Graph structure in the Web

Bröder, Arndt; Kumar, Ravi; Maghoul, Farzin; Raghavan, Prabhakar; Rajagopalan, Sridhar; Stata, Raymie; Tomkins, Andrew; Wiener, Joshua

doi:10.1016/s1389-1286(00)00083-9

Cited by 2,267 publications

(1,709 citation statements)

References 23 publications

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“…Then mH 0 (T (G)) = n i log m ni . Web graphs are known to have varying indegrees: a Zipf-distribution with parameter θ = 2.1 has been observed [2,10]. Under this distribution we obtain mH 0 (T (G)) = c · m log n + O(m), with c = ((θ − 1) i≥1 i −θ ) −1 ≈ 0.58.…”

Section: A Simple Representation Based On Binary Relationsmentioning

confidence: 82%

“…Many of the graph algorithms we mentioned are not disk-friendly, and thus the sizes of the graphs that can be analyzed by the Web mining applications, and consequently the quality of their results, is limited by the main memory size. Much effort has been spent in representing Web graphs in compressed form, so that the direct neighbors of a node can be efficiently retrieved [10,1,30,8,13]. Boldi and Vigna [8] achieve currently the least space combined with efficient navigation.…”

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confidence: 99%

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Extended Compact Web Graph Representations

Claude

Navarro

2010

Algorithms and Applications

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Abstract. Many relevant Web mining tasks translate into classical algorithms on the Web graph. Compact Web graph representations allow running these tasks on larger graphs within main memory. These representations at least provide fast navigation (to the neighbors of a node), yet more sophisticated operations are desirable for several Web analyses. We present a compact Web graph representation that, in addition, supports reverse navigation (to the nodes pointing to the given one). The standard approach to achieve this is to represent the graph and its transpose, which basically doubles the space requirement. Our structure, instead, represents the adjacency list using a compact sequence representation that allows finding the positions where a given node v is mentioned, and answers reverse navigation using that primitive. This is combined with a previous proposal based on grammar compression of the adjacency list. The combination yields interesting algorithmic problems. As a result, we achieve the smallest graph representation reported in the literature that supports direct and reverse navigation, and also obtain other variants that occupy relevant niches in the space/time tradeoff.

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Section: A Simple Representation Based On Binary Relationsmentioning

confidence: 82%

mentioning

confidence: 99%

Extended Compact Web Graph Representations

Claude

Navarro

2010

Algorithms and Applications

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“…The cell's network topology, therefore, seems to belong to the category of scale-free networks. Surprisingly, this network topology, encompassing thousands of nodes, also describes nonbiologic systems such as the world wide web (domain level) and social networks, whose study first revealed some of these networks' key characteristics (17,(22)(23)(24)(25). It should be noted that this scale-free network conclusion is based on mixed data sets (micro arrays, two hybrid screens, etc.…”

Section: The Cell's Networkmentioning

confidence: 97%

“…The cell's scale-free network uniquely exhibits the combination of a very short characteristic path length and a high clustering coefficient (16,17,19,21,22,24,30). A network could have a local path length within clusters and a different global path length spanning the network beyond the clusters.…”

Section: Scale-free Networkmentioning

confidence: 99%

Exploring the cell's network with molecular imaging

Enzmann

2006

Magnetic Resonance Imaging

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Molecular imaging is already a powerful tool for investigating molecular interactions within the cell. Interpreting molecular imaging findings will, however, take us into the more unfamiliar, nonlinear realm of networks. The network class of interest is the "scale-free" network, which characterizes not only the cell, but also surprisingly, other real work networks such as the world wide web. This network topology yields insights in how the cell is functionally organized via motifs, modules, and different types of hubs. Additional organizational information is gained from the cell's evolutionary history. Interpretation of molecular images will be deepened by a both qualitative and quantitative knowledge of the cell's network. Importantly, cell network behavior can be independent of molecular detail. For this reason, the same molecule can serve different functions in different cells or even within the same cell. Since a scalefree network's behavior is likely to be nonlinear and exhibit emergent behavior, a degree of caution is prudent in assigning cause and effect to molecular imaging findings in our effort to reengineer some of the cell's functions. Molecular imagers will need to be cognizant of the level of organization in the cell's network they are interrogating.

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“…Then the degree distribution P D (k) follows a power-law P D (k) ∼ k −γ with γ = 3 for the BA model, while for the ER and WS models, it follows a Poisson distribution. Networks whose degree distribution follows a power-law, called scale-free (SF) networks [8], are ubiquitous in real-world networks such as the world-wide web [9][10][11], the Internet [12][13][14], the citation network [15] and the author collaboration network of scientific papers [16][17][18], and the metabolic networks in biological organisms [19]. On the other hand, there also exist random networks such as the actor network whose degree distribution follows a power-law but has a sharp cut-off in its tail [20].…”

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confidence: 99%

Universal Behavior of Load Distribution in Scale-Free Networks

Uoh¹,

Kahng²,

Kim³

2011

The Structure and Dynamics of Networks

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We study a problem of data packet transport in scale-free networks whose degree distribution follows a power-law with the exponent γ. Load, or betweenness centrality of a vertex is the accumulated total number of data packets passing through that vertex when every pair of vertices send and receive a data packet along the shortest path connecting the pair. It is found that the load distribution follows a power-law with the exponent δ ≈ 2.2(1), insensitive to different values of γ in the range, 2 < γ ≤ 3, and different mean degrees, which is valid for both undirected and directed cases. Thus, we conjecture that the load exponent is a universal quantity to characterize scale-free networks.

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Graph structure in the Web

Cited by 2,267 publications

References 23 publications

Extended Compact Web Graph Representations

Extended Compact Web Graph Representations

Exploring the cell's network with molecular imaging

Universal Behavior of Load Distribution in Scale-Free Networks

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