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...both computer science and physics communities, aimed at studying properties of large-scale real-world graphs. Power law degree distributions were also noted on the graph defined by the world-wide web =-=[21, 4]-=-. Broder et al [8] studied the world-wide web from a connectivity point of view and showed that it has a large strongly connected component. Several other studies have also shown that the average diam...

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...xplaining and analyzing friendships [18] and demonstrating the small-world and navigability properties of these graphs [23, 9, 1]. For surveys of analysis of large graphs, the readers are referred to =-=[29, 28, 2, 25, 11, 10, 16]-=-. Many of these above studies were performed on static graphs whereas most real-world graphs are evolving in nature. In fact, there are very papers that study the evolution of real-world graphs; this ...

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...” principle can be analytically shown to induce power-law degree distributions. Kleinberg [17, 15] proposed a model to explain the small-world phenomenon and navigability in social networks; see also =-=[30]-=-. Leskovec et al [22] proposed a forest-fire graph model to explain the decreasing diameter phenomenon observed in citation graphs. For a survey of mathematical analysis of some of these models, the r...

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...actable mathematical models for massive graphs. Because of their evolutionary nature and their power law degree distributions, these graphs cannot be modeled by traditional Erdö–Rényi random graphs =-=[12, 6]-=-. However, there have been a few alternate models that are more faithful to observed properties. One is the so-called configuration model, which chooses a graph uniformly at random from all graphs wit...

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...xplaining and analyzing friendships [18] and demonstrating the small-world and navigability properties of these graphs [23, 9, 1]. For surveys of analysis of large graphs, the readers are referred to =-=[29, 28, 2, 25, 11, 10, 16]-=-. Many of these above studies were performed on static graphs whereas most real-world graphs are evolving in nature. In fact, there are very papers that study the evolution of real-world graphs; this ...

Citation Context

...actable mathematical models for massive graphs. Because of their evolutionary nature and their power law degree distributions, these graphs cannot be modeled by traditional Erdö–Rényi random graphs =-=[12, 6]-=-. However, there have been a few alternate models that are more faithful to observed properties. One is the so-called configuration model, which chooses a graph uniformly at random from all graphs wit...

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...xplaining and analyzing friendships [18] and demonstrating the small-world and navigability properties of these graphs [23, 9, 1]. For surveys of analysis of large graphs, the readers are referred to =-=[29, 28, 2, 25, 11, 10, 16]-=-. Many of these above studies were performed on static graphs whereas most real-world graphs are evolving in nature. In fact, there are very papers that study the evolution of real-world graphs; this ...

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...verage distance, small-world phenomenon, clustering coefficient, connected components, community structures, etc. We briefly outline some of the work in this area. Faloutsos, Faloutsos, and Faloutsos =-=[13]-=- made a crucial observation showing that the degree distribution on the internet follow a power law. Subsequently, an intense body of work followed in both computer science and physics communities, ai...

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...selves to a pre-existing node with probability proportional to the degree of the latter. This “rich get richer” principle can be analytically shown to induce power-law degree distributions. Kleinberg =-=[17, 15]-=- proposed a model to explain the small-world phenomenon and navigability in social networks; see also [30]. Leskovec et al [22] proposed a forest-fire graph model to explain the decreasing diameter ph...

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...xplaining and analyzing friendships [18] and demonstrating the small-world and navigability properties of these graphs [23, 9, 1]. For surveys of analysis of large graphs, the readers are referred to =-=[29, 28, 2, 25, 11, 10, 16]-=-. Many of these above studies were performed on static graphs whereas most real-world graphs are evolving in nature. In fact, there are very papers that study the evolution of real-world graphs; this ...

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...ternate models that are more faithful to observed properties. One is the so-called configuration model, which chooses a graph uniformly at random from all graphs with a prescribed degree distribution =-=[5, 24, 26]-=-; the degree distribution can be set to match practical observations and is usually a power law. Another approach is to use a generative model to describe the evolution of graphs. A typical example is...

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...xplaining and analyzing friendships [18] and demonstrating the small-world and navigability properties of these graphs [23, 9, 1]. For surveys of analysis of large graphs, the readers are referred to =-=[29, 28, 2, 25, 11, 10, 16]-=-. Many of these above studies were performed on static graphs whereas most real-world graphs are evolving in nature. In fact, there are very papers that study the evolution of real-world graphs; this ...

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...ant impact on the connectivity of the remaining nodes. Over time, the average distance between users in the giant component is seen to fall. This surprising result has been observed in other settings =-=[22]-=-; we show it here for online social networks. Given these findings, we draw some high-level behavioral conclusions about the structure and evolution of online social networks. First, there are two dis...

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...ternate models that are more faithful to observed properties. One is the so-called configuration model, which chooses a graph uniformly at random from all graphs with a prescribed degree distribution =-=[5, 24, 26]-=-; the degree distribution can be set to match practical observations and is usually a power law. Another approach is to use a generative model to describe the evolution of graphs. A typical example is...

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...xplaining and analyzing friendships [18] and demonstrating the small-world and navigability properties of these graphs [23, 9, 1]. For surveys of analysis of large graphs, the readers are referred to =-=[29, 28, 2, 25, 11, 10, 16]-=-. Many of these above studies were performed on static graphs whereas most real-world graphs are evolving in nature. In fact, there are very papers that study the evolution of real-world graphs; this ...

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...l other studies have also shown that the average diameter of the web is quite small [8, 3]. Online friendship and email graphs have been studied in the context of explaining and analyzing friendships =-=[18]-=- and demonstrating the small-world and navigability properties of these graphs [23, 9, 1]. For surveys of analysis of large graphs, the readers are referred to [29, 28, 2, 25, 11, 10, 16]. Many of the...

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...ternate models that are more faithful to observed properties. One is the so-called configuration model, which chooses a graph uniformly at random from all graphs with a prescribed degree distribution =-=[5, 24, 26]-=-; the degree distribution can be set to match practical observations and is usually a power law. Another approach is to use a generative model to describe the evolution of graphs. A typical example is...

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...tical observations and is usually a power law. Another approach is to use a generative model to describe the evolution of graphs. A typical example is the copying or the preferential attachment model =-=[20, 4]-=-: nodes arrive one by one, and link themselves to a pre-existing node with probability proportional to the degree of the latter. This “rich get richer” principle can be analytically shown to induce po...

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...selves to a pre-existing node with probability proportional to the degree of the latter. This “rich get richer” principle can be analytically shown to induce power-law degree distributions. Kleinberg =-=[17, 15]-=- proposed a model to explain the small-world phenomenon and navigability in social networks; see also [30]. Leskovec et al [22] proposed a forest-fire graph model to explain the decreasing diameter ph...

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...ge pattern of blogs and the emergence of bursty communities in the blogspace [19]. Structural properties of different snapshots of the world-wide web graph was studied by Fetterly et al and Cho et al =-=[14, 27]-=-. Recently, Leskovec, Kleinberg, and Faloutsos [22] considered citation graphs and showed that these exhibit densification and shrinking diameters over time. A parallel body of work is concerned with ...

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...world-wide web from a connectivity point of view and showed that it has a large strongly connected component. Several other studies have also shown that the average diameter of the web is quite small =-=[8, 3]-=-. Online friendship and email graphs have been studied in the context of explaining and analyzing friendships [18] and demonstrating the small-world and navigability properties of these graphs [23, 9,...

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...ge pattern of blogs and the emergence of bursty communities in the blogspace [19]. Structural properties of different snapshots of the world-wide web graph was studied by Fetterly et al and Cho et al =-=[14, 27]-=-. Recently, Leskovec, Kleinberg, and Faloutsos [22] considered citation graphs and showed that these exhibit densification and shrinking diameters over time. A parallel body of work is concerned with ...

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... [8, 3]. Online friendship and email graphs have been studied in the context of explaining and analyzing friendships [18] and demonstrating the small-world and navigability properties of these graphs =-=[23, 9, 1]-=-. For surveys of analysis of large graphs, the readers are referred to [29, 28, 2, 25, 11, 10, 16]. Many of these above studies were performed on static graphs whereas most real-world graphs are evolv...

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... [8, 3]. Online friendship and email graphs have been studied in the context of explaining and analyzing friendships [18] and demonstrating the small-world and navigability properties of these graphs =-=[23, 9, 1]-=-. For surveys of analysis of large graphs, the readers are referred to [29, 28, 2, 25, 11, 10, 16]. Many of these above studies were performed on static graphs whereas most real-world graphs are evolv...

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...roposed a forest-fire graph model to explain the decreasing diameter phenomenon observed in citation graphs. For a survey of mathematical analysis of some of these models, the readers are referred to =-=[7, 16]-=-. 3. MEASUREMENTS In this section we detail our study on two online social networks at Yahoo!. Each social network is presented as a directed time graph G = (V,E), i.e., every node v ∈ V and directed ...

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...xplaining and analyzing friendships [18] and demonstrating the small-world and navigability properties of these graphs [23, 9, 1]. For surveys of analysis of large graphs, the readers are referred to =-=[29, 28, 2, 25, 11, 10, 16]-=-. Many of these above studies were performed on static graphs whereas most real-world graphs are evolving in nature. In fact, there are very papers that study the evolution of real-world graphs; this ...

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...n time and use these snapshots to make inferences about the evolutionary process. This approach was used to study the linkage pattern of blogs and the emergence of bursty communities in the blogspace =-=[19]-=-. Structural properties of different snapshots of the world-wide web graph was studied by Fetterly et al and Cho et al [14, 27]. Recently, Leskovec, Kleinberg, and Faloutsos [22] considered citation g...

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...both computer science and physics communities, aimed at studying properties of large-scale real-world graphs. Power law degree distributions were also noted on the graph defined by the world-wide web =-=[21, 4]-=-. Broder et al [8] studied the world-wide web from a connectivity point of view and showed that it has a large strongly connected component. Several other studies have also shown that the average diam...