Reply to comment on "Failure of the simultaneous block diagonalization technique applied to complete and cluster synchronization of random networks"

no code implementations • 31 Jan 2022 • Shirin Panahi, Nelson Amaya, Isaac Klickstein, Galen Novello, Francesco Sorrentino

We respond briefly to a comment [1, arXiv:2110. 15493] recently posted online on our paper [2, arXiv:2108. 07893].

Cluster Synchronization of Networks via a Canonical Transformation for Simultaneous Block Diagonalization of Matrices

1 code implementation • 28 Sep 2021 • Shirin Panahi, Isaac Klickstein, Francesco Sorrentino

Our approach has several advantages as it allows us to: (1) decouple the stability problem into subproblems of minimal dimensionality while preserving physically meaningful information; (2) study stability of both orbital and equitable partitions of the network nodes and (3) obtain a parametrization of the problem in a small number of parameters.

Generating Graphs with Symmetry

1 code implementation • 15 Aug 2018 • Isaac Klickstein, Francesco Sorrentino

In the field of complex networks and graph theory, new results are typically tested on graphs generated by a variety of algorithms such as the Erd\H{o}s-R\'{e}nyi model or the Barab\'{a}si-Albert model.

Combinatorics