# Spectral clustering for dependent community Hawkes process models of temporal networks

arXiv: https://arxiv.org/abs/2505.21845 · HTML: https://mlsanity.com/paper/2505.21845/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 57 references that are in the map.
- First posted on arXiv 28 May 2025.

## Builds on (most cited first, 15 of 15)

- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Motifs in Temporal Networks](https://mlsanity.com/paper/1612.09259/) (2016)
- [Uncovering Causality from Multivariate Hawkes Integrated Cumulants](https://mlsanity.com/paper/1607.06333/) (2016)
- [Achieving Optimal Misclassification Proportion in Stochastic Block Model](https://mlsanity.com/paper/1505.03772/) (2015)
- [Spectral and matrix factorization methods for consistent community detection in multi-layer networks](https://mlsanity.com/paper/1704.07353/) (2017)
- [Global and Individualized Community Detection in Inhomogeneous Multilayer Networks](https://mlsanity.com/paper/2012.00933/) (2020)
- [A semiparametric extension of the stochastic block model for longitudinal networks](https://mlsanity.com/paper/1512.07075/) (2015)
- [A Mutually Exciting Latent Space Hawkes Process Model for Continuous-time Networks](https://mlsanity.com/paper/2205.09263/) (2022)
- [The Block Point Process Model for Continuous-Time Event-Based Dynamic Networks](https://mlsanity.com/paper/1711.10967/) (2017)
- [Mutually exciting point process graphs for modelling dynamic networks](https://mlsanity.com/paper/2102.06527/) (2021)
- [Continuous Latent Position Models for Instantaneous Interactions](https://mlsanity.com/paper/2103.17146/) (2021)
- [Modelling sparsity, heterogeneity, reciprocity and community structure in temporal interaction data](https://mlsanity.com/paper/1803.06070/) (2018)
- [The Multivariate Community Hawkes Model for Dependent Relational Events in Continuous-time Networks](https://mlsanity.com/paper/2205.00639/) (2022)
- [Gaussian Embedding of Temporal Networks](https://mlsanity.com/paper/2405.17253/) (2024)
- [Identifying Peer Influence in Therapeutic Communities Adjusting for Latent Homophily](https://mlsanity.com/paper/2203.14223/) (2022)

## Abstract (arXiv)

Temporal networks observed continuously over time through timestamped relational events data are commonly encountered in application settings including online social media communications, financial transactions, and international relations. Temporal networks often exhibit community structure and strong dependence patterns among node pairs. This dependence can be modeled through mutual excitations, where an interaction event from a sender to a receiver node increases the possibility of future events among other node pairs. We provide statistical results for a class of models that we call dependent community Hawkes (DCH) models, which combine the stochastic block model with mutually exciting Hawkes processes for modeling both community structure and dependence among node pairs, respectively. We derive a non-asymptotic upper bound on the misclustering error of spectral clustering on the event count matrix as a function of the number of nodes and communities, time duration, and the amount of dependence in the model. Our result leverages recent results on bounding an appropriate distance between a multivariate Hawkes process count vector and a Gaussian vector, along with results from random matrix theory. We also propose a DCH model that incorporates only self and reciprocal excitation along with highly scalable parameter estimation using a Generalized Method of Moments (GMM) estimator that we demonstrate to be consistent for growing network size and time duration.