Limits to detecting memory in network contacts affect epidemic predictions
Fundamental limits to identifying node and tie memory in temporal networks: marginal artefacts and spreading dynamics
Social and Information Networks
Summary
This paper finds that figuring out how network contacts remember past interactions is harder than expected. When we know who starts each contact, we can clearly separate two memory types; if not, they get mixed up and confused. In many real-world networks, one kind of memory related to individual nodes is nearly impossible to identify from contact times alone. This misidentification matters because it causes simulations of disease spreading to underestimate how big outbreaks can get.
What this means in practice
- •For epidemic modelers: Adjust disease spread simulations to account for intrinsic limits in detecting node memory, improving outbreak size predictions from contact data.
- •For network security analysts: Improve detection of communication patterns by understanding when tie reinforcement can be distinguished without knowing message initiators.
Authors
Michele Tizzani
Abstract
Temporal-network models attribute memory in contact data to either node self-excitation (branching ratio n_node) or tie reinforcement (kappa), carrying major consequences for epidemic spreading. We prove that when event initiators are observed, the two mechanisms are orthogonal: the Fisher information is block-diagonal and neither trades off against the other. In undirected proximity data, where initiators are unobserved, marginalising over them couples the mechanisms into a structural confound that survives posterior smoothing. On empirical proximity, messaging, and email records, however, a cruder failure dominates: fitted node memory is pinned to the inter-event marginal law and remains virtually invariant across latent label posterior samples (coefficient of variation below 1%). An inter-event-order shuffle test and burstiness-memory diagnostics reveal that exponential-Hawkes node memory is recovered from none, while tie reinforcement remains identifiable throughout. This near-unidentifiability is intrinsic, not an artefact of the exponential kernel: refitting flexible scale-free (sum-of-exponentials) kernels on synthetic power-law self-exciting processes fails to distinguish genuine node memory from memoryless renewal controls, with identical collapses recurring on algorithmic networks (edit bots, cloud microservices) and cortical spiking. Downstream epidemic consequences are quantitative: simulations fitted to empirical contact records under-predict outbreak sizes by up to a factor of 2.5 and shift the epidemic threshold. We conclude that observational temporal networks face a two-fold identifiability boundary: contact directionality is essential to decouple tie reinforcement, whereas heavy-tailed node self-excitation is intrinsically unidentifiable from contact timings alone.