# Modelling sparsity, heterogeneity, reciprocity and community structure in temporal interaction data

arXiv: https://arxiv.org/abs/1803.06070 · HTML: https://mlsanity.com/paper/1803.06070/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Mar 2018.

## 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)
- [Mutually exciting point process graphs for modelling dynamic networks](https://mlsanity.com/paper/2102.06527/) (2021)
- [The Multivariate Community Hawkes Model for Dependent Relational Events in Continuous-time Networks](https://mlsanity.com/paper/2205.00639/) (2022)
- [Cox-Hawkes: doubly stochastic spatiotemporal Poisson processes](https://mlsanity.com/paper/2210.11844/) (2022)
- [Spectral clustering for dependent community Hawkes process models of temporal networks](https://mlsanity.com/paper/2505.21845/) (2025)

## Abstract (arXiv)

We propose a novel class of network models for temporal dyadic interaction data. Our goal is to capture a number of important features often observed in social interactions: sparsity, degree heterogeneity, community structure and reciprocity. We propose a family of models based on self-exciting Hawkes point processes in which events depend on the history of the process. The key component is the conditional intensity function of the Hawkes Process, which captures the fact that interactions may arise as a response to past interactions (reciprocity), or due to shared interests between individuals (community structure). In order to capture the sparsity and degree heterogeneity, the base (non time dependent) part of the intensity function builds on compound random measures following Todeschini et al. (2016). We conduct experiments on a variety of real-world temporal interaction data and show that the proposed model outperforms many competing approaches for link prediction, and leads to interpretable parameters.