Vertex (graph theory)

A vertex is an individual entity in a graph, connected to other vertices by edges. Vertices may represent abstract objects, places, people, or states.

Graph (discrete mathematics): A mathematical structure consisting of vertices and edges that connect pairs of vertices. A vertex is one of the two fundamental kinds of objects in a graph.
Path (graph theory): A path is a sequence of vertices in which consecutive vertices are joined by edges. A vertex can serve as an intermediate point or endpoint along a path.
Social network analysis: Social network analysis studies relationships among people, groups, or organizations using network models. Vertices can represent people or organizations, while edges encode their relationships.
Directed graph: A directed graph is a graph whose edges have orientations from one vertex to another. A vertex's incoming and outgoing connections differ when edges have direction.
Edge (graph theory): An edge is a connection between two vertices in a graph. Edges specify which other vertices a given vertex is connected to.
Connected component: A connected component is a maximal set of vertices joined to one another by paths. The component containing a vertex identifies everything reachable from it.
Road network: A road network is a graph-based representation of locations connected by roads. Intersections or places become vertices in models used for route planning.
Multigraph: A multigraph allows multiple edges between the same pair of vertices. Parallel edges can connect the same vertices without making them distinct.
Degree (graph theory): The degree of a vertex is the number of edges incident to it. Degree measures how many direct connections a vertex has.
Articulation point: An articulation point is a vertex whose removal increases the number of connected components. Some vertices hold a graph together because paths depend on them.

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