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57
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 1407 (9 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.
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 268 (2 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
Analysis of Topological Characteristics of Huge Online Social Networking Services
 In Proceedings of the 16th international conference on World Wide Web (WWW’07
, 2007
"... Abstract — Social networking services are a fastgrowing business in the Internet. However, it is unknown if online relationships and their growth patterns are the same as in reallife social networks. In this paper, we compare the structures of three online social networking services: Cyworld, MySp ..."
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Cited by 122 (5 self)
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Abstract — Social networking services are a fastgrowing business in the Internet. However, it is unknown if online relationships and their growth patterns are the same as in reallife social networks. In this paper, we compare the structures of three online social networking services: Cyworld, MySpace, and orkut, each with more than 10 million users, respectively. We have access to complete data of Cyworld’s ilchon (friend) relationships and analyze its degree distribution, clustering property, degree correlation, and evolution over time. We also use Cyworld data to evaluate the validity of snowball sampling method, which we use to crawl and obtain partial network topologies of MySpace and orkut. Cyworld, the oldest of the three, demonstrates a changing scaling behavior over time in degree distribution. The latest Cyworld data’s degree distribution exhibits a multiscaling behavior, while those of MySpace and orkut have simple scaling behaviors with different exponents. Very interestingly, each of the two exponents corresponds to the different segments in Cyworld’s degree distribution. Certain online social networking services encourage online activities that cannot be easily copied in real life; we show that they deviate from closeknit online social networks which show a similar degree correlation pattern to reallife social networks. I.
Graph mining: Laws, generators, and algorithms
 ACM COMPUTING SURVEYS
, 2006
"... How does the Web look? How could we tell an abnormal social network from a normal one? These and similar questions are important in many fields where the data can intuitively be cast as a graph; examples range from computer networks to sociology to biology and many more. Indeed, any M : N relation i ..."
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Cited by 70 (6 self)
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How does the Web look? How could we tell an abnormal social network from a normal one? These and similar questions are important in many fields where the data can intuitively be cast as a graph; examples range from computer networks to sociology to biology and many more. Indeed, any M : N relation in database terminology can be represented as a graph. A lot of these questions boil down to the following: "How can we generate synthetic but realistic graphs?" To answer this, we must first understand what patterns are common in realworld graphs and can thus be considered a mark of normality/realism. This survey give an overview of the incredible variety of work that has been done on these problems. One of our main contributions is the integration of points of view from physics, mathematics, sociology, and computer science. Further, we briefly describe recent advances on some related and interesting graph problems.
Emergence of social conventions in complex networks
 Artificial Intelligence
, 2002
"... The emergence of social conventions in multiagent systems has been analyzed mainly in settings where every agent may interact either with every other agent or with nearest neighbours, according to some regular underlying topology. In this note we argue that these topologies are too simple if we tak ..."
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Cited by 40 (4 self)
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The emergence of social conventions in multiagent systems has been analyzed mainly in settings where every agent may interact either with every other agent or with nearest neighbours, according to some regular underlying topology. In this note we argue that these topologies are too simple if we take into account recent discoveries on real networks. These networks, one of the main examples being the Internet, are what is called complex, that is, either graphs with the smallworld property or scalefree graphs. In this note we study the efficiency of the emergence of social conventions in complex networks, that is, how fast conventions are reached. Our main result is that complex graphs make the system much more efficient than regular graphs with the same average number of links per node. Furthermore, we find out that scalefree graphs make the system as efficient as fully connected graphs.
Dynamics of Large Networks
, 2008
"... A basic premise behind the study of large networks is that interaction leads to complex collective behavior. In our work we found very interesting and counterintuitive patterns for time evolving networks, which change some of the basic assumptions that were made in the past. We then develop models ..."
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Cited by 18 (0 self)
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A basic premise behind the study of large networks is that interaction leads to complex collective behavior. In our work we found very interesting and counterintuitive patterns for time evolving networks, which change some of the basic assumptions that were made in the past. We then develop models that explain processes which govern the network evolution, fit such models to real networks, and use them to generate realistic graphs or give formal explanations about their properties. In addition, our work has a wide range of applications: it can help us spot anomalous graphs and outliers, forecast future graph structure and run simulations of network evolution. Another important aspect of our research is the study of “local ” patterns and structures of propagation in networks. We aim to identify building blocks of the networks and find the patterns of influence that these blocks have on information or virus propagation over the network. Our recent work included the study of the spread of influence in a large persontoperson
Emergence of coordination in scalefree networks
 In Web Intelligence and Agent Systems
, 2003
"... We use several models of scalefree graphs as underlying interaction graphs for a simple model of MultiAgent Systems (MAS), and study how fast the system reaches a fixedpoint, that is, the time it takes for the system to get a 90 % of the agents in the same state. The interest of these kind of gra ..."
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Cited by 15 (0 self)
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We use several models of scalefree graphs as underlying interaction graphs for a simple model of MultiAgent Systems (MAS), and study how fast the system reaches a fixedpoint, that is, the time it takes for the system to get a 90 % of the agents in the same state. The interest of these kind of graphs is in the fact that the Internet, a very plausible environment for MAS, is a scalefree graph with high clustering and ¢ knn £ , the nearest neighbor average connectivity of nodes with connectivity k, following a powerlaw. Our results show that different types of scalefree graphs make the system as efficient as fully connected graphs, in a clear agreement with our previous research (Artif. Intell. 141, pp. 175181).
Algorithms and incentives for robust ranking
 In Proceedings of the ACMSIAM Symposium on Discrete Algorithms (SODA ’07
, 2007
"... Spam in the form of link spam and click spam has become a major obstacle in the effective functioning of ranking and reputation systems. Even in the absence of spam, difficulty in eliciting feedback and selfreinforcing nature of ranking systems are known problems. In this paper, we make a case for ..."
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Cited by 13 (1 self)
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Spam in the form of link spam and click spam has become a major obstacle in the effective functioning of ranking and reputation systems. Even in the absence of spam, difficulty in eliciting feedback and selfreinforcing nature of ranking systems are known problems. In this paper, we make a case for sharing with users the revenue generated by such systems as incentive to provide useful feedback and present an incentive based ranking scheme in a realistic model of user behavior which addresses the above problems. We give an explicit ranking algorithm based on user feedback. Our incentive structure and ranking algorithm ensure that there is a profitable arbitrage opportunity for the users of the system in correcting the inaccuracies of the ranking. The system is oblivious to the source of inaccuracies (benign or
A geographic directed preferential Internet topology model
 In Proc. 13th IEEE Symp. Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS
, 2005
"... The goal of this work is to model the peering arrangements between Autonomous Systems (Ares). Most existing models of the ASgraph assume an undirected graph. However, peering arrangements are mostly asymmetric CustomerProvider arrangements, which are better modeled as directed edges. Furthermore, ..."
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Cited by 12 (3 self)
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The goal of this work is to model the peering arrangements between Autonomous Systems (Ares). Most existing models of the ASgraph assume an undirected graph. However, peering arrangements are mostly asymmetric CustomerProvider arrangements, which are better modeled as directed edges. Furthermore, it is well known that the ASgraph, and in particular its clustering structure, is influenced by geography. We introduce a new model that describes the ASgraph as a directed graph, with an edge going from the customer to the provider, but also models symmetric peertopeer arrangements, and takes geography into account. We are able to mathematically analyze its powerlaw exponent and number of leaves. Beyond the analysis, we have implemented our model as a synthetic network generator we call GDTANG. Experimentation with GDTANG shows that the networks it produces are more realistic than those generated by other network generators, in terms of its powerlaw exponent, fractions of customerprovider and symmetric peering arrangements, and the size of its dense core. We believe that our model is the first to manifest realistic regional dense cores that have a clear geographic flavor. Our synthetic networks also exhibit path inflation effects that are similar to those observed in the real AS graph.