Netzes

Netzes is a term used to describe a class of network-like structures in mathematics and computer science. In this context, a netz (plural netze or netzes) is a collection of entities, called nodes, connected by relations, called edges, to model complex interdependencies among components. Netzes generalize standard data structures such as graphs and hypergraphs by supporting multiple edge types, directionality, optional weights, and higher-order relations among groups of nodes.

A netz consists of a set N of nodes and a set E of edges. Each edge pairs one or more nodes and may carry attributes such as direction, weight, or type. Some variants allow multiple parallel edges between the same nodes (multinet) or hyperedges that connect more than two nodes (hypernetz). Dynamic nets allow the node and edge sets to evolve over time.

Common operations on nets include computing paths and connectivity, identifying components, and measuring properties such as degree, centrality, and clustering. Nets can be combined through operations like union, intersection, and product, or decomposed into subnets and motifs. Visualization and algorithmic analysis of netzes draw on graph theory, network science, and related fields.

Applications for nets appear across disciplines: modeling social and communication networks, transportation and logistics, biological interaction networks, and knowledge graphs. In practice, specific domains may prefer established terms (graph, hypergraph, multiplex network) but may use netz terminology to emphasize higher-order or time-varying relations.

See also: graph theory, network science, hypergraph, multiplex network, dynamic network.