# The Multivariate Community Hawkes Model for Dependent Relational Events in Continuous-time Networks

arXiv: https://arxiv.org/abs/2205.00639 · HTML: https://mlsanity.com/paper/2205.00639/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 59 references that are in the map.
- First posted on arXiv 2 May 2022.

## Builds on (most cited first, 18 of 18)

- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [Motifs in Temporal Networks](https://mlsanity.com/paper/1612.09259/) (2016)
- [Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel](https://mlsanity.com/paper/1309.4111/) (2013)
- [Lecture Notes: Temporal Point Processes and the Conditional Intensity Function](https://mlsanity.com/paper/1806.00221/) (2018)
- [COEVOLVE: A Joint Point Process Model for Information Diffusion and Network Co-evolution](https://mlsanity.com/paper/1507.02293/) (2015)
- [Community Detection in Degree-Corrected Block Models](https://mlsanity.com/paper/1607.06993/) (2016)
- [Achieving Optimal Misclassification Proportion in Stochastic Block Model](https://mlsanity.com/paper/1505.03772/) (2015)
- [Discovering Latent Network Structure in Point Process Data](https://mlsanity.com/paper/1402.0914/) (2014)
- [Stochastic Block Model and Community Detection in the Sparse Graphs: A spectral algorithm with optimal rate of recovery](https://mlsanity.com/paper/1501.05021/) (2015)
- [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)
- [The Block Point Process Model for Continuous-Time Event-Based Dynamic Networks](https://mlsanity.com/paper/1711.10967/) (2017)
- [Disentangling homophily, community structure and triadic closure in networks](https://mlsanity.com/paper/2101.02510/) (2021)
- [Modelling sparsity, heterogeneity, reciprocity and community structure in temporal interaction data](https://mlsanity.com/paper/1803.06070/) (2018)
- [Higher-Order Spectral Clustering under Superimposed Stochastic Block Model](https://mlsanity.com/paper/1812.06515/) (2018)
- [Surfacing Estimation Uncertainty in the Decay Parameters of Hawkes Processes with Exponential Kernels](https://mlsanity.com/paper/2104.01029/) (2021)
- [Modeling Human Dynamics and Lifestyle Using Digital Traces](https://mlsanity.com/paper/2005.06542/) (2020)

## Built on by (most cited first, 5 of 5)

- [A Mutually Exciting Latent Space Hawkes Process Model for Continuous-time Networks](https://mlsanity.com/paper/2205.09263/) (2022)
- [Opal: Private Memory for Personal AI](https://mlsanity.com/paper/2604.02522/) (2026)
- [Efficient Estimation for Longitudinal Networks via Adaptive Merging](https://mlsanity.com/paper/2211.07866/) (2022)
- [Spectral clustering for dependent community Hawkes process models of temporal networks](https://mlsanity.com/paper/2505.21845/) (2025)
- [Credit Attribution in Timestamped Soccer Networks Using Multivariate Hawkes Processes](https://mlsanity.com/paper/2610.12775/) (2026)

## Abstract (arXiv)

The stochastic block model (SBM) is one of the most widely used generative models for network data. Many continuous-time dynamic network models are built upon the same assumption as the SBM: edges or events between all pairs of nodes are conditionally independent given the block or community memberships, which prevents them from reproducing higher-order motifs such as triangles that are commonly observed in real networks. We propose the multivariate community Hawkes (MULCH) model, an extremely flexible community-based model for continuous-time networks that introduces dependence between node pairs using structured multivariate Hawkes processes. We fit the model using a spectral clustering and likelihood-based local refinement procedure. We find that our proposed MULCH model is far more accurate than existing models both for predictive and generative tasks.