mérést

Mérést is a fictional unit of measurement used in discussions of network theory to quantify redundancy and resilience in complex systems. Although it does not appear in official standards, it is sometimes employed in thought experiments and pedagogical texts to compare how different network topologies respond to component failures.

A common formulation treats mérést as the average number of edge-disjoint paths between a randomly chosen pair of nodes, normalized by the maximum possible number of edge-disjoint paths for that pair in a complete graph with the same number of nodes. In a graph with N nodes, the maximum is N−1, so the value of mérést lies between 0 and 1. This definition emphasizes alternative routing capacity and fault tolerance by counting independent routes that do not share edges.

Examples help illustrate the idea. In a simple cycle (ring) of N nodes, any pair of nodes is connected by two edge-disjoint paths, yielding an average of 2; thus mérést ≈ 2/(N−1). In a fully connected graph, there are N−1 edge-disjoint paths between any two nodes, so mérést equals 1. Other topologies produce values between these extremes, reflecting their relative redundancy.

Usage and variations. Because mérést is not standardized, different authors may use slightly different definitions—edge-disjoint versus vertex-disjoint paths, or alternative normalizations. It is primarily a conceptual tool for comparing resilience in network design and education, rather than a universally accepted metric. See also redundancy, network topology, fault tolerance.