Networks: The Visual Language of Complexity

TL;DR

This paper explores how network theory models complex systems, highlighting the limitations of existing growth models and the importance of internal mechanisms and hypergraph extensions in capturing system-specific properties.

Contribution

It provides a comprehensive review of network evolution mechanisms, emphasizing the role of tinkering and hypergraphs in modeling complexity.

Findings

Preferential attachment explains some properties but not all.

Internal tinkering mechanisms generate modular structures.

Hypergraphs better capture environmental interactions.

Abstract

Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to represent inter-dependencies among many system components, facilitating the study of both local and global properties. However, it is unclear whether we can define a universal theoretical framework for evolving networks. While basic growth mechanisms, like preferential attachment, recapitulate common properties such as the power-law degree distribution, they fall short in capturing other system-specific properties. Tinkering, on the other hand, has shown to be very successful in generating modular or nested structures "for-free", highlighting the role of internal, non-adaptive mechanisms in the evolution of complexity. Different network extensions, like hypergraphs, have been recently developed to integrate exogenous factors in evolutionary models, as pairwise interactions are insufficient to capture environmentally-mediated species associations. As we confront global societal and climatic challenges, the study of network and hypergraphs provides valuable insights, emphasizing the importance of scientific exploration in understanding and managing complexity.