Meshedness coefficient¶
In graph theory, the meshedness coefficient is a graph invariant of planar graphs that measures the number of bounded faces of the graph, as a fraction of the possible number of faces for other planar graphs with the same number of vertices.
Core Idea¶
Meshedness coefficient is treated here as the recurring mathematics, logic, and statistics identity summarized by this source-grounded definition: In graph theory, the meshedness coefficient is a graph invariant of planar graphs that measures the number of bounded faces of the graph, as a fraction of the possible number of faces for other planar graphs with the same number of vertices. In graph theory, the meshedness coefficient is a graph invariant of planar graphs that measures the number of bounded faces of the graph, as a fraction of the possible number of faces for other planar.
Scope of Application¶
-
Definition. The meshedness coefficient is used to compare the general cycle structure of a connected planar graph to two extreme relevant references.
-
Applications. The meshedness coefficient can be used to estimate the redundancy of a network.
-
Applications. This parameter along with the algebraic connectivity which measures the robustness of the network, may be used to quantify the topological aspect of network resilience in water distribution networks.
-
Applications. It has also been used to characterize the network structure of streets in urban areas.
-
Definition. The other extreme is represented by maximal planar graphs, planar graphs with the highest possible number of edges and faces for a given number of vertices.
Clarity¶
A clear use of Meshedness coefficient names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In graph theory, the meshedness coefficient is a graph invariant of planar graphs that measures the number of bounded faces of the graph, as a fraction of the possible number of faces for other planar graphs with the same number of vertices.
Manages Complexity¶
Meshedness coefficient compresses multiple mathematics, logic, and statistics details into a stable diagnostic relation. The source shows both the central mechanism—the meshedness coefficient is used to compare the general cycle structure of a connected planar graph to two extreme relevant references.—and the practical consequence—and that if there are m edges then the number of bounded faces is m − n + 1 (the same as the circuit rank of.
Abstract Reasoning¶
- Type the carrier. Identify the mathematics, logic, and statistics entities to which the claim applies.
- State the relation. Use the source-grounded identity: In graph theory, the meshedness coefficient is a graph invariant of planar graphs that measures the number of bounded faces of the graph, as a fraction of the possible number of faces for other planar graphs with the same number of vertices.
- Check operation and conditions.
Knowledge Transfer¶
Within the home domain. Knowledge about Meshedness coefficient transfers literally when a new case preserves the same carrier type, relation, and recognition test. The meshedness coefficient is used to compare the general cycle structure of a connected planar graph to two extreme relevant references. The meshedness coefficient can be used to estimate the redundancy of a network. Beyond the home domain. No canonical parent is asserted for Meshedness coefficient. An outside case receives the specialist name only when the same typed roles and rejection conditions can be filled literally; otherwise the comparison remains an analogy pending later graph densification.
Relationships to Other Abstractions¶
Current abstraction Meshedness coefficient Domain-specific
Parents (1) — more general patterns this builds on
-
Meshedness coefficient is a kind of Ratio Prime
Meshedness coefficient is a strict kind of Ratio: its frozen identity entails the parent's defining structure while adding domain-specific restrictions.
Hierarchy path (1) — routes to 1 parentless root
- Meshedness coefficient → Ratio → Comparison → Self Checking
Neighborhood in Abstraction Space¶
Meshedness coefficient sits in a sparse region of the domain-specific corpus (74th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Unclustered & Miscellaneous (2551 abstractions)
Nearest neighbors
- Even-hole-free graph — 0.84
- Tree (Graph Theory) — 0.83
- Maximal independent set — 0.83
- Moore graph — 0.83
- Cubic Graph — 0.82
Computed from structural-signature embeddings · 2026-10-08