{"uid":"cap_wPg2QOEDD6--5HZPZpXCv","slug":"halowerk-simple-graph-complete-maximal-clique-family-verifier-9e2b2626","name":"Halowerk Simple Graph Complete Maximal Clique Family Verifier","description":"Verify the full vertex family of maximal cliques so overlapping all-to-all groups retain their identities.","url":"https://detect.halowerk.com/v1/F-REST-B15/simple-graph-complete-maximal-clique-family?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["cliques"],"properties":{"cliques":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["n","edges"],"properties":{"n":{"type":"integer","maximum":10,"minimum":1},"edges":{"type":"array","items":{"type":"array","items":{"type":"integer","maximum":12,"minimum":0},"maxItems":2,"minItems":2},"maxItems":100,"minItems":0}},"additionalProperties":false},"claim":{}},"additionalProperties":false}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_BKo8cXjq9QOVxuGLSvh5k","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Verifies that a submitted family of cliques constitutes the complete set of maximal cliques for a given simple graph, ensuring all overlapping all-to-all subgroups are accounted for.","exampleAgentPrompt":"Can you check whether the clique family I've listed covers all maximal cliques for my 5-node graph with edges [[0,1],[1,2],[2,3],[3,4],[0,4],[1,3]]? Here's the claimed clique set I want verified.","exampleUseCases":[{"title":"Community detection validation in social network","prompt":"I've built a 7-node friendship graph with edges [[0,1],[0,2],[1,2],[3,4],[3,5],[4,5],[2,3]] and identified these cliques: [[0,1,2],[3,4,5],[2,3]] — can you verify that this is the complete maximal clique family and nothing is missing?"},{"title":"Algorithm output correctness check","prompt":"My clique-finding algorithm returned a family of cliques for a 6-node graph with edges [[0,1],[1,2],[0,2],[3,4],[4,5],[3,5]] — please verify the output is correct and no maximal clique has been overlooked."},{"title":"Graph database integrity audit","prompt":"I need to confirm that the maximal clique family we stored for a 4-node graph with edges [[0,1],[1,2],[2,3],[0,3]] is still complete and accurate — can you run the verification against our claimed cliques?"}],"resultDescription":"The endpoint returns a verification result indicating whether the submitted clique family is exactly the complete set of maximal cliques for the given graph, flagging any missing or spurious cliques and confirming that all overlapping all-to-all subgroups retain their identities.","failureModes":["Graph too large (n > 10 nodes) returns a validation error","Edge list exceeds 100 edges, triggering a schema rejection","Node indices in edges exceed n-1, causing an invalid graph error","Malformed clique claim structure returns a 400 bad request","Claimed cliques contain non-existent edges, resulting in a verification failure response"],"whenToPreferThis":"Choose this endpoint when you need to formally verify the completeness of a maximal clique enumeration on a small simple graph (up to 10 nodes, 100 edges) rather than computing cliques from scratch. It is ideal for validating algorithm outputs, auditing stored clique families, or confirming that community detection results are exhaustive.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:38:43.201Z","isFirstParty":false,"canonicalSlug":"halowerk-simple-graph-complete-maximal-clique-family-verifier-9e2b2626"}