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1,301
Spectral properties of the Laplacian of multiplex networks. Physical Review E,
, 2013
"... One of the more challenging tasks in the understanding of dynamical properties of models on top of complex networks is to capture the precise role of multiplex topologies. In a recent paper, Gómez et al. [Phys. Rev. Lett. 110, 028701 (2013)], some of the authors proposed a framework for the study ..."
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Cited by 5 (1 self)
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One of the more challenging tasks in the understanding of dynamical properties of models on top of complex networks is to capture the precise role of multiplex topologies. In a recent paper, Gómez et al. [Phys. Rev. Lett. 110, 028701 (2013)], some of the authors proposed a framework for the study
Laplacian eigenmaps and spectral techniques for embedding and clustering.
 Proceeding of Neural Information Processing Systems,
, 2001
"... Abstract Drawing on the correspondence between the graph Laplacian, the LaplaceBeltrami op erator on a manifold , and the connections to the heat equation , we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in ..."
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Cited by 668 (7 self)
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Abstract Drawing on the correspondence between the graph Laplacian, the LaplaceBeltrami op erator on a manifold , and the connections to the heat equation , we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded
Consistency of spectral clustering
, 2004
"... Consistency is a key property of statistical algorithms, when the data is drawn from some underlying probability distribution. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of a popular family of spe ..."
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Cited by 572 (15 self)
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of spectral clustering algorithms, which cluster the data with the help of eigenvectors of graph Laplacian matrices. We show that one of the two of major classes of spectral clustering (normalized clustering) converges under some very general conditions, while the other (unnormalized), is only consistent
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 502 (0 self)
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divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a
Consensus and cooperation in networked multiagent systems
 Proceedings of the IEEE
, 2007
"... Summary. This paper provides a theoretical framework for analysis of consensus algorithms for multiagent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, timedelays, and performance guarantees. An ove ..."
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Cited by 807 (4 self)
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networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster
Variability of Absorption and Optical Properties of Key Aerosol Types Observed in Worldwide Locations
 JOURNAL OF THE ATMOSPHERIC SCIENCES
, 2002
"... Aerosol radiative forcing is a critical, though variable and uncertain, component of the global climate. Yet climate models rely on sparse information of the aerosol optical properties. In situ measurements, though important in many respects, seldom provide measurements of the undisturbed aerosol in ..."
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Cited by 263 (30 self)
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in the entire atmospheric column. Here, 8 yr of worldwide distributed data from the AERONET network of groundbased radiometers were used to remotely sense the aerosol absorption and other optical properties in several key locations. Established procedures for maintaining and calibrating the global network
The effect of network topology on the spread of epidemics
 IN IEEE INFOCOM
, 2005
"... Many network phenomena are well modeled as spreads of epidemics through a network. Prominent examples include the spread of worms and email viruses, and, more generally, faults. Many types of information dissemination can also be modeled as spreads of epidemics. In this paper we address the question ..."
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Cited by 216 (8 self)
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the question of what makes an epidemic either weak or potent. More precisely, we identify topological properties of the graph that determine the persistence of epidemics. In particular, we show that if the ratio of cure to infection rates is smaller than the spectral radius of the graph, then the mean epidemic
1Structural Analysis of Laplacian Spectral Properties with Application to Electric Transmission Networks
"... Abstract—The spectrum of the Laplacian matrix of a network plays a key role in a wide range of dynamical problems associated with the network, from transient stability analysis of power networks to distributed control of formations. Using methods from algebraic graph theory and convex optimization, ..."
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, we study the relationship between structural features of a network and spectral properties of its Laplacian matrix. We illustrate our results by studying the influence of structural properties on the Laplacian eigenvalues of the American (western states), French and Spanish highvoltage transmission
Transmission capacity of wireless ad hoc networks with successive . . .
 IEEE TRANS. ON INFO. THEORY
, 2005
"... The transmission capacity of a wireless ad hoc network can be defined as the maximum allowable area spectral efficiency such that the outage probability does not exceed some specified threshold. This work studies the improvement in transmission capacity obtainable with successive interference cance ..."
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Cited by 190 (42 self)
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The transmission capacity of a wireless ad hoc network can be defined as the maximum allowable area spectral efficiency such that the outage probability does not exceed some specified threshold. This work studies the improvement in transmission capacity obtainable with successive interference
Laplacian dynamics and multiscale modular structure in networks
 ArXiv
, 2009
"... Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a dynamical process taking place on the graph. The timescale of th ..."
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Cited by 35 (3 self)
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Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a dynamical process taking place on the graph. The time
Results 1  10
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