Weighted network¶
A network whose edges carry numerical weights representing strength, capacity, cost, frequency, distance or another declared relation magnitude.
Core Idea¶
Weight semantics and direction must be explicit, larger can mean stronger or more costly, absent edges differ from zero-weight edges and many unweighted metrics require adapted definitions. Each node pair’s relation is assigned a numeric value, producing a weighted adjacency matrix whose aggregation and path rules quantify intensity, cost and heterogeneous connectivity. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Weighted network belongs to network science and is useful where the analyst can specify the typed network science carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the node and edge sets, directedness and multiplicity, weight domain units and semantics, zero missing and negative-value conventions, weighted adjacency representation, node strength, path-composition rule, normalization and thresholding and weighted versions of distance clustering centrality and community analysis are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the node and edge sets, directedness and multiplicity, weight domain units and semantics, zero missing and negative-value conventions, weighted adjacency representation, node strength, path-composition rule, normalization and thresholding and weighted versions of distance clustering centrality and community analysis are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Weighted network. Weighted network compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed network science carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the node and edge sets, directedness and multiplicity, weight domain units and semantics, zero missing and negative-value conventions, weighted adjacency representation, node strength, path-composition rule, normalization and thresholding and weighted versions of distance clustering centrality and community analysis are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of network science because they reuse the typed network science carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, Each node pair’s relation is assigned a numeric value, producing a weighted adjacency matrix whose aggregation and path rules quantify intensity, cost and heterogeneous connectivity., and type the carrier, state every parameter and convention in the definition, test that the node and edge sets, directedness and multiplicity, weight domain units and semantics, zero missing and negative-value conventions, weighted adjacency representation, node strength, path-composition rule, normalization and thresholding and weighted versions of distance clustering centrality and community analysis are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Weighted network Domain-specific
Parents (1) — more general patterns this builds on
-
Weighted network is a kind of Relation Prime
The proposed strict upward parent is
prime:relation.
Hierarchy path (1) — routes to 1 parentless root
- Weighted network → Relation
Neighborhood in Abstraction Space¶
Weighted network sits in a crowded region of the domain-specific corpus (14th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Network Evolution & Community Structure (19 abstractions)
Nearest neighbors
- Modularity (networks) — 0.94
- Fitness model (network theory) — 0.93
- Community structure — 0.93
- Louvain method — 0.92
- Biased random walk on a graph — 0.91
Computed from structural-signature embeddings · 2026-09-08