8,937 research outputs found
Detecting and Characterizing Small Dense Bipartite-like Subgraphs by the Bipartiteness Ratio Measure
We study the problem of finding and characterizing subgraphs with small
\textit{bipartiteness ratio}. We give a bicriteria approximation algorithm
\verb|SwpDB| such that if there exists a subset of volume at most and
bipartiteness ratio , then for any , it finds a set
of volume at most and bipartiteness ratio at most
. By combining a truncation operation, we give a local
algorithm \verb|LocDB|, which has asymptotically the same approximation
guarantee as the algorithm \verb|SwpDB| on both the volume and bipartiteness
ratio of the output set, and runs in time
, independent of the size of the
graph. Finally, we give a spectral characterization of the small dense
bipartite-like subgraphs by using the th \textit{largest} eigenvalue of the
Laplacian of the graph.Comment: 17 pages; ISAAC 201
Unifying Sparsest Cut, Cluster Deletion, and Modularity Clustering Objectives with Correlation Clustering
Graph clustering, or community detection, is the task of identifying groups
of closely related objects in a large network. In this paper we introduce a new
community-detection framework called LambdaCC that is based on a specially
weighted version of correlation clustering. A key component in our methodology
is a clustering resolution parameter, , which implicitly controls the
size and structure of clusters formed by our framework. We show that, by
increasing this parameter, our objective effectively interpolates between two
different strategies in graph clustering: finding a sparse cut and forming
dense subgraphs. Our methodology unifies and generalizes a number of other
important clustering quality functions including modularity, sparsest cut, and
cluster deletion, and places them all within the context of an optimization
problem that has been well studied from the perspective of approximation
algorithms. Our approach is particularly relevant in the regime of finding
dense clusters, as it leads to a 2-approximation for the cluster deletion
problem. We use our approach to cluster several graphs, including large
collaboration networks and social networks
Querying cohesive subgraphs by keywords
© 2018 IEEE. Keyword search problem has been widely studied to retrieve related substructures from graphs for a keyword set. However, existing well-studied approaches aim at finding compact trees/subgraphs containing the keywords, and ignore a critical measure, density, to reflect how strongly and stablely the keyword nodes are connected in the substructure. In this paper, we study the problem of finding a cohesive subgraph containing the query keywords based on the k-Truss model, and formulate it as minimal dense truss search problem, i.e., finding minimal subgraph with maximum trussness covering the keywords. We first propose an efficient algorithm to find the dense truss with the maximum trussness containing keywords based on a novel hybrid KT-Index (Keyword-Truss Index). Then, we develop a novel refinement approach to extract the minimal dense truss based on the anti-monotonicity property of k-Truss. Experimental studies on real datasets show the outperformance of our method
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