Sequence Nets

TL;DR

This paper introduces a new class of networks called sequence nets, generated from sequences of letters with specific connectivity rules, offering a modular structure that is analytically tractable and more representative of real-world networks.

Contribution

It classifies two- and three-letter sequence nets, discovering new classes, and demonstrates their analytical tractability and potential for modeling complex real-world networks.

Findings

Full classification of two- and three-letter sequence nets.

Discovery of two new classes of two-letter sequence nets.

Retention of analytical properties similar to threshold nets.

Abstract

We study a new class of networks, generated by sequences of letters taken from a finite alphabet consisting of $m$ letters (corresponding to $m$ types of nodes) and a fixed set of connectivity rules. Recently, it was shown how a binary alphabet might generate threshold nets in a similar fashion [Hagberg et al., Phys. Rev. E 74, 056116 (2006)]. Just like threshold nets, sequence nets in general possess a modular structure reminiscent of everyday life nets, and are easy to handle analytically (i.e., calculate degree distribution, shortest paths, betweenness centrality, etc.). Exploiting symmetry, we make a full classification of two- and three-letter sequence nets, discovering two new classes of two-letter sequence nets. The new sequence nets retain many of the desirable analytical properties of threshold nets while yielding richer possibilities for the modeling of everyday life complex networks more faithfully.