Edge (graph theory)

An edge is a connection between two vertices in a graph. Depending on the graph, it may be undirected or directed, weighted or unweighted, and may connect a vertex to itself.

Graph (discrete mathematics): A graph is a mathematical structure consisting of vertices and edges that encode relationships. Edges are the connecting elements in this broader mathematical structure.
Directed graph: A directed graph is a graph whose edges have orientations, distinguishing an edge from one vertex to another from the reverse. An edge's orientation determines which endpoint is its source and which is its target.
Shortest path problem: The shortest path problem seeks a least-cost route between vertices in a graph. Edge lengths or weights determine the cost of each candidate route.
Arc (graph theory): An arc is an oriented connection between vertices, especially in a directed graph. The term highlights orientation, unlike the usual undirected sense of edge.
Vertex (graph theory): A vertex is a point in a graph that may be joined to other vertices by edges. An edge is defined by the vertex or vertices it connects.
Weighted graph: A weighted graph assigns a numerical value to each edge, such as a cost, distance, or capacity. An edge weight adds quantitative information to the connection.
Minimum spanning tree: A minimum spanning tree is a least-weight set of edges connecting every vertex in a connected weighted graph without cycles. It selects edges that connect all vertices at minimum total weight.
Hypergraph: A hypergraph is a structure whose hyperedges can connect any number of vertices. Its connections can involve more than the two endpoints typical of graph edges.
Incidence (graph theory): Incidence is the relation between a graph's vertices and edges, indicating which vertices are endpoints of which edges. It formalizes how edges attach to their endpoints.
Loop (graph theory): A loop is an edge whose two endpoints are the same vertex. It is the special case in which an edge returns to its starting vertex.

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