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2. Calculus on finite weighted graphs - Wikipedia

   en.wikipedia.org/wiki/Calculus_on_finite...

   Calculus on finite weighted graphs is used in a wide range of applications from different fields such as image processing, machine learning, and network analysis. A non-exhaustive list of tasks in which finite weighted graphs have been employed is: image denoising [2] [3] image segmentation [4] image inpainting [2] [5] tomographic ...

3. Louvain method - Wikipedia

   en.wikipedia.org/wiki/Louvain_method

   represents the edge weight between nodes i and j; see Adjacency matrix; ⁠ ⁠ and ⁠ ⁠ are the sum of the weights of the edges attached to nodes i and j, respectively; m is the sum of all of the edge weights in the graph; N is the total number of nodes in the graph;

4. Graph theory - Wikipedia

   en.wikipedia.org/wiki/Graph_theory

   A graph structure can be extended by assigning a weight to each edge of the graph. Graphs with weights, or weighted graphs, are used to represent structures in which pairwise connections have some numerical values. For example, if a graph represents a road network, the weights could represent the length of each road.

5. Shortest path problem - Wikipedia

   en.wikipedia.org/wiki/Shortest_path_problem

   Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.

6. Johnson's algorithm - Wikipedia

   en.wikipedia.org/wiki/Johnson's_algorithm

   The first three stages of Johnson's algorithm are depicted in the illustration below. The graph on the left of the illustration has two negative edges, but no negative cycles. The center graph shows the new vertex q, a shortest path tree as computed by the Bellman–Ford algorithm with q as starting vertex, and the values h(v) computed at each other node as the length of the shortest path from ...

7. Reverse-delete algorithm - Wikipedia

   en.wikipedia.org/wiki/Reverse-delete_algorithm

   The next largest edge is FG so the algorithm will check if deleting this edge will further disconnect the graph. Since deleting the edge will not further disconnect the graph, the edge is then deleted. The next largest edge is edge BD so the algorithm will check this edge and delete the edge. The next edge to check is edge EG, which will not be ...

8. Minimum cut - Wikipedia

   en.wikipedia.org/wiki/Minimum_cut

   The dashed line in green represents one of the minimum cuts of this graph, crossing only two edges. [1] In graph theory, a minimum cut or min-cut of a graph is a cut (a partition of the vertices of a graph into two disjoint subsets) that is minimal in some metric. Variations of the minimum cut problem consider weighted graphs, directed graphs ...

9. Glossary of graph theory - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_graph_theory

   A numerical value, assigned as a label to a vertex or edge of a graph. The weight of a subgraph is the sum of the weights of the vertices or edges within that subgraph. weighted graph A graph whose vertices or edge s have been assigned weight s. A vertex-weighted graph has weights on its vertices and an edge-weighted graph has weights on its edges.