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We propose to measure the membership degree of a node (v) to a community (c) by the inverse of the minimal shortest path that links (v) to one of the leaders of (c).
To further illustrate obtaining such a correlation is nontrivial, we perform a negative control experiment by looking at the correlation between the "absolute" sporulation efficiency change caused by deleting a gene and the averaged or minimal shortest path from each gene to EMG and MMG.
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Furthermore, a characteristic of the tumor network not found on the normal was the existence of a small subset of low connected TFs with a remarkable contribution to minimal shortest paths (closeness centrality, see figure in Additional file 2).
Both clusters contain interactions with a minimal shortest-path length of 2, indicating that they are not embedded in complexes.
The aim of the classical VRP is finding a set of routes at a minimal cost (finding the shortest path, minimizing the number of vehicles, etc).
Yet Swift had made the bargain we all do: the Interstate highways "carried us without incident, without drama.They offered up food and lodging with minimal fuss.They carved the shortest path all the way home".
In this study, three optimization models have been considered: the modified minimal spanning tree, the shortest path and the out-of-kilter algorithms.
Network construction in ExPlain implements the Dijkstra algorithm as core to find the shortest path (minimal cost) tree whose reaction cascades are weighted by the sum of the involved edge costs.
The shortest path length, as minimal number of steps needed to reach one metabolite from another, allows working on a small subset of identified metabolites keeping in the same the information of the whole network structure.
Differently from the shortest path networks, the minimal connecting networks are quite compact.
As minimizing or constraining the average shortest path of a graph is difficult, we chose to look for a minimal set that also had a small radius.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com