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209
Towards Capturing Representative ASLevel Internet Topologies
 Computer Networks Journal
, 2002
"... Recent studies concerning the Internet connectivity at the AS level have attracted considerable attention. These studies have exclusively relied on the BGP data from Oregon routeviews [1] to derive some unexpected and intriguing results. The Oregon routeviews data sets reflect AS peering relations ..."
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Cited by 158 (22 self)
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Recent studies concerning the Internet connectivity at the AS level have attracted considerable attention. These studies have exclusively relied on the BGP data from Oregon routeviews [1] to derive some unexpected and intriguing results. The Oregon routeviews data sets reflect AS peering relationships, as reported by BGP, seen from a handful of vantage points in the global Internet. The possibility that these data sets from Oregon routeviews may provide only a very sketchy picture of the complete interAS connections that exist in the actual Internet has received surprisingly little scrutiny. In this paper, we will use the term "AS peering relationship" to mean that there is "at least one direct routerlevel connection" between two existing ASs, and that these two ASs agree to exchange traffic by enabling BGP between them. By augmenting the Oregon routeviews data sets with BGP summary information from a large number of Internet Looking Glass sites and with routing policy information from Internet Routing Registry (IRR) databases, we find that (1) a significant number of existing AS connections remain hidden from most BGP routing tables, (2) the AS connections to tier1 ASs are in general more easily observed than those to non tier1 ASs, and (3) there are at least about 2550% more AS connections in the Internet than commonlyused BGPderived AS maps reveal (but only about 2% more ASs). These findings point out the need for an increased awareness of and a more critical attitude toward the applicability and completeness of given data sets at hand when establishing the generality of any particular observations about the Internet.
The degree sequence of a scalefree random graph process. Random Structures and Algorithms
, 2001
"... ABSTRACT: Recently, Barabási and Albert [2] suggested modeling complex realworld networks such as the worldwide web as follows:consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number of earlier vertices, selected with probabilities proport ..."
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Cited by 157 (2 self)
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ABSTRACT: Recently, Barabási and Albert [2] suggested modeling complex realworld networks such as the worldwide web as follows:consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number of earlier vertices, selected with probabilities proportional to their degrees. In [2] and, with Jeong, in [3], Barabási and Albert suggested that after many steps the proportion P�d � of vertices with degree d should obey a power law P�d � α d −γ. They obtained γ = 2�9 ± 0�1 by experiment and gave a simple heuristic argument suggesting that γ = 3. Here we obtain P�d � asymptotically for all d ≤ n 1/15, where n is the number of vertices, proving as a consequence that γ = 3.
Measuring and Analyzing the Characteristics of Napster and Gnutella Hosts
, 2003
"... The popularity of peertopeer multimedia file sharing applications such as Gnutella and Napster has created a flurry of recent research activity into peertopeer architectures. We believe that the proper evaluation of a peertopeer system must take into account the characteristics of the peers th ..."
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Cited by 117 (0 self)
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The popularity of peertopeer multimedia file sharing applications such as Gnutella and Napster has created a flurry of recent research activity into peertopeer architectures. We believe that the proper evaluation of a peertopeer system must take into account the characteristics of the peers that choose to participate in it. Surprisingly, however, few of the peertopeer architectures currently being developed are evaluated with respect to such considerations. In this paper, we remedy this situation by performing a detailed measurement study of the two popular peertopeer file sharing systems, namely Napster and Gnutella. In particular, our measurement study seeks to characterize the population of enduser hosts that participate in these two systems. This characterization includes the bottleneck bandwidths between these hosts and the Internet at large, IPlevel latencies to send packets to these hosts, how often hosts connect and disconnect from the system, how many files hosts share and download, the degree of cooperation between the hosts, and several correlations between these characteristics. Our measurements show that there is significant heterogeneity and lack of cooperation across peers participating in these systems.
Mathematical results on scalefree random graphs
 Handbook of Graphs and Networks
, 2003
"... Recently there has been much interest in studying largescale realworld networks and attempting to model their properties using random graphs. Although the study of realworld networks as graphs goes back some time, recent activity perhaps started with the paper of Watts and Strogatz [55] about the ..."
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Cited by 103 (2 self)
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Recently there has been much interest in studying largescale realworld networks and attempting to model their properties using random graphs. Although the study of realworld networks as graphs goes back some time, recent activity perhaps started with the paper of Watts and Strogatz [55] about the ‘smallworld
The phase transition in inhomogeneous random graphs, preprint available from http://www.arxiv.org/abs/math.PR/0504589
"... Abstract. 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. ..."
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Cited by 98 (30 self)
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Abstract. 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
Collecting the Internet ASlevel Topology
 ACM SIGCOMM Computer Communications Review (CCR
, 2005
"... At the interdomain level, the Internet topology can be represented by a graph with Autonomous Systems (ASes) as nodes and AS peerings as links. This ASlevel topology graph has been widely used in a variety of research efforts. Conventionally this topology graph is derived from routing tables colle ..."
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Cited by 81 (11 self)
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At the interdomain level, the Internet topology can be represented by a graph with Autonomous Systems (ASes) as nodes and AS peerings as links. This ASlevel topology graph has been widely used in a variety of research efforts. Conventionally this topology graph is derived from routing tables collected by RouteViews or RIPE RIS. In this work, we assemble the most complete ASlevel topology by extending the conventional method along two dimensions. First, in addition to using data from RouteViews and RIPE RIS, we also collect data from many other sources, including route servers, looking glasses, and routing registries. Second, in addition to using routing tables, we also accumulate topological information from routing updates over time. The resulting topology graph on a recent day contains 44 % more links and 3 % more nodes than that from using RouteViews routing tables alone. Our data collection and topology generation process have been automated, and we publish the latest topology on the web on a daily basis. 1.
ON THE COVERINGS OF GRAPHS
, 1980
"... Let p(n) denote the smallest integer with the property that any graph with n vertices can be covered by p(n) complete bipartite subgraphs. We prove a conjecture of J.C. Bermond by showing p(n) = n + o(n 11’14+c) for any positive E. ..."
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Cited by 69 (6 self)
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Let p(n) denote the smallest integer with the property that any graph with n vertices can be covered by p(n) complete bipartite subgraphs. We prove a conjecture of J.C. Bermond by showing p(n) = n + o(n 11’14+c) for any positive E.
2005), 'Network dynamics and field evolution: The growth of interorganizational collaboration in the life sciences
 American Journal of Sociology
"... A recursive analysis of network and institutional evolution is offered to account for the decentralized structure of the commercial field of the life sciences. Four alternative logics of attachment—accumulative advantage, homophily, followthetrend, and multiconnectivity—are tested to explain the s ..."
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Cited by 64 (7 self)
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A recursive analysis of network and institutional evolution is offered to account for the decentralized structure of the commercial field of the life sciences. Four alternative logics of attachment—accumulative advantage, homophily, followthetrend, and multiconnectivity—are tested to explain the structure and dynamics of interorganizational collaboration in biotechnology. Using multiple novel methods, the authors demonstrate how different rules for affiliation shape network evolution. Commercialization strategies pursued by early corporate entrants are supplanted by universities, research institutes, venture capital, and small firms. As organizations increase their collaborative activities and diversify their ties to others, cohesive subnetworks form, characterized by multiple, independent pathways. These structural components, in turn, condition the choices and opportunities available to members of a field, thereby reinforcing an attachment logic based on differential connections to diverse partners.
Structural Cohesion and Embeddedness: A hierarchical conception of social groups.
 American Sociological Review
, 2000
"... While questions about social cohesion lie at the core of our discipline, definitions are often vague and difficult to operationalize. We link research on social cohesion and social embeddedness by developing a conception of structural cohesion based on network nodeconnectivity. Structural cohesion i ..."
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Cited by 58 (11 self)
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While questions about social cohesion lie at the core of our discipline, definitions are often vague and difficult to operationalize. We link research on social cohesion and social embeddedness by developing a conception of structural cohesion based on network nodeconnectivity. Structural cohesion is defined as the minimum number of actors who, if removed from a group, would disconnect the group. A structural dimension of embeddedness can then be defined through the hierarchical nesting of these cohesive structures. We demonstrate the empirical applicability of our conception of nestedness in two dramatically different substantive settings and discuss additional theoretical implications with reference to a wide array of substantive fields. "...social solidarity is a wholly moral phenomenon which by itself is not amenable to exact observation and especially not to measurement." (Durkheim, (1893 [1984], p.24) "The social structure [of the dyad] rests immediately on the one and on the other of the two, and the secession of either would destroy the whole. ... As soon, however, as there is a sociation of three, a group continues to exist even in case one of the members drops out." (Simmel (1908 [1950], p. 123)
Eigenvalues of Random Power Law Graphs
, 2003
"... Many graphs arising in various information networks exhibit the “power law” behavior – the number of vertices of degree k is proportional to k −β for some positive β. We show that if β > 2.5, the largest eigenvalue of a random power law graph is almost surely (1+o(1)) √ m where m is the maximum deg ..."
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Cited by 44 (7 self)
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Many graphs arising in various information networks exhibit the “power law” behavior – the number of vertices of degree k is proportional to k −β for some positive β. We show that if β > 2.5, the largest eigenvalue of a random power law graph is almost surely (1+o(1)) √ m where m is the maximum degree. When 2 < β < 2.5, the largest eigenvalue is heavily concentrated at cm 3−β for some constant c depending on β and the average degree. This result follows from a more general theorem which shows that the largest eigenvalue of a random graph with a given expected degree sequence is determined by m, the maximum degree, and ˜ d, the weighted average of the squares of the expected degrees. We show that λ is almost surely (1 + o(1)) max { ˜ d, √ m} provided some minor condition is satisfied. Our results have implications on the usage of spectral techniques in many areas related to pattern detection and information retrieval.