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1,051
The structure and function of complex networks
 SIAM REVIEW
, 2003
"... Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, ..."
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Cited by 2578 (7 self)
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Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the smallworld effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
On the Minimum Node Degree and Connectivity of a Wireless Multihop Network
 ACM MobiHoc
, 2002
"... This paper investigates two fundamental characteristics of a wireless multihop network: its minimum node degree and its k–connectivity. Both topology attributes depend on the spatial distribution of the nodes and their transmission range. Using typical modeling assumptions — a random uniform distri ..."
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Cited by 321 (4 self)
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This paper investigates two fundamental characteristics of a wireless multihop network: its minimum node degree and its k–connectivity. Both topology attributes depend on the spatial distribution of the nodes and their transmission range. Using typical modeling assumptions — a random uniform distribution of the nodes and a simple link model — we derive an analytical expression that enables the determination of the required range r0 that creates, for a given node density ρ, an almost surely k–connected network. Equivalently, if the maximum r0 of the nodes is given, we can find out how many nodes are needed to cover a certain area with a k–connected network. We also investigate these questions by various simulations and thereby verify our analytical expressions. Finally, the impact of mobility is discussed. The results of this paper are of practical value for researchers in this area, e.g., if they set the parameters in a network–level simulation of a mobile ad hoc network or if they design a wireless sensor network. Categories and Subject Descriptors C.2 [Computercommunication networks]: Network architecture and design—wireless communication, network communications, network topology; G.2.2 [Discrete mathematics]: Graph theory; F.2.2 [Probability and statistics]: Stochastic processes
Connected Components in Random Graphs with Given Expected Degree Sequences
 ANNALS OF COMBINATORICS
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On the privacy preserving properties of random data perturbation techniques
 In ICDM
, 2003
"... Privacy is becoming an increasingly important issue in many data mining applications. This has triggered the development of many privacypreserving data mining techniques. A large fraction of them use randomized data distortion techniques to mask the data for preserving the privacy of sensitive data ..."
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Cited by 188 (6 self)
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Privacy is becoming an increasingly important issue in many data mining applications. This has triggered the development of many privacypreserving data mining techniques. A large fraction of them use randomized data distortion techniques to mask the data for preserving the privacy of sensitive data. This methodology attempts to hide the sensitive data by randomly modifying the data values often using additive noise. This paper questions the utility of the random value distortion technique in privacy preservation. The paper notes that random objects (particularly random matrices) have “predictable ” structures in the spectral domain and it develops a random matrixbased spectral filtering technique to retrieve original data from the dataset distorted by adding random values. The paper presents the theoretical foundation of this filtering method and extensive experimental results to demonstrate that in many cases random data distortion preserve very little data privacy. 1.
The phase transition in inhomogeneous random graphs
, 2005
"... The ‘classical’ random graph models, in particular G(n, p), are ‘homogeneous’, in the sense that the degrees (for example) tend to be concentrated around a typical value. Many graphs arising in the real world do not have this property, having, for example, powerlaw degree distributions. Thus there ..."
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Cited by 181 (31 self)
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The ‘classical’ random graph models, in particular G(n, p), are ‘homogeneous’, in the sense that the degrees (for example) tend to be concentrated around a typical value. Many graphs arising in the real world do not have this property, having, for example, powerlaw degree distributions. Thus there has been a lot of recent interest in defining and studying ‘inhomogeneous ’ random graph models. One of the most studied properties of these new models is their ‘robustness’, or, equivalently, the ‘phase transition ’ as an edge density parameter is varied. For G(n, p), p = c/n, the phase transition at c = 1 has been a central topic in the study of random graphs for well over 40 years. Many of the new inhomogenous models are rather complicated; although there are exceptions, in most cases precise questions such as determining exactly the critical point of the phase transition are approachable only when there is independence between the edges. Fortunately, some models studied have this already, and others can be approximated by models with
Agreement over random networks
 IEEE Trans. Autom. Control
, 2005
"... Abstract—We consider the agreement problem over random information networks. In a randomnetwork, the existence of an information channel between a pair of units at each time instance is probabilistic and independent of other channels; hence, the topology of the network varies over time. In such a f ..."
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Cited by 159 (3 self)
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Abstract—We consider the agreement problem over random information networks. In a randomnetwork, the existence of an information channel between a pair of units at each time instance is probabilistic and independent of other channels; hence, the topology of the network varies over time. In such a framework, we address the asymptotic agreement for the networked units via notions from stochastic stability. Furthermore, we delineate on the rate of convergence as it relates to the algebraic connectivity of random graphs. Index Terms—Agreement problem, networked systems, random graphs, stochastic stability, supermartingales. I.
A General Model of Web Graphs
, 2003
"... We describe a very general model of a random graph process whose proportional degree sequence obeys a power law. Such laws have recently been observed in graphs associated with the world wide web. ..."
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Cited by 117 (6 self)
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We describe a very general model of a random graph process whose proportional degree sequence obeys a power law. Such laws have recently been observed in graphs associated with the world wide web.
NeighborhoodBased Models for Social Networks
 Sociological Methodology
, 2002
"... Harrison White and several anonymous reviewers for valuable comments on the work. We argue that social networks can be modeled as the outcome of processes that occur in overlapping local regions of the network, termed local social neighborhoods. Each neighborhood is conceived as a possible site of i ..."
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Cited by 99 (8 self)
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Harrison White and several anonymous reviewers for valuable comments on the work. We argue that social networks can be modeled as the outcome of processes that occur in overlapping local regions of the network, termed local social neighborhoods. Each neighborhood is conceived as a possible site of interaction and corresponds to a subset of possible network ties. In this paper, we discuss hypotheses about the form of these neighborhoods, and we present two new and theoretically plausible ways in which neighborhoodbased models for networks can be constructed. In the first, we introduce the notion of a setting structure, a directly hypothesized (or observed) set of exogenous constraints on possible neighborhood forms. In the second, we propose higherorder neighborhoods that are generated, in part, by the outcome of interactive network processes themselves. Applications of both approaches to model construction are presented, and the developments are considered within a general conceptual framework of locale for social networks. We show how assumptions about neighborhoods can be cast within a hierarchy of increasingly complex models; these models represent a progressively greater capacity for network processes to “reach ” across a network through long cycles or semipaths. We argue that this class of models holds new promise for the development of empirically plausible models for networks and networkbased processes. 2 1.