Graafimalli

Graafimalli, or graph model, is a formal representation used to describe relationships between objects. In its simplest form it consists of a set V of vertices (nodes) and a set E of edges (links) connecting pairs of vertices. Edges may be directed or undirected, and may carry weights or attributes that quantify the strength or type of the relationship. Depending on constraints, a graafimalli can be simple (no parallel edges or loops) or more complex as a multigraph or pseudograph.

Components and types: A directed graph (digraph) uses ordered pairs for edges, capturing direction. An undirected graph uses unordered pairs. Weighted graphs assign a numeric value to edges. A property graph associates attributes with both vertices and edges. Graphs can be represented in memory as adjacency lists or matrices and are stored in specialized databases known as graph databases or as RDF/knowledge graphs in semantic web contexts.

Applications and analysis: Graph models underpin network analysis across domains such as social networks, transportation, telecommunications, biology, and information retrieval. Common tasks include determining connectivity, finding paths (shortest, all, or specific types), ranking nodes by centrality, and detecting communities or clusters. Many algorithms exist, like Dijkstra’s for shortest paths, Prim’s and Kruskal’s for minimum spanning trees, and PageRank for node importance.

Relation to data modeling: In databases, graafimallit enable natural representation of entities and their relationships. They support queries about relationships and can scale to large, interconnected datasets using graph processing frameworks and graph databases.