Exploring Structural Characteristics of Lattices in Real World

Abstract

There are two important models for data analysis and knowledge system: data cube lattices and concept lattices. They both essentially have lattice structures, which are actually irregular in our real world. However, their structural characteristics and relationship are not yet clear. To the best of our knowledge, no work has paid enough attention to this challenging issue from the perspective of graph data, in spite of the importance of structures in lattice data. In this paper, we first tackle the structural statistics of lattice data from three aspects: the degree distribution, clustering coefficient, and average path length. We demonstrated by various datasets that data cube lattices and concept lattices share similarities underlying their topology, which are, in general, different from random networks and complex networks. Specifically, lattice data follow the Poisson distribution and have smaller clustering coefficient and greater average path length. We further discuss and explain these characteristics intrinsically by building the analytical model and the generating mechanism.