Abstract. Several algorithms that generate the set of all formal concepts and diagram graphs of concept lattices are considered. Some modifications of wellknown algorithms are proposed. Algorithmic complexity of the algorithms is studied both theoretically (in the worst case) and experimentally. Conditions of preferable use of some algorithms are given in terms of density/sparseness of underlying formal contexts. Principles of comparing practical performance of algorithms are discussed.

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We present an application of formal concept analysis aimed at representing a meaningful structure of knowledge communities in the form of a lattice-based taxonomy. The taxonomy groups together agents (community members) who develop a set of notions. If no constraints are imposed on how it is built, a knowledge community taxonomy may become extremely complex and difficult to analyze. We consider two approaches to building a concise representation respecting the underlying structural relationships, while hiding uninteresting and/or superfluous information: a pruning strategy based on the notion of concept stability and a representational improvement based on nested line diagrams and "zooming". We illustrate the methods on two examples: a community of embryologists and a community of researchers in complex systems.

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