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Spectral density of the nonbacktracking operator
"... PACS 89.20.a – Interdisciplinary applications of physics PACS 89.75.Hc – Networks and genealogical trees PACS 02.10.Yn – Matrix theory Abstract –The nonbacktracking operator was recently shown to provide a significant improvement when used for spectral clustering of sparse networks. In this paper ..."
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that there exists a paramagnetic phase, leading to zero spectral density, that is stable outside a circle of radius ρ, where ρ is the leading eigenvalue of the nonbacktracking operator. We observe a secondorder phase transition at the edge of this circle, between a zero and a nonzero spectral density. The fact
Eigenvalues of Nonbacktracking Walks in a Cycle with Random Loops
, 2007
"... In this paper we take a very special model of a random nonregular graph and study its nonbacktracking spectrum. We study graphs consisting of a cycle with some random loops added; the graphs are not regular and their nonbacktracking spectrum does not seem to be confined to some onedimensional se ..."
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In this paper we take a very special model of a random nonregular graph and study its nonbacktracking spectrum. We study graphs consisting of a cycle with some random loops added; the graphs are not regular and their nonbacktracking spectrum does not seem to be confined to some one
Assessing Percolation Threshold Based on HighOrder NonBacktracking Matrices
"... ABSTRACT Percolation threshold of a network is the critical value such that when nodes or edges are randomly selected with probability below the value, the network is fragmented but when the probability is above the value, a giant component connecting a large portion of the network would emerge. As ..."
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with the same largest eigenvalue as the 2ndorder nonbacktracking matrix to improve computation efficiency. Finally, we use both synthetic networks and 42 real networks to illustrate that the use of the 2ndorder nonbacktracking matrix does give better lower bound for assessing percolation threshold than
Epidemic Thresholds in Real Networks
"... How will a virus propagate in a real network? How long does it take to disinfect a network given particular values of infection rate and virus death rate? What is the single best node to immunize? Answering these questions is essential for devising networkwide strategies to counter viruses. In addi ..."
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Cited by 101 (10 self)
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How will a virus propagate in a real network? How long does it take to disinfect a network given particular values of infection rate and virus death rate? What is the single best node to immunize? Answering these questions is essential for devising networkwide strategies to counter viruses
Node Immunization on Large Graphs: Theory and Algorithms
"... Abstract—Given a large graph, like a computer communication network, which k nodes should we immunize (or monitor, or remove), to make it as robust as possible against a computer virus attack? This problem, referred to as the Node Immunization problem, is the core building block in many highimpact ..."
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Abstract—Given a large graph, like a computer communication network, which k nodes should we immunize (or monitor, or remove), to make it as robust as possible against a computer virus attack? This problem, referred to as the Node Immunization problem, is the core building block in many high
• Node influence
"... (2) Correlation based networks • Estimating correlations from time series • Partial correlations • Dependency network ..."
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(2) Correlation based networks • Estimating correlations from time series • Partial correlations • Dependency network
Spectral clustering of graphs with the bethe hessian
 in Advances in Neural Information Processing Systems, 2014
"... Spectral clustering is a standard approach to label nodes on a graph by studying the (largest or lowest) eigenvalues of a symmetric real matrix such as e.g. the adjacency or the Laplacian. Recently, it has been argued that using instead a more complicated, nonsymmetric and higher dimensional opera ..."
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Spectral clustering is a standard approach to label nodes on a graph by studying the (largest or lowest) eigenvalues of a symmetric real matrix such as e.g. the adjacency or the Laplacian. Recently, it has been argued that using instead a more complicated, nonsymmetric and higher dimensional
Fractional Immunization in Networks
"... Preventing contagion in networks is an important problem in public health and other domains. Targeting nodes to immunize based on their network interactions has been shown to be far more effective at stemming infection spread than immunizing random subsets of nodes. However, the assumption that sele ..."
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Cited by 2 (1 self)
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Preventing contagion in networks is an important problem in public health and other domains. Targeting nodes to immunize based on their network interactions has been shown to be far more effective at stemming infection spread than immunizing random subsets of nodes. However, the assumption
Fractional Immunization in Networks
"... Preventing contagion in networks is an important problem in public health and other domains. Targeting nodes to immunize based on their network interactions has been shown to be far more effective at stemming infection spread than immunizing random subsets of nodes. However, the assumption that sele ..."
Abstract
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Preventing contagion in networks is an important problem in public health and other domains. Targeting nodes to immunize based on their network interactions has been shown to be far more effective at stemming infection spread than immunizing random subsets of nodes. However, the assumption
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