# Transtemporal edges and crosslayer edges in incompressible high-order networks

## TL;DR

This paper investigates the topological properties of incompressible high-order networks, revealing their short diameters, high connectivity, and the presence of transtemporal and crosslayer edges, which challenge traditional snapshot-based representations.

## Contribution

It provides a theoretical analysis of incompressible high-order networks, highlighting their unique properties and the significance of transtemporal and crosslayer edges in real-world network modeling.

## Key findings

- Networks have very short diameter and high k-connectivity.
- Incompressible networks exhibit transtemporal and crosslayer edges.
- Snapshot representations are inadequate for dynamic networks with such edges.

## Abstract

This work presents some outcomes of a theoretical investigation of incompressible high-order networks defined by a generalized graph representation. We study some of their network topological properties and how these may be related to real-world complex networks. We show that these networks have very short diameter, high k-connectivity, degrees of the order of half of the network size within a strong-asymptotically dominated standard deviation, and rigidity with respect to automorphisms. In addition, we demonstrate that incompressible dynamic (or dynamic multilayered) networks have transtemporal (or crosslayer) edges and, thus, a snapshot-like representation of dynamic networks is inaccurate for capturing the presence of such edges that compose underlying structures of some real-world networks.