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In network theory, the Wiener connector is a means of maximizing efficiency in connecting specified "query vertices" in a network. Given a connected, undirected graph and a set of query vertices in a graph, the minimum Wiener connector is an induced subgraph that connects the query vertices and minimizes the sum of shortest path distances among all pairs of vertices in the subgraph. In combinatorial optimization, the minimum Wiener connector problem is the problem of finding the minimum Wiener connector. It can be thought of as a version of the classic Steiner tree problem (one of Karp's 21 NP-complete problems), where instead of minimizing the size of the tree, the objective is to minimize the distances in the subgraph.The minimum Wiener connector was first presented by Ruchansky et al. in 2015.The minimum Wiener connector has applications in many domains where there is a graph structure and an interest in learning about connections between sets of individuals. For example, given a set of patients infected with a viral disease, which other patients should be checked to find the culprit? Or given a set of proteins of interest, which other proteins participate in pathways with them?
The Wiener connector was named in honor of chemist Harry Wiener who first introduced the Wiener Index.

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