Simultaneous, polynomial-time layout of context bigraph and lattice digraph

Abstract

Formal Concept Analysis (FCA) takes as input the bipartite context graph and produces a directed acyclic graph representing the lattice of formal concepts. Excepting possibly the supremum and infimum, the set of formal concepts corresponds to the set of proper maximal bicliques in the context bigraph. This paper proposes polynomial-time graph layouts which emphasise maximal bicliques in the context bigraph and facilitate “reading” directed paths in the lattice digraph. These layouts are applied to sub-contexts of the InfoVis 2004 data set which are indivisible by the Carve divide-and-conquer FCA algorithm. The paper also investigates the relationship between vertex proximity in the bigraph layout and co-membership of maximal bicliques, and demonstrates the significant reduction of edge crossings in the digraph layout.