# Maximum entropy approaches for the study of triadic motifs in the Mergers & Acquisitions network

## TL;DR

This paper applies maximum entropy models to analyze triadic motifs in the Mergers & Acquisitions network, revealing higher-order structural patterns and differences from randomized models.

## Contribution

It introduces maximum entropy configuration models for M&A networks to study higher-order motifs, extending previous methods used in economic and financial networks.

## Key findings

- Triadic motifs differ significantly from randomized models.
- Higher-order structures reveal organizational principles of M&A networks.
- Weighted and binary networks show distinct motif patterns.

## Abstract

In the past years statistical physics has been successfully applied for complex networks modelling. In particular, it has been shown that the maximum entropy principle can be exploited in order to construct graph ensembles for real-world networks which maximize the randomness of the graph structure keeping fixed some topological constraint. Such ensembles can be used as null models to detect statistically significant structural patterns and to reconstruct the network structure in cases of incomplete information. Recently, these randomizing methods have been used for the study of self-organizing systems in economics and finance, such as interbank and world trade networks, in order to detect topological changes and, possibly, early-warning signals for the economical crisis. In this work we consider the configuration models with different constraints for the network of mergers and acquisitions (M&As), Comparing triadic and dyadic motifs, for both the binary and weighted M&A network, with the randomized counterparts can shed light on its organization at higher order level.