PageRank in Undirected Random Graphs

Avrachenkov, Konstantin; Kadavankandy, Arun; Prokhorenkova, Liudmila; Райгородский, А. М.

doi:10.1007/978-3-319-26784-5_12

Cited by 8 publications

References 41 publications

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Distribution of centrality measures on undirected random networks via the cavity method

Bartolucci,

Caccioli,

Caravelli

et al. 2024

Proc. Natl. Acad. Sci. U.S.A.

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The Katz centrality of a node in a complex network is a measure of the node’s importance as far as the flow of information across the network is concerned. For ensembles of locally tree-like undirected random graphs, this observable is a random variable. Its full probability distribution is of interest but difficult to handle analytically because of its “global” character and its definition in terms of a matrix inverse. Leveraging a fast Gaussian Belief Propagation-Cavity algorithm to solve linear systems on tree-like structures, we show that i) the Katz centrality of a single instance can be computed recursively in a very fast way, and ii) the probability P ( K ) that a random node in the ensemble of undirected random graphs has centrality K satisfies a set of recursive distributional equations, which can be analytically characterized and efficiently solved using a population dynamics algorithm. We test our solution on ensembles of Erdős-Rényi and Scale Free networks in the locally tree-like regime, with excellent agreement. The analytical distribution of centrality for the configuration model conditioned on the degree of each node can be employed as a benchmark to identify nodes of empirical networks with over- and underexpressed centrality relative to a null baseline. We also provide an approximate formula based on a rank- 1 projection that works well if the network is not too sparse, and we argue that an extension of our method could be efficiently extended to tackle analytical distributions of other centrality measures such as PageRank for directed networks in a transparent and user-friendly way.

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Distribution of centrality measures on undirected random networks via the cavity method

Bartolucci,

Caccioli,

Caravelli

et al. 2024

Proc. Natl. Acad. Sci. U.S.A.

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Detecting susceptible communities and individuals in hospital contact networks: a model based on social network analysis

Yang,

Peng,

Siet

et al. 2023

Connection Science

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Inference in OSNs via Lightweight Partial Crawls

Avrachenkov

Ribeiro

Sreedharan

2016

Proceedings of the 2016 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Science

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Are Online Social Network (OSN) A users more likely to form friendships with those with similar attributes? Do users at an OSN B score content more favorably than OSN C users? Such questions frequently arise in the context of Social Network Analysis (SNA) but often crawling an OSN network via its Application Programming Interface (API) is the only way to gather data from a third party. To date, these partial API crawls are the majority of public datasets and the synonym of lack of statistical guarantees in incompletedata comparisons, severely limiting SNA research progress. Using regenerative properties of the random walks, we propose estimation techniques based on short crawls that have proven statistical guarantees. Moreover, our short crawls can be implemented in massively distributed algorithms. We also provide an adaptive crawler that makes our method parameter-free, significantly improving our statistical guarantees. We then derive the Bayesian approximation of the posterior of the estimates, and in addition, obtain an estimator for the expected value of node and edge statistics in an equivalent configuration model or Chung-Lu random graph model of the given network (where nodes are connected randomly) and use it as a basis for testing null hypotheses. The theoretical results are supported with simulations on a variety of real-world networks.

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PageRank in Undirected Random Graphs

Cited by 8 publications

References 41 publications

Distribution of centrality measures on undirected random networks via the cavity method

Distribution of centrality measures on undirected random networks via the cavity method

Detecting susceptible communities and individuals in hospital contact networks: a model based on social network analysis

Inference in OSNs via Lightweight Partial Crawls

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