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Stochastic kronecker graphs
 Proceedings of the 5th Workshop on Algorithms and Models for the WebGraph
, 2007
"... A random graph model based on Kronecker products of probability matrices has been recently proposed as a generative model for largescale realworld networks such as the web. This model simultaneously captures several wellknown properties of realworld networks; in particular, it gives rise to a he ..."
Abstract

Cited by 27 (2 self)
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A random graph model based on Kronecker products of probability matrices has been recently proposed as a generative model for largescale realworld networks such as the web. This model simultaneously captures several wellknown properties of realworld networks; in particular, it gives rise to a heavytailed degree distribution, has a low diameter, and obeys the densification power law. Most properties of Kronecker products of graphs (such as connectivity and diameter) are only rigorously analyzed in the deterministic case. In this paper, we study the basic properties of stochastic Kronecker products based on an initiator matrix of size two (which is the case that is shown to provide the best fit to many realworld networks). We will show a phase transition for the emergence of the giant component and another phase transition for connectivity, and prove that such graphs have constant diameters beyond the connectivity threshold, but are not searchable using a decentralized algorithm. 1
Optimized Graph Search using Multi Level Graph Clustering
, 2009
"... Abstract. Graphs find a variety of use in numerous domains especially because of their capability to model common problems. The social networking graphs that are used for social networking analysis, a feature given by various social networking sites are an example of this. Graphs can also be visual ..."
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Abstract. Graphs find a variety of use in numerous domains especially because of their capability to model common problems. The social networking graphs that are used for social networking analysis, a feature given by various social networking sites are an example of this. Graphs can also be visualized in the search engines to carry search operations and provide results. Various searching algorithms have been developed for searching in graphs. In this paper we propose that the entire network graph be clustered. The larger graphs are clustered to make smaller graphs. These smaller graphs can again be clustered to further reduce the size of graph. The search is performed on the smallest graph to identify the general path, which may be further build up to actual nodes by working on the individual clusters involved. Since many searches are carried out on the same graph, clustering may be done once and the data may be used for multiple searches over the time. If the graph changes considerably, only then we may recluster the graph.