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In applications, finite weighted graphs represent a finite number of entities by the graph's vertices, any pairwise relationships between these entities by graph edges, and the significance of a relationship by an edge weight function.
In this graph, the widest path from Maldon to Feering has bandwidth 29, and passes through Clacton, Tiptree, Harwich, and Blaxhall. In graph algorithms, the widest path problem is the problem of finding a path between two designated vertices in a weighted graph, maximizing the weight of the minimum-weight edge in the path.
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph.A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges.
A planar graph and its minimum spanning tree. Each edge is labeled with its weight, which here is roughly proportional to its length. A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. [1]
A weighted directed graph associates a value (weight) with every edge in the directed graph. The weight of a directed walk (or trail or path) in a weighted directed graph is the sum of the weights of the traversed edges. Sometimes the words cost or length are used instead of weight.
A weighted graph or a network [9] [10] is a graph in which a number (the weight) is assigned to each edge. [11] Such weights might represent for example costs, lengths or capacities, depending on the problem at hand. Such graphs arise in many contexts, for example in shortest path problems such as the traveling salesman problem.
A directed graph is called weakly connected if replacing all of its directed edges with undirected edges produces a connected (undirected) graph. weight 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
In graph theory and combinatorial optimization, a closure of a directed graph is a set of vertices C, such that no edges leave C. The closure problem is the task of finding the maximum-weight or minimum-weight closure in a vertex-weighted directed graph. [1] [2] It may be solved in polynomial time using a reduction to the maximum flow problem.