Related papers: Network Capacity Bound for Personalized PageRank i…
In a former paper we simplified the proof of a theorem on personalized random walk that is fundamental to graph nodes clustering and generalized it to bipartite graphs for a specific case where the proobability of random jump was…
In this paper new results on personalized PageRank are shown. We consider directed graphs that may contain dangling nodes. The main result presented gives an analytical characterization of all the possible values of the personalized…
Many complex systems can be described as multiplex networks in which the same nodes can interact with one another in different layers, thus forming a set of interacting and co-evolving networks. Examples of such multiplex systems are social…
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…
Personalalized PageRank uses random walks to determine the importance or authority of nodes in a graph from the point of view of a given source node. Much past work has considered how to compute personalized PageRank from a given source…
Hypergraphs offer an explicit formalism to describe multibody interactions in complex systems. To connect dynamics and function in systems with these higher-order interactions, network scientists have generalised random-walk models to…
Node influence metrics have been applied to many applications, including ranking web pages on internet, or locations on spatial networks. PageRank is a popular and effective algorithm for estimating node influence. However, conventional…
Connections among entities are everywhere. From social media interactions to web page hyperlinks, networks are frequently used to represent such complex systems. Node ranking is a fundamental task that provides the strategy to identify…
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…
PageRank is a well-known algorithm for measuring centrality in networks. It was originally proposed by Google for ranking pages in the World-Wide Web. One of the intriguing empirical properties of PageRank is the so-called `power-law…
A key feature of neural network architectures is their ability to support the simultaneous interaction among large numbers of units in the learning and processing of representations. However, how the richness of such interactions trades off…
Higher-order networks are efficient representations of sequential data. Unlike the classic first-order network approach, they capture indirect dependencies between items composing the input sequences by the use of \textit{memory-nodes}. We…
This paper develops a generalization of the PageRank model of page centralities in the global webgraph of hyperlinks. The webgraph of adjacencies is generalized to a valued directed graph, and the scalar dampening coefficient for walks…
We study the spread of influence in a social network based on the Linear Threshold model. We derive an analytical expression for evaluating the expected size of the eventual influenced set for a given initial set, using the probability of…
Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of efforts have been devoted to calculating graphlet statistics where random walk based approaches are…
Recently it has been recognized that many complex social, technological and biological networks have a multilayer nature and can be described by multiplex networks. Multiplex networks are formed by a set of nodes connected by links having…
The PageRank algorithm enables to rank the nodes of a network through a specific eigenvector of the Google matrix, using a damping parameter $\alpha \in ]0,1[$. Using extensive numerical simulations of large web networks, with a special…
In this work we introduce and study a nonlocal version of the PageRank. In our approach, the random walker explores the graph using longer excursions than just moving between neighboring nodes. As a result, the corresponding ranking of the…
Google's PageRank method was developed to evaluate the importance of web-pages via their link structure. The mathematics of PageRank, however, are entirely general and apply to any graph or network in any domain. Thus, PageRank is now…
A hypergraph is a useful combinatorial object to model ternary or higher-order relations among entities. Clustering hypergraphs is a fundamental task in network analysis. In this study, we develop two clustering algorithms based on…