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609
The Small World of Human Language
 Proceedings of The Royal Society of London. Series B, Biological Sciences
, 2001
"... this paper, we show that the cooccurrence of words in sentences relies on the network structure of the lexicon, the properties of which are analysed in depth. As we will show in this paper, human language can be described in terms of a graph of word interactions. This graph has some unexpected prop ..."
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Cited by 132 (8 self)
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this paper, we show that the cooccurrence of words in sentences relies on the network structure of the lexicon, the properties of which are analysed in depth. As we will show in this paper, human language can be described in terms of a graph of word interactions. This graph has some unexpected properties (shared by other biological and technological networks (Amaral et al. 2000; Strogatz 2001)) that might underlie its diversity and exibility, and create new questions about its origins and organization
CoClustering of Biological Networks and Gene Expression Data
, 2002
"... Motivation: Large scale gene expression data are often analyzed by clustering genes based on gene expression data alone, though apriori knowledge in the form of biological networks is available. The use of this additional information promises to improve exploratory analysis considerably. ..."
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Cited by 120 (6 self)
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Motivation: Large scale gene expression data are often analyzed by clustering genes based on gene expression data alone, though apriori knowledge in the form of biological networks is available. The use of this additional information promises to improve exploratory analysis considerably.
Network and epidemic model.
 Journal of The Royal Society Interface,
, 2005
"... Networks and the epidemiology of directly transmitted infectious diseases are fundamentally linked. The foundations of epidemiology and early epidemiological models were based on population wide randommixing, but in practice each individual has a finite set of contacts to whom they can pass infect ..."
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Cited by 109 (2 self)
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Networks and the epidemiology of directly transmitted infectious diseases are fundamentally linked. The foundations of epidemiology and early epidemiological models were based on population wide randommixing, but in practice each individual has a finite set of contacts to whom they can pass infection; the ensemble of all such contacts forms a 'mixing network'. Knowledge of the structure of the network allows models to compute the epidemic dynamics at the population scale from the individuallevel behaviour of infections. Therefore, characteristics of mixing networksand how these deviate from the randommixing normhave become important applied concerns that may enhance the understanding and prediction of epidemic patterns and intervention measures. Here, we review the basis of epidemiological theory (based on randommixing models) and network theory (based on work from the social sciences and graph theory). We then describe a variety of methods that allow the mixing network, or an approximation to the network, to be ascertained. It is often the case that time and resources limit our ability to accurately find all connections within a network, and hence a generic understanding of the relationship between network structure and disease dynamics is needed. Therefore, we review some of the variety of idealized network types and approximation techniques that have been utilized to elucidate this link. Finally, we look to the future to suggest how the two fields of network theory and epidemiological modelling can deliver an improved understanding of disease dynamics and better public health through effective disease control.
PowerLaws and the ASlevel Internet Topology
 IEEE/ACM Transactions on Networking
, 2003
"... In this paper, we study and characterize the topology of the Internet at the Autonomous System level. First, we show that the topology can be described efficiently with powerlaws. The elegance and simplicity of the powerlaws provide a novel perspective into the seemingly uncontrolled Internet struc ..."
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Cited by 109 (11 self)
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In this paper, we study and characterize the topology of the Internet at the Autonomous System level. First, we show that the topology can be described efficiently with powerlaws. The elegance and simplicity of the powerlaws provide a novel perspective into the seemingly uncontrolled Internet structure. Second, we show that powerlaws appear consistently over the last 5 years. We also observe that the powerlaws hold even in the most recent and more complete topology [10] with correlation coefficient above 99% for the degree powerlaw. In addition, we study the evolution of the powerlaw exponents over the 5 year interval and observe a variation for the degree based powerlaw of less than 10%. Third, we provide relationships between the exponents and other topological metrics.
How the global structure of protein interaction networks evolves,”
 Proceedings of the Royal Society B,
, 2003
"... Two processes can influence the evolution of protein interaction networks: addition and elimination of interactions between proteins, and gene duplications increasing the number of proteins and interactions. The rates of these processes can be estimated from available Saccharomyces cerevisiae genom ..."
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Cited by 105 (2 self)
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Two processes can influence the evolution of protein interaction networks: addition and elimination of interactions between proteins, and gene duplications increasing the number of proteins and interactions. The rates of these processes can be estimated from available Saccharomyces cerevisiae genome data and are sufficiently high to affect network structure on short timescales. For instance, more than 100 interactions may be added to the yeast network every million years, a fraction of which adds previously unconnected proteins to the network. Highly connected proteins show a greater rate of interaction turnover than proteins with few interactions. From these observations one can explain (without natural selection on global network structure) the evolutionary sustenance of the most prominent network feature, the distribution of the frequency P(d ) of proteins with d neighbours, which is broadtailed and consistent with a power law, that is: P(d )~d 2g .
Biological network comparison using graphlet degree distribution
 Bioinformatics
"... Motivation: Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally infeasible, and thus heuristics, such as the degr ..."
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Cited by 102 (1 self)
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Motivation: Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally infeasible, and thus heuristics, such as the degree distribution, clustering coefficient, diameter, and relative graphlet frequency distribution have been sought. It is easy to demonstrate that two networks are different by simply showing a short list of properties in which they differ. It is much harder to show that two networks are similar, as it requires demonstrating their similarity in all of their exponentially many properties. Clearly, it is computationally prohibitive to analyze all network properties, but the larger the number of constraints we impose in determining network similarity, the more likely it
Evolving protein interaction networks through gene duplication
 J. Theor. Biol
"... The topology of the proteome map revealed by recent largescale hybridization methods has shown that the distribution of proteinprotein interactions is highly heterogeneous, with many proteins having few links while a few of them are heavily connected. This particular topology is shared by other ce ..."
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Cited by 86 (2 self)
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The topology of the proteome map revealed by recent largescale hybridization methods has shown that the distribution of proteinprotein interactions is highly heterogeneous, with many proteins having few links while a few of them are heavily connected. This particular topology is shared by other cellular networks, such as metabolic pathways, and it has been suggested to be responsible for the high mutational homeostasis displayed by the genome of some organisms. In this paper we explore a recent model of proteome evolution that has been shown to reproduce many of the features displayed by its real counterparts. The model is based on gene duplication plus rewiring of the newly created genes. The statistical features displayed by the proteome of wellknown organisms are reproduced, suggesting that the overall topology of the protein maps naturally emerges from the two leading mechanisms considered by the model. I.
On Cubical Graphs
 JOURNAL OF COMBINATORIAL THEORY (B) 18, 86 % (1975)
, 1975
"... It is frequently of interest to represent a given graph G as a subgraph of a graph H which has some special structure. A particularly useful class of graphs in which to embed G is the class of ndimensional cubes. This has found applications, for example, in coding theory, data transmission, and lin ..."
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Cited by 82 (5 self)
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It is frequently of interest to represent a given graph G as a subgraph of a graph H which has some special structure. A particularly useful class of graphs in which to embed G is the class of ndimensional cubes. This has found applications, for example, in coding theory, data transmission, and linguistics. In this note, we study the structure of those graphs 6, called cubical graphs (not to be confused with cubic graphs, those graphs for which all vertices have degree 3), which can be embedded into an ndimensional cube. A basic technique used is the investigation of graphs which are critically nonembeddable, i.e., which can not be embedded but all of whose subgrapbs can be embedded.
Complex networks: smallworld, scalefree and beyond
 IEEE Circuits Syst. Mag
, 2003
"... Abstract: In the past few years, the discovery of smallworld and scalefree properties of many natural and artificial complex networks has stimulated a great deal of interest in studying the underlying organizing principles of various complex networks, which has led to dramatic advances in this eme ..."
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Cited by 77 (5 self)
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Abstract: In the past few years, the discovery of smallworld and scalefree properties of many natural and artificial complex networks has stimulated a great deal of interest in studying the underlying organizing principles of various complex networks, which has led to dramatic advances in this emerging and active field of research. The present article reviews some basic concepts, important progress, and significant results in the current studies of various complex networks, with emphasis on the relationship between the topology and the dynamics of such complex networks. Some fundamental properties and typical complex network models are described, and as an example the epidemic dynamics are analyzed and discussed in some detail. Finally, the important issue of robustness versus fragility of dynamical synchronization in complex networks is introduced and discussed. Index terms – complex network, smallworld network, scalefree network, synchronization, robustness
Directed scalefree graphs.
 In SODA’03,
, 2003
"... Abstract We introduce a model for directed scalefree graphs that grow with preferential attachment depending in a natural way on the inand outdegrees. We show that the resulting inand outdegree distributions are power laws with different exponents, reproducing observed properties of the worldw ..."
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Cited by 76 (5 self)
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Abstract We introduce a model for directed scalefree graphs that grow with preferential attachment depending in a natural way on the inand outdegrees. We show that the resulting inand outdegree distributions are power laws with different exponents, reproducing observed properties of the worldwide web. We also derive exponents for the distribution of in(out) degrees among vertices with fixed out(in) degree. We conclude by suggesting a corresponding model with hidden variables.