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111
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 2591 (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.
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 257 (6 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 COMPUT SURV (CSUR
, 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 in ..."
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Cited by 131 (7 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.
Directed ScaleFree Graphs
"... We introduce a model for directed scalefree graphs that grow with preferential attachment depending in a natural way on the in and outdegrees. We show that the resulting in and outdegree distributions are power laws with different exponents, reproducing observed properties of the worldwide web. ..."
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Cited by 74 (5 self)
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We introduce a model for directed scalefree graphs that grow with preferential attachment depending in a natural way on the in and outdegrees. We show that the resulting in and 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.
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 65 (5 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.
The richclub phenomenon in the Internet topology
 IEEE Comm. Lett
"... Abstract—We show that the Internet topology at the autonomous system (AS) level has a richclub phenomenon. The rich nodes, which are a small number of nodes with large numbers of links, are very well connected to each other. The richclub is a core tier that we measured using the richclub connect ..."
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Cited by 53 (11 self)
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Abstract—We show that the Internet topology at the autonomous system (AS) level has a richclub phenomenon. The rich nodes, which are a small number of nodes with large numbers of links, are very well connected to each other. The richclub is a core tier that we measured using the richclub connectivity and the nodenode link distribution. We obtained this core tier without any heuristic assumption between the ASs. The richclub phenomenon is a simple qualitative way to differentiate between power law topologies and provides a criterion for new network models. To show this, we compared the measured richclub of the AS graph with networks obtained using the Barabási–Albert (BA) scalefree network model, the Fitness BA model and the Inet–3.0 model. Index Terms—Internet, modeling, networks, topology. I.
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 31 (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 25 (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).