Better Fewer but Better: Community Search with Outliers
Francesco Bonchi, Lorenzo Severini, Mauro Sozio

TL;DR
This paper introduces a novel community search approach that allows dropping outliers among query vertices to find more meaningful, cohesive subgraphs, addressing limitations of existing methods that include all query vertices.
Contribution
It studies community search with outliers, proposing algorithms for optimizing cohesiveness measures while dropping up to k query vertices, and analyzes their computational complexity.
Findings
Proposed algorithms for community search with outliers.
Analyzed hardness of the optimization problems.
Provided exact and approximation algorithms.
Abstract
Given a set of vertices in a network, that we believe are of interest for the application under analysis, community search is the problem of producing a subgraph potentially explaining the relationships existing among the vertices of interest. In practice this means that the solution should add some vertices to the query ones, so to create a connected subgraph that exhibits some "cohesiveness" property. This problem has received increasing attention in recent years: while several cohesiveness functions have been studied, the bulk of the literature looks for a solution subgraphs containing all the query vertices. However, in many exploratory analyses we might only have a reasonable belief about the vertices of interest: if only one of them is not really related to the others, forcing the solution to include all of them might hide the existence of much more cohesive and meaningful…
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