PageRank, one part of the search engine Google, is one of the most prominent link-based rankings of documents in the World Wide Web. Usually it is described as a Markov chain modeling a specific random surfer. In this article, an alternative representation as a power series is given. Nonetheless, it is possible to interpret the values as probabilities in a random surfer setting, differing from the usual one.Using the new description we restate and extend some results concerning the convergence of the standard iteration used for PageRank. Furthermore we take a closer look at sinks and sources, leading to some suggestions for faster implementations.

In this paper we define a type of cohesive subgroups -called communities -in hypergraphs, based on the edge connectivity of subhypergraphs. We describe a simple algorithm for the construction of these sets and show, based on examples from image segmentation and information retrieval, that these groups may be useful for the analysis and accessibility of large graphs and hypergraphs.

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Using a peer-to-peer approach for live multimedia streaming applications offers the promise to obtain a highly scalable, decentralized, and robust distribution service. When constructing streaming topologies, however, specific care has to be taken in order to ensure that quality of service requirements in terms of delay, jitter, packet loss, and stability against deliberate denial of service attacks are met. In this paper, we concentrate on the latter requirement of stability against denial-of-service attacks. We present an analytical model to assess the stability of overlay streaming topologies and describe attack strategies. Building on this, we describe topologies, which are optimally stable toward perfect attacks based on global knowledge, and give a mathematical proof of their optimality. The formal construction and analysis of these topologies using global knowledge lead us to strategies for distributed procedures, which are able to construct resilient topologies in scenarios, where global knowledge can not be gathered. Experimental results show that the topologies created in such a real-world scenario are close to optimally stable toward perfect denial of service attacks.

This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively." Brinkmeier, Michael; Fischer, Mathias; Grau, Sascha; Schäfer, Günter; Strufe, Thorsten: Methods for improving resilience in communication networks and P2P overlays URN:urn:nbn:de:gbv:ilm1-2015210316