Skew-symmetric graph¶
In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by reversing all of its edges, under an isomorphism that is an involution without any fixed points.
Core Idea¶
Skew-symmetric graph is treated here as the recurring computer science and information systems identity summarized by this source-grounded definition: In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by reversing all of its edges, under an isomorphism that is an involution without any fixed points. In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by reversing all of its edges, under an isomorphism.
Scope of Application¶
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Polar/switch graphs, double covering graphs, and bidire. This equivalence is the one used by to model problems of matching in terms of skew-symmetric graphs; in that application, the two subsets of edges at each vertex are the unmatched.
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Definition. As defined, e.g., by , a skew-symmetric graph G is a directed graph, together with a function σ mapping vertices of G to other vertices of G, satisfying the following properties.
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Definition. One may use the third property to extend σ to an orientation-reversing function on the edges of G.
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Matching. If the length function is allowed to have negative lengths, the existence of a negative regular cycle may be tested in polynomial time.
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Matching. Given additionally a non-negative length function on the edges of the graph that assigns the same length to any edge e and to σ(e), the shortest regular path connecting a.
Clarity¶
A clear use of Skew-symmetric graph 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, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by reversing all of its edges, under an isomorphism that is an involution without any fixed points.
Manages Complexity¶
Skew-symmetric graph compresses multiple computer science and information systems details into a stable diagnostic relation. The source shows both the central mechanism—if such a partition exists, a satisfying assignment may be formed by assigning a true value to every variable in S and a false value to every variable in σ(S).—and the practical consequence—as defined, e.g., by , a skew-symmetric graph G is a directed graph.
Abstract Reasoning¶
- Type the carrier. Identify the computer science and information systems entities to which the claim applies.
- State the relation. Use the source-grounded identity: In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by reversing all of its edges, under an isomorphism that is an involution without any fixed points.
- Check operation and conditions.
Knowledge Transfer¶
Within the home domain. Knowledge about Skew-symmetric graph transfers literally when a new case preserves the same carrier type, relation, and recognition test. This equivalence is the one used by to model problems of matching in terms of skew-symmetric graphs; in that application, the two subsets of edges at each vertex are the unmatched edges and the matched edges. As defined, e.g., by , a skew-symmetric graph G is a.
Relationships to Other Abstractions¶
Current abstraction Skew-symmetric graph Domain-specific
Parents (1) — more general patterns this builds on
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Skew-symmetric graph is a kind of Network Prime
Skew-symmetric graph is a domain-specific kind of network under its frozen identity and differentia.
Hierarchy path (1) — routes to 1 parentless root
- Skew-symmetric graph → Network → Reservoir-Flux Network → Conservation Laws → Invariance
Neighborhood in Abstraction Space¶
Skew-symmetric graph sits in a moderately populated region (41st percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Data Structures & Graph Variants (17 abstractions)
Nearest neighbors
- Block Graph — 0.88
- Graph Toughness — 0.88
- Split graph — 0.88
- Maximal independent set — 0.87
- Graph isomorphism — 0.86
Computed from structural-signature embeddings · 2026-10-08