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2,336
The LargeScale Organization of Metabolic Networks
, 2000
"... In a cell or microorganism the processes that generate mass, energy, information transfer, and cell fate specification are seamlessly integrated through a complex network of various cellular constituents and reactions. However, despite the key role these networks play in sustaining various cellular ..."
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Cited by 555 (7 self)
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In a cell or microorganism the processes that generate mass, energy, information transfer, and cell fate specification are seamlessly integrated through a complex network of various cellular constituents and reactions. However, despite the key role these networks play in sustaining various cellular functions, their largescale structure is essentially unknown. Here we present the first systematic comparative mathematical analysis of the metabolic networks of 43 organisms representing all three domains of life. We show that, despite significant variances in their individual constituents and pathways, these metabolic networks display the same topologic scaling properties demonstrating striking similarities to the inherent organization of complex nonbiological systems. This suggests that the metabolic organization is not only identical for all living organisms, but complies with the design principles of robust and errortolerant networks, and may represent a common blueprint for the largescale organization of interactions among all cellular constituents.
Critical Power for Asymptotic Connectivity in Wireless Networks
, 1998
"... : In wireless data networks each transmitter's power needs to be high enough to reach the intended receivers, while generating minimum interference on other receivers sharing the same channel. In particular, if the nodes in the network are assumed to cooperate in routing each others ' pack ..."
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Cited by 520 (19 self)
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: In wireless data networks each transmitter's power needs to be high enough to reach the intended receivers, while generating minimum interference on other receivers sharing the same channel. In particular, if the nodes in the network are assumed to cooperate in routing each others ' packets, as is the case in ad hoc wireless networks, each node should transmit with just enough power to guarantee connectivity in the network. Towards this end, we derive the critical power a node in the network needs to transmit in order to ensure that the network is connected with probability one as the number of nodes in the network goes to infinity. It is shown that if n nodes are placed in a disc of unit area in ! 2 and each node transmits at a power level so as to cover an area of ßr 2 = (log n + c(n))=n, then the resulting network is asymptotically connected with probability one if and only if c(n) ! +1. 1 Introduction Wireless communication systems consist of nodes which share a common commu...
A Critical Point For Random Graphs With A Given Degree Sequence
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
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Cited by 497 (8 self)
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Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 then almost surely all components in such graphs are small. We can apply these results to G n;p ; G n;M , and other wellknown models of random graphs. There are also applications related to the chromatic number of sparse random graphs.
PAMAS  Power Aware MultiAccess protocol with Signalling for Ad Hoc Networks
, 1998
"... In this paper we develop a new multiaccess protocol for ad hoc radio networks. The protocol is based on the original MACA protocol with the adition of a separate signalling channel. The unique feature of our protocol is that it conserves battery power at nodes by intelligently powering off nodes t ..."
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Cited by 433 (8 self)
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In this paper we develop a new multiaccess protocol for ad hoc radio networks. The protocol is based on the original MACA protocol with the adition of a separate signalling channel. The unique feature of our protocol is that it conserves battery power at nodes by intelligently powering off nodes that are not actively transmitting or receiving packets. The manner in which nodes power themselves off does not influence the delay or throughput characteristics of our protocol. We illustrate the power conserving behavior of PAMAS via extensive simulations performed over ad hoc networks containing 1020 nodes. Our results indicate that power savings of between 10 % and 70 % are attainable in most systems. Finally, we discuss how the idea of power awareness can be built into other multiaccess protocols as well.
Evolution of networks
 Adv. Phys
, 2002
"... We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence rece ..."
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Cited by 403 (3 self)
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We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number of them are scalefree and show striking resilience against random breakdowns. In spite of large sizes of these networks, the distances between most their vertices are short — a feature known as the “smallworld” effect. We discuss how growing networks selforganize into scalefree structures and the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation in these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in Nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems
Inferring Web Communities from Link Topology
, 1998
"... The World Wide Web grows through a decentralized, almost anarchic process, and this has resulted in a large hyperlinked corpus without the kind of logical organization that can be built into more traditionallycreated hypermedia. To extract meaningful structure under such circumstances, we develop a ..."
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Cited by 400 (4 self)
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The World Wide Web grows through a decentralized, almost anarchic process, and this has resulted in a large hyperlinked corpus without the kind of logical organization that can be built into more traditionallycreated hypermedia. To extract meaningful structure under such circumstances, we develop a notion of hyperlinked communities on the www through an analysis of the link topology. Byinvoking a simple, mathematically clean method for de ning and exposing the structure of these communities, we are able to derive anumber of themes: The communities can be viewed as containing a core of central, "authoritative" pages linked together by "hub pages"; and they exhibit a natural type of hierarchical topic generalization that can be inferred directly from the pattern of linkage. Our investigation shows that although the process by which users of the Web create pages and links is very di cult to understand at a "local" level, it results in a much greater degree of orderly highlevel structure than has typically been assumed.
Complex networks: Structure and dynamics
, 2006
"... Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highly interconnected dynamical units. The first approach to capture the global properties of such systems is to ..."
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Cited by 385 (9 self)
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Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highly interconnected dynamical units. The first approach to capture the global properties of such systems is to model them as graphs whose nodes represent the dynamical units, and whose links stand for the interactions between them. On the one hand, scientists have to cope with structural issues, such as characterizing the topology of a complex wiring architecture, revealing the unifying principles that are at the basis of real networks, and developing models to mimic the growth of a network and reproduce its structural properties. On the other hand, many relevant questions arise when studying complex networks ’ dynamics, such as learning how a large ensemble of dynamical systems that interact through a complex wiring topology can behave collectively. We review the major concepts and results recently achieved in the study of the structure and dynamics of complex networks, and summarize the relevant applications of these ideas in many different disciplines,
The Web as a graph: measurements, models, and methods
, 1999
"... . The pages and hyperlinks of the WorldWide Web may be viewed as nodes and edges in a directed graph. This graph is a fascinating object of study: it has several hundred million nodes today, over a billion links, and appears to grow exponentially with time. There are many reasons  mathematical, ..."
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Cited by 375 (10 self)
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. The pages and hyperlinks of the WorldWide Web may be viewed as nodes and edges in a directed graph. This graph is a fascinating object of study: it has several hundred million nodes today, over a billion links, and appears to grow exponentially with time. There are many reasons  mathematical, sociological, and commercial  for studying the evolution of this graph. In this paper we begin by describing two algorithms that operate on the Web graph, addressing problems from Web search and automatic community discovery. We then report a number of measurements and properties of this graph that manifested themselves as we ran these algorithms on the Web. Finally, we observe that traditional random graph models do not explain these observations, and we propose a new family of random graph models. These models point to a rich new subfield of the study of random graphs, and raise questions about the analysis of graph algorithms on the Web. 1 Overview Few events in the history of comput...
Structure and evolution of online social networks
 In Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
, 2006
"... In this paper, we consider the evolution of structure within large online social networks. We present a series of measurements of two such networks, together comprising in excess of five million people and ten million friendship links, annotated with metadata capturing the time of every event in the ..."
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Cited by 375 (4 self)
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In this paper, we consider the evolution of structure within large online social networks. We present a series of measurements of two such networks, together comprising in excess of five million people and ten million friendship links, annotated with metadata capturing the time of every event in the life of the network. Our measurements expose a surprising segmentation of these networks into three regions: singletons who do not participate in the network; isolated communities which overwhelmingly display star structure; and a giant component anchored by a wellconnected core region which persists even in the absence of stars. We present a simple model of network growth which captures these aspects of component structure. The model follows our experimental results, characterizing users as either passive members of the network; inviters who encourage offline friends and acquaintances to migrate online; and linkers who fully participate in the social evolution of the network.
Scalefree characteristics of random networks: The topology of the worldwide web
 PHYSICA A
, 2000
"... The worldwide web forms a large directed graph, whose vertices are documents and edges are links pointing from one document to another. Here we demonstrate that despite its apparent random character, the topology of this graph has a number of universal scalefree characteristics. We introduce a mod ..."
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Cited by 333 (0 self)
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The worldwide web forms a large directed graph, whose vertices are documents and edges are links pointing from one document to another. Here we demonstrate that despite its apparent random character, the topology of this graph has a number of universal scalefree characteristics. We introduce a model that leads to a scalefree network, capturing in a minimal fashion the selforganization processes governing the worldwide web.