Cliques Are Bricks for k-CT Graphs

Abstract

Many real networks in biology, chemistry, industry, ecological systems, or social networks have an inherent structure of simplicial complexes reflecting many-body interactions. Over the past few decades, a variety of complex systems have been successfully described as networks whose links connect interacting pairs of nodes. Simplicial complexes capture the many-body interactions between two or more nodes and generalized network structures to allow us to go beyond the framework of pairwise interactions. Therefore, to analyze the topological and dynamic properties of simplicial complex networks, the closed trail metric is proposed here. In this article, we focus on the evolution of simplicial complex networks from clicks and k-CT graphs. This approach is used to describe the evolution of real simplicial complex networks. We conclude with a summary of composition k-CT graphs (glued graphs); their closed trail distances are in a specified range.

Keywords

• cyclic distance
• closed trail distance
• glued graph
• cyclic structure
• higher-order structure