MathNetwork/MathlibGraph
MathlibGraph: The Multinetwork of Mathlib Dependency graph of Mathlib (commit 534cf0b, 2 Feb 2026), the largest formal mathematics library for Lean 4 (v4.28.0-rc1). Three dependency layers (declarations, modules, namespaces), each with nodes, edges, and precomputed network metrics. Quick Stats Declarations Modules Namespaces (k=2) Nodes 308,129 7,564 10,097 Edges 8,436,366 20,881 332,081 (weighted) DAG depth 83 154 7 (after SCC condensation)… See the full description on the dataset page: https://huggingface.co/datasets/MathNetwork/MathlibGraph.
0466
1module,decl_count,in_degree,out_degree,pagerank,betweenness,dag_layer,community_id,cohesion,import_utilization_median2Mathlib,0,1432,0,0.1544680350469632,0.0,154,2,0.0,0.03Mathlib.Algebra.AddConstMap.Basic,143,4,1,5.312841394298201e-05,1.0053958106922567e-05,57,0,0.19516562220232767,0.0122703246916687634Mathlib.Algebra.AddConstMap.Equiv,85,1,1,8.22757021903631e-05,1.7485144533778382e-08,58,2,0.4457831325301205,0.048951048951048955Mathlib.Algebra.AddTorsor.Basic,47,5,2,6.641813193263963e-05,0.0002077004484873,39,0,0.031932773109243695,0.009740259740259746Mathlib.Algebra.AddTorsor.Defs,59,1,3,3.981517404965969e-05,6.1452865881559704e-06,24,0,0.029847834568864612,0.0126182965299684547Mathlib.Algebra.AffineMonoid.Basic,18,1,1,4.8788619866274786e-05,2.2095810622149704e-08,62,2,0.19607843137254902,0.0102564102564102568Mathlib.Algebra.AffineMonoid.Embedding,8,4,1,0.0001332588876382,1.5590459017994453e-05,75,10,0.02097902097902098,0.09Mathlib.Algebra.AffineMonoid.Irreducible,21,2,1,5.8465554495581534e-05,4.0673776689289226e-08,62,0,0.026143790849673203,0.0388278388278388310Mathlib.Algebra.AffineMonoid.UniqueSums,2,2,1,0.0002109960772442,7.540468580191927e-08,76,10,0.02631578947368421,0.687511Mathlib.Algebra.Algebra.Basic,139,9,6,0.0001937715638065,0.00130562835772,59,0,0.006878189483026403,0.03030303030303030412Mathlib.Algebra.Algebra.Bilinear,60,2,7,5.6259309920141245e-05,0.0003209628788306,64,10,0.0240343347639485,0.0385515385515385513Mathlib.Algebra.Algebra.Defs,106,1,21,4.3802622817645654e-05,0.0002292665333996,41,11,0.003421694328639975,0.0138408304498269914Mathlib.Algebra.Algebra.Epi,28,2,2,5.1451042485192955e-05,5.7793943089222825e-05,69,10,0.043993231810490696,0.04227941176470588515Mathlib.Algebra.Algebra.Equiv,325,2,7,7.616245121473451e-05,0.0006528222842727,61,10,0.0732056926384765,0.166091954022988516Mathlib.Algebra.Algebra.Field,7,2,1,5.507420865377527e-05,2.428757202703653e-06,42,11,0.0,0.0227716330513988317Mathlib.Algebra.Algebra.Hom,174,1,5,6.458337483975409e-05,0.0006612652569099,60,10,0.023987691446954333,0.0215827338129496418Mathlib.Algebra.Algebra.Hom.Rat,8,2,1,5.198342838462998e-05,8.288933639961865e-06,61,10,0.09,0.02011494252873563219Mathlib.Algebra.Algebra.IsSimpleRing,1,2,1,7.971454465215416e-05,0.0002989557001871,60,10,0.0,0.0490516677567037320Mathlib.Algebra.Algebra.NonUnitalHom,168,1,6,4.813441312178015e-05,0.0001278916814608,61,10,0.08427635497319834,0.04022988505747126421Mathlib.Algebra.Algebra.NonUnitalSubalgebra,338,4,3,0.0002174635957666,0.0005725765390727,62,10,0.13786112519006588,0.0422360248447204922Mathlib.Algebra.Algebra.Operations,220,9,7,0.0003104210512232,0.0019172122848339,65,0,0.051525618883131834,0.0333333333333333323Mathlib.Algebra.Algebra.Opposite,93,1,2,4.640175315818341e-05,6.630961057402704e-05,62,10,0.07407407407407407,0.04307692307692307524Mathlib.Algebra.Algebra.Pi,69,2,15,7.002923111023895e-05,0.0001465443237358,63,10,0.09230769230769231,0.0162459093034128125Mathlib.Algebra.Algebra.Prod,46,1,3,4.640175315818341e-05,0.000171520248967,62,10,0.1186046511627907,0.01846153846153846326Mathlib.Algebra.Algebra.Rat,13,3,11,4.9859380293079455e-05,0.0001290036900502,43,10,0.013224821973550356,0.04651162790697674427Mathlib.Algebra.Algebra.RestrictScalars,28,1,6,4.0592851626479135e-05,0.0003570283710226,63,5,0.11873840445269017,0.01515151515151515228Mathlib.Algebra.Algebra.Shrink,4,2,2,6.970058338018219e-05,1.231174051208944e-05,63,5,0.08928571428571429,0.1026785714285714229Mathlib.Algebra.Algebra.Spectrum.Basic,138,5,6,8.900548492226257e-05,0.0004108816863821,68,10,0.04479283314669653,0.00668896321070234130Mathlib.Algebra.Algebra.Spectrum.Pi,30,2,1,6.173665998443308e-05,1.327197503952737e-05,70,6,0.007272727272727273,0.02409638554216867631Mathlib.Algebra.Algebra.Spectrum.Quasispectrum,166,3,5,7.71594772139848e-05,0.0001261536638937,69,6,0.06853256604760659,0.04347826086956521632Mathlib.Algebra.Algebra.StrictPositivity,16,2,1,5.818787031218613e-05,2.16628964728072e-05,70,6,0.06389776357827476,0.01703073978155613233Mathlib.Algebra.Algebra.Subalgebra.Basic,367,3,8,0.0001230395836768,0.0009259808960493,63,10,0.07719515430188345,0.01183431952662721934Mathlib.Algebra.Algebra.Subalgebra.Centralizer,24,2,1,6.16343365160396e-05,5.2746852676898116e-08,71,10,0.0144,0.0340056285178236435Mathlib.Algebra.Algebra.Subalgebra.Directed,16,1,1,4.091442750772966e-05,1.213536267469088e-05,67,10,0.02510460251046025,0.00460829493087557636Mathlib.Algebra.Algebra.Subalgebra.IsSimpleOrder,1,3,1,7.44326813418369e-05,2.853913213845612e-05,79,10,0.0,0.04166666666666666437Mathlib.Algebra.Algebra.Subalgebra.Lattice,217,2,20,8.799448695197882e-05,0.0014989562941197,66,10,0.05746669317955856,0.0753963339113202938Mathlib.Algebra.Algebra.Subalgebra.Matrix,3,2,1,8.161883874519548e-05,4.3712861334445944e-08,66,10,0.02631578947368421,0.01084527473389136139Mathlib.Algebra.Algebra.Subalgebra.MulOpposite,66,2,1,0.0001271759065506,6.870997989245377e-06,67,10,0.08879023307436182,0.01953366806520393340Mathlib.Algebra.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05,0.0004715476760787,39,0,0.01838235294117647,0.05371352785145889489Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset,51,3,1,9.866073213880238e-05,6.805492529323545e-08,55,0,0.007633587786259542,0.05357142857142857490Mathlib.Algebra.GroupWithZero.Action.Pointwise.Set,51,4,7,0.0001033751067714,0.0002514215384448,46,0,0.010510510510510511,0.058313498809928595491Mathlib.Algebra.GroupWithZero.Action.Prod,25,2,2,7.06580447255732e-05,3.898834652403639e-05,28,0,0.03225806451612903,0.04195804195804196492Mathlib.Algebra.GroupWithZero.Action.TransferInstance,15,2,2,6.016782089494006e-05,2.0986361923225556e-05,49,0,0.06557377049180328,0.07380182299323729493Mathlib.Algebra.GroupWithZero.Action.Units,26,3,7,5.285894394524105e-05,0.0002210304258895,26,0,0.013888888888888888,0.055865921787709494494Mathlib.Algebra.GroupWithZero.Associated,247,2,10,0.0001677649779457,0.0003681740152786,30,0,0.1391357646337726,0.0642165579924916495Mathlib.Algebra.GroupWithZero.Basic,134,4,7,6.552252685374542e-05,0.0001234743874681,19,0,0.018459579885423297,0.021673936750272627496Mathlib.Algebra.GroupWithZero.Center,13,2,1,5.2679396497298686e-05,8.511182985611974e-06,31,0,0.027777777777777776,0.027011494252873563497Mathlib.Algebra.GroupWithZero.Commute,21,2,3,7.121399494460881e-05,0.0001250710133253,24,0,0.042328042328042326,0.13020833333333334498Mathlib.Algebra.GroupWithZero.Conj,4,2,1,5.3870648258554866e-05,4.269358842491736e-06,32,0,0.0,0.015093273035613341499Mathlib.Algebra.GroupWithZero.Defs,262,3,7,5.713702149451513e-05,0.0001485980803679,17,0,0.004413291796469367,0.02631578947368421500Mathlib.Algebra.GroupWithZero.Divisibility,32,2,8,6.539629511134948e-05,0.0001777558691626,23,0,0.028428093645484948,0.042510775862068965501Mathlib.Algebra.GroupWithZero.Equiv,12,2,4,4.436081989689814e-05,3.3884511124079736e-05,23,0,0.05714285714285714,0.03749132875070947502Mathlib.Algebra.GroupWithZero.Hom,101,2,8,5.115877011510175e-05,0.0001130809353999,21,0,0.030432461292044848,0.006666666666666667503Mathlib.Algebra.GroupWithZero.Idempotent,5,2,2,6.076449983222581e-05,3.6663113658508594e-05,21,0,0.08333333333333333,0.07171554841301728504Mathlib.Algebra.GroupWithZero.Indicator,33,4,2,6.187441031500076e-05,7.040641418229311e-05,39,0,0.039755351681957186,0.0505Mathlib.Algebra.GroupWithZero.InjSurj,39,2,9,5.514692314013017e-05,8.493357054641143e-05,19,0,0.03684210526315789,0.022900763358778626506Mathlib.Algebra.GroupWithZero.Int,0,2,1,7.111178212615113e-05,4.4734221816905894e-08,21,2,0.0,0.0507Mathlib.Algebra.GroupWithZero.Invertible,18,2,4,6.26636811208991e-05,0.0001100905082062,24,0,0.030612244897959183,0.023793103448275864508Mathlib.Algebra.GroupWithZero.Nat,7,3,7,4.88066777438504e-05,3.885414159670833e-05,18,0,0.0013812154696132596,0.09541984732824428509Mathlib.Algebra.GroupWithZero.NeZero,4,2,4,5.738280866638727e-05,3.9657301870114006e-05,18,0,0.0022222222222222222,0.056129321957790745510Mathlib.Algebra.GroupWithZero.NonZeroDivisors,141,5,8,9.181277777847184e-05,0.000854333546141,50,0,0.05688622754491018,0.048582995951417005511Mathlib.Algebra.GroupWithZero.Opposite,51,2,2,4.802107218212004e-05,5.3079045411018686e-05,24,0,0.07537688442211055,0.053905553905553905512Mathlib.Algebra.GroupWithZero.Pi,26,3,2,5.1252805844001056e-05,3.251663259816069e-05,20,0,0.034934497816593885,0.0213903743315508513Mathlib.Algebra.GroupWithZero.Pointwise.Finset,25,2,1,5.0731644018399034e-05,2.6720188665601976e-06,54,0,0.03496503496503497,0.016318480802430015514Mathlib.Algebra.GroupWithZero.Pointwise.Set.Basic,17,2,1,4.731747467535255e-05,1.2450567343670429e-05,38,0,0.036036036036036036,0.014078645235361653515Mathlib.Algebra.GroupWithZero.Pointwise.Set.Card,2,3,1,6.384036836664842e-05,1.1467340623402987e-07,57,0,0.0,0.015267175572519083516Mathlib.Algebra.GroupWithZero.Prod,26,2,2,5.692995777233625e-05,0.0001244668394572,25,0,0.02390438247011952,0.01635940693073612517Mathlib.Algebra.GroupWithZero.ProdHom,33,3,1,6.291111116127321e-05,2.9331124977642904e-06,26,0,0.06634304207119741,0.02843601895734597518Mathlib.Algebra.GroupWithZero.Range,50,3,1,0.000108001506029,7.908919798761834e-05,61,0,0.0720164609053498,0.009478672985781991519Mathlib.Algebra.GroupWithZero.Regular,21,2,4,5.19123171854941e-05,6.618813815333815e-05,18,0,0.0967741935483871,0.019083969465648856520Mathlib.Algebra.GroupWithZero.Semiconj,20,2,2,5.500300029976648e-05,4.753829056998351e-05,23,0,0.061452513966480445,0.03814655172413793521Mathlib.Algebra.GroupWithZero.Shrink,4,3,1,0.00011381252405,6.994057813511353e-08,50,0,0.0,0.06666666666666667522Mathlib.Algebra.GroupWithZero.Subgroup,34,2,5,7.935966796332381e-05,0.0002535349925484,61,0,0.03146853146853147,0.017434988179669028523Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero,3,2,1,4.645654877284227e-05,5.595246250809081e-08,33,0,0.07407407407407407,0.027003423461189127524Mathlib.Algebra.GroupWithZero.Submonoid.Instances,38,2,1,4.955852760119505e-05,7.446946880906588e-06,48,0,0.05405405405405406,0.0008635578583765112525Mathlib.Algebra.GroupWithZero.Submo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lgebra.Basic,88,2,1,8.105092017450772e-05,7.120885161372568e-06,75,10,0.043914680050188205,0.061687214997466641127Mathlib.Algebra.QuadraticAlgebra.Defs,248,2,2,6.656714718006271e-05,3.262572045584757e-05,74,10,0.32645161290322583,0.105555555555555561128Mathlib.Algebra.QuadraticAlgebra.NormDeterminant,1,2,1,0.0001144175100604,4.95412428457054e-08,83,10,0.0,0.0122177658942364821129Mathlib.Algebra.QuadraticDiscriminant,32,4,3,0.0002067011016454,0.000163555503233,52,6,0.03379224030037547,0.01130Mathlib.Algebra.Quandle,317,3,1,5.586357736826888e-05,7.309643639725083e-08,50,0,0.7398543184183143,0.022240259740259741131Mathlib.Algebra.Quaternion,618,4,3,0.0001317772585677,5.1848858259225614e-05,74,10,0.2172067501811782,0.1094786729857821132Mathlib.Algebra.QuaternionBasis,73,3,1,8.653289980032141e-05,8.209122710521749e-06,75,10,0.12680115273775217,0.0138248847926267291133Mathlib.Algebra.Quotient,15,1,1,7.029841227458541e-05,0.0002701663900978,21,0,0.0021390374331550803,0.01134Mathlib.Algebra.Regular.Basic,68,2,5,4.173345391384991e-05,2.5341965566804504e-05,20,0,0.12087912087912088,0.010381392412328531135Mathlib.Algebra.Regular.Defs,32,1,1,4.833064608886452e-05,7.767826648446473e-05,15,0,0.03382663847780127,0.01136Mathlib.Algebra.Regular.Opposite,38,1,2,4.211630272582503e-05,1.9537264497760316e-05,23,0,0.10112359550561797,0.025641025641025641137Mathlib.Algebra.Regular.Pi,16,1,1,4.427597230985461e-05,1.3864396688354637e-08,27,2,0.0,0.0222222222222222231138Mathlib.Algebra.Regular.Pow,3,2,1,5.258850171832894e-05,3.488417166334606e-05,47,0,0.043478260869565216,0.027083949157552471139Mathlib.Algebra.Regular.Prod,22,2,1,4.8512252241370056e-05,3.9217856262333285e-08,27,0,0.13636363636363635,0.0233062330623306221140Mathlib.Algebra.Regular.SMul,45,4,7,5.865604946519774e-05,0.0001488328184291,26,0,0.1543778801843318,0.0062656641604010021141Mathlib.Algebra.Regular.ULift,27,2,1,4.9708698565134455e-05,3.4846570128888685e-08,27,0,0.06976744186046512,0.0165458937198067621142Mathlib.Algebra.Ring.Action.Basic,31,3,7,6.284680701343309e-05,0.0001708648733089,28,0,0.02864816472694718,0.0280373831775700931143Mathlib.Algebra.Ring.Action.ConjAct,5,2,4,6.348169856432872e-05,9.236602246300464e-05,55,10,0.0,0.05055074744295831144Mathlib.Algebra.Ring.Action.End,13,2,1,8.620409745676552e-05,1.6699189531856237e-05,40,0,0.025,0.137037037037037041145Mathlib.Algebra.Ring.Action.Field,1,3,2,5.1916137058495665e-05,1.9113096350320204e-05,29,0,0.0,0.0454545454545454561146Mathlib.Algebra.Ring.Action.Group,5,3,2,6.599200146512426e-05,0.000194950695586,39,0,0.023255813953488372,0.0434782608695652161147Mathlib.Algebra.Ring.Action.Invariant,23,2,1,5.75585394394436e-05,6.489581754718344e-06,36,11,0.07692307692307693,0.0179804168262130071148Mathlib.Algebra.Ring.Action.Pointwise.Finset,7,3,1,5.9053666829819165e-05,4.3747554081536794e-08,54,0,0.0,0.0259740259740259761149Mathlib.Algebra.Ring.Action.Pointwise.Set,15,2,5,5.589951444180505e-05,9.6510577173127e-05,47,0,0.0,0.030212084833933571150Mathlib.Algebra.Ring.Action.Rat,8,2,3,4.1867535528657184e-05,2.17145059827772e-05,26,0,0.01680672268907563,0.053928072625698331151Mathlib.Algebra.Ring.Action.Submonoid,13,2,1,4.598561640736417e-05,2.943253565725181e-05,44,0,0.07462686567164178,0.0160761850882775831152Mathlib.Algebra.Ring.Action.Subobjects,6,3,1,6.565123372959372e-05,5.60769661453168e-05,35,0,0.02631578947368421,0.129032258064516131153Mathlib.Algebra.Ring.AddAut,6,4,2,9.073461169495475e-05,4.879812054220939e-05,33,0,0.023809523809523808,0.040969899665551841154Mathlib.Algebra.Ring.Associated,8,2,1,6.089586183547097e-05,3.30871079871248e-05,31,0,0.08928571428571429,0.0212899623062962441155Mathlib.Algebra.Ring.Associator,26,2,2,4.469209351575629e-05,1.3981656652923636e-05,31,0,0.09876543209876543,0.00243902439024390241156Mathlib.Algebra.Ring.Aut,27,2,2,4.9485077442722406e-05,0.0001600425036216,39,0,0.08379888268156424,0.022394566564177871157Mathlib.Algebra.Ring.Basic,68,6,5,8.598864986992413e-05,0.000339055535193,23,0,0.025177887246852763,0.0201923076923076931158Mathlib.Algebra.Ring.BooleanRing,177,6,1,8.502188391533196e-05,4.646767101262243e-06,47,0,0.23651452282157676,0.0181159420289855081159Mathlib.Algebra.Ring.Center,11,2,1,5.115728791709629e-05,1.2056610763853309e-05,32,0,0.012987012987012988,0.0222846441947565541160Mathlib.Algebra.Ring.Centralizer,4,2,1,4.990712667051801e-05,5.737182780574692e-06,31,0,0.0,0.016244131455399061161Mathlib.Algebra.Ring.CentroidHom,211,5,1,0.0001061863492374,4.2471834793257685e-06,52,0,0.2665330661322645,0.0172413793103448271162Mathlib.Algebra.Ring.CharZero,33,5,6,7.387639131707648e-05,0.0002895052460506,36,0,0.0125,0.019108280254777071163Mathlib.Algebra.Ring.Commute,63,3,4,0.000108478257603,0.0002694210132764,26,0,0.026703499079189688,0.214285714285714271164Mathlib.Algebra.Ring.CompTypeclasses,45,1,4,4.264215766032852e-05,0.0001264223878522,39,0,0.005198695920345405,0.0247349823321554761165Mathlib.Algebra.Ring.Defs,426,4,32,6.681981184615478e-05,0.0005485553930129,19,0,0.00157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