Associationsheight

Associationsheight is a term used in discussions of knowledge representation and cognitive science to describe a metric for the vertical depth of an associative network. It captures how far, on average, concepts lie from core concepts within a network of associations and thus provides a coarse measure of the hierarchical complexity of the knowledge structure.

Definition. Given a directed graph G=(V,E) where nodes are concepts and directed edges indicate associative links, a root set R⊆V represents core concepts. For a node v, define its height h(v) as the length of the longest directed path from any root r∈R to v. The associationsheight AH(G) can be defined as the mean height AH(G) = (1/|V|) Σ_{v∈V} h(v), or in alternative form as the height distribution across V. Variants may weight edges by confidence.

Measurement and computation. To compute AH, extract a knowledge graph from text corpora or interaction data, identify roots, and compute heights. If cycles exist, roots can be assigned or the graph transformed into a DAG by condensation of strongly connected components; longest-path algorithms (dynamic programming for DAGs) yield h(v).

Applications. AH can be used in evaluating semantic search, structuring knowledge graphs, or studying cognitive organization of concepts in experiments. It offers a scalable summary of how deeply an associative network is built around core ideas.

Limitations. The value depends on root selection, edge definitions, and data quality. Different corpora or extraction methods yield different AH values. Critics note that height alone may obscure breadth, centrality, or link strength; thus AH is best used with complementary metrics such as centrality or clustering.

See also: semantic network, knowledge graph, graph depth, longest-path problem.