional vector representations. Typical key applications, which have effectively been addressed using network…

A sufficient condition for the uniqueness of multinomial sequential unbiased estimators is provided generalizing a classical result for binomial samples. Unbiased estimators are applied to infer the parameters of multidimensional or…

Graph Neural Networks (GNNs) have emerged as a powerful technique for learning on relational data. Owing to the relatively limited number of message passing steps they perform -- and hence a smaller receptive field -- there has been…

Permutation entropy has become a standard tool for time series analysis that exploits the temporal properties of these data sets. Many current applications use an approach based on Shannon entropy, which implicitly assumes an underlying…

Centrality is an important notion in network analysis and is used to measure the degree to which network structure contributes to the importance of a node in a network. While many different centrality measures exist, most of them apply to…

Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…

We introduce weighted Markovian graphs, a random walk model that decouples the transition dynamics of a Markov chain from (random) edge weights representing the cost of traversing each edge. This decoupling allows us to study the…

Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the…