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Generalized threshold-based epidemics in random graphs: the power of extreme values [article]

Michele Garetto and Emilio Leonardi and Giovanni Luca Torrisi
2016 arXiv   pre-print
Specifically, we consider i) a generalized version of bootstrap percolation in G(n,p) with random activation thresholds and random node-to-node influences; ii) different random graph models, including  ...  The common thread of our work is to show the surprising sensitivity of the critical seed set size to extreme values of distributions, which makes some systems dramatically vulnerable to large-scale outbreaks  ...  SUMMARY OF CONTRIBUTIONS In this work we extend the approach of [6] along three 'orthogonal' directions that allow us to study more general threshold-based epidemic processes in inhomogeneous scenarios  ... 
arXiv:1603.04643v1 fatcat:sbefzlkkofcelpsjekq2gn75uy

Generalized Threshold-Based Epidemics in Random Graphs

Michele Garetto, Emilio Leonardi, Giovanni Luca Torrisi
2016 Proceedings of the 2016 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Science - SIGMETRICS '16  
Specifically, we consider i) a generalized version of bootstrap percolation in G(n, p) with random activation thresholds and random node-tonode influences; ii) different random graph models, including  ...  The common thread of our work is to show the surprising sensitivity of the critical seed set size to extreme values of distributions, which makes some systems dramatically vulnerable to large-scale outbreaks  ...  SUMMARY OF CONTRIBUTIONS In this work we extend the approach of [6] along three 'orthogonal' directions that allow us to study more general threshold-based epidemic processes in inhomogeneous scenarios  ... 
doi:10.1145/2896377.2901455 dblp:conf/sigmetrics/GarettoLT16 fatcat:zfjoii2syjb2fbg5xjtvfq333m

Bernoulli Graph Bounds for Generalrandom Graphs

Carter T. Butts
2011 Sociological methodology  
General random graphs (i.e., stochastic models for networks incorporating heterogeneity and/or dependence among edges) are increasingly widely used in the study of social and other networks, but few techniques  ...  of tie formation mechanisms on epidemic potential in sexual contact networks, and robustness testing of inhomogeneous Bernoulli models based on geographical covariates. 1 See, e.g., Wasserman and Robins  ...  for θ 2 in this case gives us θ 2 < log(2 /β)/2 as the threshold parameter value.  ... 
doi:10.1111/j.1467-9531.2011.01246.x fatcat:hndph42nqnbwjk2qb47svl6tny

Graph mining

Deepayan Chakrabarti, Christos Faloutsos
2006 ACM Computing Surveys  
Indeed, any M : N relation in database terminology can be represented as a graph. A lot of these questions boil down to the following: "How can we generate synthetic but realistic graphs?"  ...  To answer this, we must first understand what patterns are common in real-world graphs and can thus be considered a mark of normality/realism.  ...  The epidemic threshold. The spread of infections depends not on the exact values of β and δ, but on their ration β/δ.  ... 
doi:10.1145/1132952.1132954 fatcat:jbc67scdzbe4vj5o5fjerdy6xq

Graph product multilayer networks: spectral properties and applications

Hiroki Sayama
2017 Journal of Complex Networks  
Applications of GPMNs are discussed in three areas: predicting epidemic thresholds, modeling propagation in nontrivial space and time, and analyzing higher-order properties of self-similar networks.  ...  This paper aims to establish theoretical foundations of graph product multilayer networks (GPMNs), a family of multilayer networks that can be obtained as a graph product of two or more factor networks  ...  Therefore, we can estimate the epidemic threshold on a random network generated with this model by calculating the largest eigenvalue of P ⊗ R.  ... 
doi:10.1093/comnet/cnx042 fatcat:kruvevvcafhhpehdy6svqhcrhu

Controlling Graph Dynamics with Reinforcement Learning and Graph Neural Networks [article]

Eli A. Meirom, Haggai Maron, Shie Mannor, Gal Chechik
2021 arXiv   pre-print
We consider the problem of controlling a partially-observed dynamic process on a graph by a limited number of interventions.  ...  We successfully apply our approach to two popular problems that fall into our framework: prioritizing which nodes should be tested in order to curb the spread of an epidemic, and influence maximization  ...  Figure S4 shows that the epidemic spread speed is slower under the RLGN policy in all graphs. In general, there are two extreme configuration regimes.  ... 
arXiv:2010.05313v3 fatcat:7f4lgugoubakhitff5iqbzjof4

Epidemic Thresholds on Scale-Free Graphs: the Interplay between Exponent and Preferential Choice

Ph. Blanchard, C.-H. Chang, T. Krüger
2003 Annales de l'Institute Henri Poincare. Physique theorique  
We show for a model of scale-free graphs with biased partner choice that knowing the exponent for the degree distribution is in general not sufficient to decide epidemic threshold properties for exponents  ...  less than three.We show that the connectivity between the high degree vertices and therefore the diameter is the relevant geometric quantity for epidemic threshold estimations.Absence of epidemic threshold  ...  In this article we want to discuss a specific model of scale-free-graphs based on a partner choice strategy and its epidemic threshold properties.  ... 
doi:10.1007/s00023-003-0975-1 fatcat:vhrgoh5mene5jiqhvxcxov42da

Discontinuous percolation transitions in epidemic processes, surface depinning in random media, and Hamiltonian random graphs

Golnoosh Bizhani, Maya Paczuski, Peter Grassberger
2012 Physical Review E  
To demonstrate this, we present and relate the continuous and first order behaviors in two different classes of models: The first are generalized epidemic processes (GEP) that describe in their spatially  ...  The second class consists of exponential ("Hamiltonian", or formally equilibrium) random graph models and includes the Strauss and the 2-star model, where 'chemical potentials' control the densities of  ...  They are both formulated in terms of a partition function and are generalizations of the standard Erdös-Renyi (ER) random graph [45] .  ... 
doi:10.1103/physreve.86.011128 pmid:23005389 fatcat:e4vy6qze65f7lc7adbbtrmtlhu

Inhomogeneous percolation models for spreading phenomena in random graphs

Luca Dall'Asta
2005 Journal of Statistical Mechanics: Theory and Experiment  
Generating functions approach is exploited in order to get a generalization of the Molloy-Reed Criterion for inhomogeneous joint site bond percolation in correlated random graphs.  ...  In particular, for the site percolation with inhomogeneous edge transmission, we obtain the explicit expressions of the percolation threshold for many interesting cases, that are analyzed by means of simple  ...  Acknowledgments The author is particularly grateful to A. Barrat for illuminating discussions and the careful reading of the manuscript.  ... 
doi:10.1088/1742-5468/2005/08/p08011 fatcat:pbbvd3j735e5xcdngvm5t7tace

Graph Theory and Networks in Biology [article]

Oliver Mason, Mark Verwoerd
2006 arXiv   pre-print
In this paper, we present a survey of the use of graph theoretical techniques in Biology.  ...  In particular, we discuss recent work on identifying and modelling the structure of bio-molecular networks, as well as the application of centrality measures to interaction networks and research on the  ...  Science Foundation Ireland is not responsible for any use of data appearing in this publication.  ... 
arXiv:q-bio/0604006v1 fatcat:nrafbzn7kzdfvkawrfuwqattz4

Distinguishing Infections on Different Graph Topologies [article]

Chris Milling, Constantine Caramanis, Shie Mannor, Sanjay Shakkottai
2013 arXiv   pre-print
We show that the identifiability condition we give is fairly mild, and in particular, is satisfied by two common graph topologies: the grid, and the Erdos-Renyi graphs.  ...  The core, therefore, of this paper, is to obtain an understanding of the diagnostic power of network information.  ...  Random Sickness In this section we provide simulation-based evidence of the theoretical results for the Threshold Ball Algorithm and Threshold Tree Algorithm.  ... 
arXiv:1309.6545v1 fatcat:wlbk7oszzrhpfhfabyk2j57yo4

Structural properties of scale-free networks [chapter]

Reuven Cohen, Shlomo Havlin, Daniel ben-Avraham
2004 Handbook of Graphs and Networks  
We study percolation in scale-free networks and show that in the regime £ © the networks are resilient to random breakdown and the percolation transition occurs only in the limit of extreme dilution.  ...  In most random network models the structure is locally tree-like (since most loops occur 1.2 Small and Ultra-Small Worlds 7 Minimal graphs and lower bound We begin by showing that the radius of any scale-free  ...  DbA thanks the support of the National Science Foundation (USA).  ... 
doi:10.1002/3527602755.ch4 fatcat:q5vtarvswbhllk7xtkuqjht4xm

Multivariate Generating Functions for Information Spread on Multi-Type Random Graphs [article]

Yaron Oz, Ittai Rubinstein, Muli Safra
2022 arXiv   pre-print
We construct multivariate generating functions and use multi-type branching processes to derive an equation for the size of the large out-components in multi-type random graphs with a general class of  ...  We use our methods to analyse the spread of epidemics and verify the results with population based simulations  ...  Acknowledgements The work is supported in part by the Israeli Science Foundation Center of Excellence, the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation  ... 
arXiv:2106.12057v2 fatcat:su3bis65qfctrny2d4efiv4y34

Benchmark graphs for testing community detection algorithms

Andrea Lancichinetti, Santo Fortunato, Filippo Radicchi
2008 Physical Review E  
Here we introduce a new class of benchmark graphs, that account for the heterogeneity in the distributions of node degrees and of community sizes.  ...  However, the special graphs adopted in actual tests have a structure that does not reflect the real properties of nodes and communities found in real networks.  ...  Such heterogeneity is responsible for a number of remarkable features of real networks, such as resilience to random failures/attacks ͓9͔, and the absence of a threshold for percolation ͓10͔ and epidemic  ... 
doi:10.1103/physreve.78.046110 pmid:18999496 fatcat:zubxucruo5hdhnjbephsda2yse

Modelling Complex Networks: Cameo Graphs And Transport Processes [article]

Philippe Blanchard, Dimitry Volchenkov
2007 arXiv   pre-print
In particular, we have studied the complex transport network of Venetian canals by means of random walks.  ...  We discuss a model accounting for the creation and development of transport networks based on the Cameo principle which refers to the idea of distribution of resources, including land, water, minerals,  ...  Acknowledgment The support from the Volkswagen Foundation (Germany) in the framework of the project "Network formation rules, random set graphs and generalized epidemic processes" is gratefully acknowledged  ... 
arXiv:0711.2176v1 fatcat:kybc6fqvybacfdongvsgcpelei
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