grafstrukturen

Grafstrukturen refers to the study of graphs in mathematics and computer science. A graph consists of a set of vertices (also called nodes) and a set of edges that connect pairs of vertices. Edges may be undirected, meaning a connection has no direction, or directed (arcs), in which case each edge has a source and a target. Graphs can be represented in memory by an adjacency matrix or an adjacency list, and they provide a convenient abstraction for modeling relationships and interactions in many systems.

Common graph types include simple graphs (no loops or multiple edges), multigraphs (allowing parallel edges), weighted graphs (edges carry a numeric value), directed graphs, bipartite graphs (vertices split into two sets with edges only across), and planar graphs (that can be drawn on a plane without crossing edges).

Key concepts include degree (number of incident edges), path (a sequence of edges connecting vertices), cycle (a closed path), connectivity (whether any two vertices can be joined by a path), and components (maximal connected subgraphs). Subgraphs, induced subgraphs, and spanning trees are important constructions. Graph isomorphism asks whether two graphs have the same structure, ignoring labeling.

Graph algorithms address many problems, such as finding shortest paths (Dijkstra, Bellman-Ford), traversing graphs (breadth-first and depth-first search), detecting cycles, and computing minimum spanning trees (Kruskal, Prim). Applications span computer networks, social networks, transportation, scheduling, chemistry, and circuit design. Graph theory provides a flexible, abstraction-friendly framework for analyzing relational data.