By Evimaria Terzi, Marco Winkler (auth.), Alan Frieze, Paul Horn, Paweł Prałat (eds.)

ISBN-10: 3642212867

ISBN-13: 9783642212864

This e-book constitutes the refereed court cases of the eighth foreign Workshop on Algorithms and types for the Web-Graph, WAW 2011, held in Atlanta, GA, in may perhaps 2011 - co-located with RSA 2011, the fifteenth foreign convention on Random constructions and Algorithms.

The thirteen revised complete papers awarded including 1 invited lecture have been conscientiously reviewed and chosen from 19 submissions. Addressing a large choice of subject matters regarding the examine of the Web-graph equivalent to theoretical and empirical research, the papers characteristic unique learn when it comes to algorithmic and mathematical research in all components concerning the World-Wide internet with specific concentration to the view of advanced information as networks.

**Read or Download Algorithms and Models for the Web Graph: 8th International Workshop, WAW 2011, Atlanta, GA, USA, May 27-29, 2011. Proceedings PDF**

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**Extra info for Algorithms and Models for the Web Graph: 8th International Workshop, WAW 2011, Atlanta, GA, USA, May 27-29, 2011. Proceedings**

**Example text**

In social graphs, for large community size k, the (α, β)-communities are well clustered into a small number of disjoint cores, and there are no isolated (α, β)-communities scattered between these densely-clustered 28 J. He et al. cores. The number of cores decreases as k increases and becomes relatively small for large k. The cores obtained for a smaller k either disappear or merge into the cores obtained for a larger k. Moreover, the cores correspond to dense regions of the graph, and there are no bridges of intermediate (α, β)-communities connecting one core to another.

V t V s , and T ⊆ V t ¯ (s) |e(S, T ) − e(S)e(T )| ≤ λ ¯ T¯). e(S)e(T )e(S)e( r 2. Due to the fact σ0 Now we consider the case that s > , let e(S, T ) = (s) (4) = 1, we have to use the weaker expansion theorem 7 in [22]. Note that E r! t! V s , V t = We get the following theorem. Theorem 8. For 1 ≤ t < r2 < s < s + t ≤ r, S ⊆ Vs , and T ⊆ Vt , let )| e(S, T ) = |E(|E(S,T . If |x ∩ y| = min{t, 2s − r} for any x ∈ S and y ∈ T , then (Vs ),(Vt ))| we have 1 ¯ (s) e(S)e(T )e(S)e( ¯ T¯). | e(S, T ) − e(S)e(T )| ≤ λ (5) 2 Nevertheless, we have the following strong edge expansion theorem for r2 < s ≤ r − 1.

We see visually that there are nine natural clusters. More interestingly we see that these clusters are arranged symmetrically along two axes. , 9}. Instead they have the structure {1, 2, 3} × {1, 2, 3}. An example of such a structure would be the separation of academic papers along two factors, {Physics, Mathematics, Biology} and {West Coast, Midwest, East Coast}. The nine clusters (with examples like physics articles from the West or biology articles from the Midwest) have underlying structure.

### Algorithms and Models for the Web Graph: 8th International Workshop, WAW 2011, Atlanta, GA, USA, May 27-29, 2011. Proceedings by Evimaria Terzi, Marco Winkler (auth.), Alan Frieze, Paul Horn, Paweł Prałat (eds.)

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