Count edges in the complete simple graph Kₙ. Formula and complete-graph edges remain visible in one place for independent verification.
The count sets density denominators, tournament matchups, pairwise comparisons, and maximum simple-graph size.
A complete graph connects every unordered pair of distinct vertices, giving C(n,2)=n(n−1)/2 edges.
Pair each new vertex with every earlier vertex, or evaluate the binomial coefficient C(n,2).
An unexpected Complete Graph Edge result usually points to field assignment or operand order before it points to the algorithm.
K₈ has 28 edges because there are 28 unordered pairs among eight vertices. This Complete Graph Edge example can be compared with two-part restriction.
Directed graphs, loops, and parallel edges follow different counting rules. If the Complete Graph Edge assumptions do not fit, consider maximum comparison.
Kₙ can be checked from Kₙ₋₁ by adding n−1 new edges.
The result can also be recovered from degrees. Every vertex of Kₙ has degree n−1, so the degree sum is n(n−1); the handshaking lemma divides that sum by two because each edge touches two vertices. This independent route catches the common mistake of reporting n(n−1) edges.
Keep the Complete Graph Edge ordering and membership rules attached to Vertex count n. Read the result under that same Complete Graph Edge convention.
List a small nonempty Complete Graph Edge example. When allowed, compare it with an empty Complete Graph Edge case.
Trace Complete Graph Edge back through Vertex count n and the fixed condition. Those entries should support the displayed Complete-graph edges. For a sensitivity check, alter the fixed condition only. Compare that Complete Graph Edge result with the first Complete-graph edges, keeping both cases visible.
A complete graph connects every unordered pair of distinct vertices, giving C(n,2)=n(n−1)/2 edges.
The count sets density denominators, tournament matchups, pairwise comparisons, and maximum simple-graph size.
Directed graphs, loops, and parallel edges follow different counting rules.