Weighted graph

A weighted graph is a graph whose edges carry numerical values called weights. These values can represent quantities such as distance, cost, capacity, or strength.

Graph theory: The mathematical study of graphs, structures made of vertices connected by edges. Weighted graphs extend ordinary graph structures by attaching values to edges.
Shortest path problem: The problem of finding a path between vertices with minimum total edge cost. It treats edge weights as costs and combines them along candidate paths.
Transportation network: A network of routes and transfer points used to move people or goods. Edge weights can encode travel time, distance, fares, or transport capacity.
Unweighted graph: A graph whose edges have no numerical weights assigned to them. It preserves connectivity while omitting the edge values that distinguish weighted graphs.
Vertex (graph theory): A vertex is a point in a graph representing an entity or state. Vertices are the endpoints between which weighted edges express relationships.
Dijkstra's algorithm: An algorithm for finding shortest paths from one source when all edge weights are nonnegative. It efficiently solves a central route-finding problem on nonnegative weighted graphs.
Social network analysis: The study of relationships and structures among people, groups, or organizations using network methods. Weighted ties can represent interaction frequency, trust, or relationship strength.
Weighted directed graph: A directed graph whose edges carry numerical weights. It combines edge values with orientation, a common variant of weighted graphs.
Edge (graph theory): An edge is a connection between two vertices in a graph. Weights are attached to these connections.
Bellman–Ford algorithm: An algorithm that finds single-source shortest paths and detects reachable negative-weight cycles. It handles negative edge weights that Dijkstra's algorithm cannot generally accommodate.

Linked from 12 pages