# How Clustering Affects the Convergence of Decentralized Optimization over Networks: A Monte-Carlo-based Approach

arXiv: https://arxiv.org/abs/2407.01460 · HTML: https://mlsanity.com/paper/2407.01460/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2024.

## Built on by (most cited first, 2 of 2)

- [Accelerating Decentralized Optimization via Overlapping Local Steps](https://mlsanity.com/paper/2601.01493/) (2026)
- [Using Non-Lipschitz Signum-based Functions for Distributed Optimization and Machine Learning: Trade-off Between Con-vergence Rate and Optimality Gap](https://mlsanity.com/paper/2608.01220/) (2026)

## Abstract (arXiv)

Decentralized algorithms have gained substantial interest owing to advancements in cloud computing, Internet of Things (IoT), intelligent transportation networks, and parallel processing over sensor networks. The convergence of such algorithms is directly related to specific properties of the underlying network topology. Specifically, the clustering coefficient is known to affect, for example, the controllability/observability and the epidemic growth over networks. In this work, we study the effects of the clustering coefficient on the convergence rate of networked optimization approaches. In this regard, we model the structure of large-scale distributed systems by random scale-free (SF) and clustered scale-free (CSF) networks and compare the convergence rate by tuning the network clustering coefficient. This is done by keeping other relevant network properties (such as power-law degree distribution, number of links, and average degree) unchanged. Monte-Carlo-based simulations are used to compare the convergence rate over many trials of SF graph topologies. Furthermore, to study the convergence rate over real case studies, we compare the clustering coefficient of some real-world networks with the eigenspectrum of the underlying network (as a measure of convergence rate). The results interestingly show higher convergence rate over low-clustered networks. This is significant as one can improve the learning rate of many existing decentralized machine-learning scenarios by tuning the network clustering.