1959
DOI: 10.1007/bf01386390
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A note on two problems in connexion with graphs

Abstract: We consider a points (nodes), some or all pairs of which are connected by a branch; the length of each branch is given. We restrict ourselves to the case where at least one path exists between any two nodes. We now consider two problems.

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Cited by 19,662 publications
(10,286 citation statements)
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“…This is performed with the algorithm of Dijkstra. [10] In order to detect further potential pathways of interest, all edges of the current MCP are removed, then Dijkstra's algorithm is applied again, and so on until no new MCP can be found. An example of MCP is displayed in Figure 1.…”
Section: Methodsmentioning
confidence: 99%
“…This is performed with the algorithm of Dijkstra. [10] In order to detect further potential pathways of interest, all edges of the current MCP are removed, then Dijkstra's algorithm is applied again, and so on until no new MCP can be found. An example of MCP is displayed in Figure 1.…”
Section: Methodsmentioning
confidence: 99%
“…This insures that graph nodes are only connected to their closest neighbors. Given the Planning Graph, the optimal path to the goal is determined by the activation-diffusion mechanism (Burnod 1991;Hasselmo 2005), based on the Dijkstra's algorithm for finding the shortest path between two nodes in a graph (Dijkstra 1959). More specifically, during goal planning, the Planning expert first determines its location using a position value and then calculates the direction toward the goal using goal value.…”
Section: Planning Expertmentioning
confidence: 99%
“…This distance corresponds to the radii of the largest spherical probe that can, respectively, be placed at the node or travel along the edge, without colliding with any atom. For a particular probe radius (for example, 1.625 Å for CH 4 probe), a graph propagation algorithm-a variation of the Dijkstra shortest path algorithm 35 -is then used to identify the probe-accessible regions of the Voronoi network, v. v is a periodic subgraph representing the guest-molecule-accessible region of the void space. Voronoi networks obtained for different materials can be compared to produce a measure of shape similarity between the void space networks of materials.…”
Section: ' Introductionmentioning
confidence: 99%