Community Detection using the Edge Laplacian Dynamics vis-a-vis Ricci Flow
Abstract
It has been found that utilizing the geometric properties of the graph dynamics can bring out crucial information of the data that a statistical analysis will not. The properties of Ricci flow bring out hidden dynamics of the data in the same way as decomposition of smooth manifolds. In this paper we explore an alternative to Ricci flow, where we find that we can bring out similar properties like it using a simpler and well defined Edge Laplacian to practice community detection in graphs. Moreover, the results obtained by the present approach show that a flow driven by the Edge Laplacian yields results similar to those of the Ricci flow. In contrast, computing the Forman-Ricci curvature requires looping over the adjacent edges, while computing Olivier-Ricci curvature involves the computation of Wasserstein distance and probability distribution associated with the graph nodes, making the Edge Laplacian approach computationally more efficient.
Related
- Eigenvalue comparison theorems for the Witten-Laplacian and the weighted p-Laplacian on complete manifolds with a modified Ricci curvature bounded from below
- Sharp lower bound of the first eigenvalue of the p-Laplacian under integral Ricci curvature
- Eigenspaces of Preserved Graph Laplacian Eigenvalues under Positive Edge-Weight Addition
- Ollivier--Ricci Idleness Functions and Edge-Connectivity of Hypergraphs
- Laplacian Pair State Transfer on Edge Coronas
BibTeX
@misc{bhandari2026community,
title = {{Community Detection using the Edge Laplacian Dynamics vis-a-vis Ricci Flow}},
author = {Pratibha Bhandari and Soumyendu Raha},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38988},
eprint = {2609.38988},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38988},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Community Detection using the Edge Laplacian Dynamics vis-a-vis Ricci Flow
AU - Pratibha Bhandari
AU - Soumyendu Raha
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.38988
UR - https://arxiv.org/abs/2609.38988
AB - It has been found that utilizing the geometric properties of the graph dynamics can bring out crucial information of the data that a statistical analysis will not. The properties of Ricci flow bring out hidden dynamics of the data in the same way as decomposition of smooth manifolds. In this paper we explore an alternative to Ricci flow, where we find that we can bring out similar properties like it using a simpler and well defined Edge Laplacian to practice community detection in graphs. Moreover, the results obtained by the present approach show that a flow driven by the Edge Laplacian yields results similar to those of the Ricci flow. In contrast, computing the Forman-Ricci curvature requires looping over the adjacent edges, while computing Olivier-Ricci curvature involves the computation of Wasserstein distance and probability distribution associated with the graph nodes, making the Edge Laplacian approach computationally more efficient.
ER -