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We present a combinatorial problem which consists in finding irreducible Krajewski diagrams from finite geometries. This problem boils down to placing arrows into a quadratic array with some additional constraints. The Krajewski diagrams play a central role in the description of finite noncommutative geometries. They allow to localise the standard model of particle physics within the set of all Yang–Mills–Higgs models. Program summary: Title of program:ko0 and ko6 Catalogue identifier:ADZZ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADZZ_v1_0.html Program obtainable from: CPC Program Library, Queen''s University of Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.:4875 No. of bytes in distributed program, including test data, etc.:29 933 Distribution format:tar.gz Programming language used:C++ Computer:Simple PC Operating system:Any, where C++ runs RAM:Depending on the global parameters ‘DIMENSION’ and ‘MAX_LEVEL’, a few KB to some MB Classification:5, 11.1 Nature of problem:Automatised classification of almost-commutative geometries via Krajewski diagrams. Solution method:Combinatorial generation of all possible Krajewski diagrams and identification of the irreducible ones. Equivalence classes of irreducibles = classification. Running time:Depending on the global parameters ‘DIMENSION’ and ‘MAX_LEVEL’, running time reaches from seconds () to weeks () on a standard PC. [Copyright &y& Elsevier]