# Temporal networks: slowing down diffusion by long lasting interactions

arXiv: https://arxiv.org/abs/1305.2938 · HTML: https://mlsanity.com/paper/1305.2938/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 May 2013.

## Built on by (most cited first, 2 of 2)

- [Matrix-weighted networks for modeling multidimensional dynamics](https://mlsanity.com/paper/2410.05188/) (2024)
- [Decentralised Federated Learning over Temporal Networks: The Role of Heterogeneities](https://mlsanity.com/paper/2607.03171/) (2026)

## Abstract (arXiv)

Interactions among units in complex systems occur in a specific sequential order thus affecting the flow of information, the propagation of diseases, and general dynamical processes. We investigate the Laplacian spectrum of temporal networks and compare it with that of the corresponding aggregate network. First, we show that the spectrum of the ensemble average of a temporal network has identical eigenmodes but smaller eigenvalues than the aggregate networks. In large networks without edge condensation, the expected temporal dynamics is a time-rescaled version of the aggregate dynamics. Even for single sequential realizations, diffusive dynamics is slower in temporal networks. These discrepancies are due to the noncommutability of interactions. We illustrate our analytical findings using a simple temporal motif, larger network models and real temporal networks.