REMFlow Library Brings Relational Event Modelling to the Python Ecosystem

Social and organizational interaction data are routinely captured as discrete, chronologically ordered occurrences, such as colleagues exchanging workplace emails, students speaking in a seminar, or social media accounts publishing threaded replies. Conventional analytical workflows frequently compress these dynamic event sequences into static summary graphs, aggregating interactions into persistent edge weights across arbitrary observational windows. Although static network representations capture overarching connection structures, they discard the temporal ordering of interactions, precise inter-event waiting times, reciprocal dynamics, and the exact set of behavioral alternatives accessible to actors at each point in time. Relational event models, initially formulated to study dynamic social actions as continuous-time point processes, directly address these analytical limitations by evaluating each observed event against its historical context and the admissible counterfactual choices available when the event occurred.

The underlying mathematical foundation of relational event modelling defines each observed interaction as a timestamped directed event tuple connecting an initiator to a designated target within an evolving system. In this formal setup, an event history accumulates all prior interactions observed before a given time point, while a dynamic risk set delineates every sender-receiver pair capable of generating an action at that specific moment. Endogenous statistical terms—such as immediate reciprocity, repeated interaction inertia, degree activity, popularity, shared transitivity partners, and multi-actor participation shifts—are computed directly from the preceding interaction history, while exogenous covariates incorporate actor-level or dyadic attributes provided by the researcher. These combined terms enter a log-linear intensity formulation where an event’s instantaneous rate is determined by a baseline intensity modulated by the exponential product of model coefficients and calculated statistics. For ordinal specifications, the framework conditions on an event taking place and models categorical selection across the active risk set, whereas exact-time formulations incorporate elapsed inter-event durations using piecewise-constant survival contributions, ensuring that observed choices are statistically evaluated against every valid alternative that did not happen.

Historically, mature computational tooling for relational event models has been heavily concentrated in the R ecosystem through specialized packages such as relevent, remify, remstats, remstimate, and goldfish, alongside broader model families implemented in dream and remverse. Conversely, while Python maintains widely adopted packages for static network analysis, temporal graph representation, point-process simulation, and survival modelling—including NetworkX, Reticula, pathpy, tick, HawkesPyLib, lifelines, and PyTorch Geometric Temporal—none of these general libraries natively construct relational risk sets, history-dependent network statistics, and REM likelihoods within a single coordinated pipeline. As a consequence, researchers attempting relational event analysis in Python were previously forced to develop project-specific glue code, compounding technical implementation effort and hindering the inspection and reproducibility of critical analytical choices. REMFlow directly resolves this software-integration gap by establishing a modular, inspectable architecture partitioned across core components: history preparation in history.py, statistic generation in stats.py, parameter estimation in estimate.py, execution management in backends.py, higher-level workflows in model.py, tabular formatting in reporting.py, and visualization utilities in plotting.py.

Executing relational event models involves substantial computational and memory demands that grow rapidly with population scale and event history length. For a system of actors generating typed events across a series of time steps, a complete directed risk set encompasses quadratic sender-receiver pairings for every distinct event type, requiring extensive operations for dense gradient and likelihood assembly. Furthermore, fully materialized double-precision statistic arrays demand significant memory capacity, where storing just four float64 statistics across twenty-five thousand events among one hundred actors requires approximately 7.38 gibibytes of memory, and one thousand events among five hundred actors requires 7.44 gibibytes. These memory footprints quickly exceed the physical working limits of standard personal workstations once intermediate matrices, index tables, and background operating system processes are accommodated. Although REMFlow implements case-control sampling to curtail repeated likelihood evaluations, the current release executes sampling downstream of risk-set and statistic generation, meaning that initial preprocessing peaks persist. To manage numerical performance within these boundaries, the library incorporates a flexible backend architecture supporting default NumPy execution alongside specialized JAX selectors targeting central processing units and graphics processing units.

To guarantee statistical rigor and codebase dependability, the software was evaluated through an extensive automated verification pipeline alongside formal numerical comparisons against reference implementations in R. The library’s continuous integration framework runs across GitHub Actions, combining Ruff automated linting, strict mypy static type checking, unit and regression tests through pytest, JAX consistency validation, and documentation generation. In its current release, the test suite comprises 461 automated tests that achieve 85.92 percent statement coverage across the core Python modules. Numerical validation confirmed that REMFlow replicates established R implementations across eight exact-time relational models fitted to empirical classroom interactions, matching published coefficients, standard errors, maximized log-likelihoods, and Bayesian information criterion scores within standard numerical convergence tolerances.

The practical utility and end-to-end analytical workflow of REMFlow are demonstrated in the paper through a detailed classroom interaction case study drawn from empirical educational research. The dataset tracks directed verbal exchanges among eighteen students and instructors across two consecutive school days, distinguishing an orderly initial session of 228 events from a subsequent disruptive session comprising 284 events. Following the removal of whole-class broadcast events and self-directed utterances, each observed speech event was statistically contrasted against 306 directed sender-receiver alternatives simultaneously present within the physical room. The investigation evaluated four nested exact-time model specifications for each instructional day: a simple baseline rate model, an expanded demographic model incorporating sender and receiver gender, a structural proximity model adding physical seating adjacency and self-reported friendship nominations, and a fully specified behavioural model incorporating instructor indicator flags, directional prior-contact frequencies, and five distinct participation-shift statistics that capture immediate conversational dynamics such as turn-taking, reciprocal replies, and conversational dominance.

Statistical evaluation of the classroom models revealed that the fully specified relational formulation achieved the lowest Bayesian information criterion on both instructional days, outperforming simpler demographic formulations. For the orderly first day, the full model recorded an optimized log-likelihood of -473.468299 and a BIC score of 1022.947437, matching the benchmark estimates generated by the R package relevent to six decimal places. Similarly, for the second day, the full model returned a log-likelihood of -382.584120 and a BIC of 844.253879 in Python, matching R’s output of 844.253880. Substantively, incorporating gender attributes alone yielded negligible explanatory improvement, whereas adding relational history and participation shifts substantially improved model fit. The immediate reciprocal reply statistic, designated PSAB_BA, exhibited the largest positive coefficient across both days, confirming strong conversational turn-taking tendencies, while seating adjacency and friendship nominations maintained persistent positive associations. Diagnostic assessments demonstrated that the full specification assigned the top probability rank to the actual observed interaction in 51.3 percent of events on day one and 55.3 percent on day two, placing the true event within the top ten percent of candidate alternatives for over three-quarters of all observed instances.

To rigorously examine boundary conditions and parameter identification, Frąszczak evaluated REMFlow against a controlled exact-time synthetic benchmark comprising twenty-five actors and one hundred simulated events, where each occurrence was compared against six hundred admissible alternatives. Data were generated from predetermined parameters: a baseline rate parameter of 0.25, an AB-BA reciprocal participation-shift parameter of -1.00, and a sender-recency parameter of 4.00. Estimation successfully recovered regular parameters, with REMFlow yielding a baseline coefficient of 0.219176 (standard error 0.134616) and a recency coefficient of 3.947238 (standard error 0.544761), matching R estimates of 0.219174 and 3.947240. However, because the simulated sequence contained zero instances of immediate reciprocal reply, the likelihood function approached its supremum asymptotically as the reciprocal coefficient approached negative infinity. Consequently, REMFlow reported a divergent point estimate of -16.981877 with an extreme standard error of 12416.784476, while relevent halted at an iteration limit yielding -9.575548 with a standard error of 305.780383. This controlled experiment highlights that numerical optimizer convergence does not guarantee substantive parameter identification, emphasizing the vital necessity of inspecting data tables, raw event frequencies, and standard errors before drawing empirical inferences.

Expanding beyond basic dyadic exchanges, the library supports discrete action types and categorical covariates, as demonstrated through a specialized misinformation propagation workflow tracking user accounts across conversational platforms. In this operational demonstration, risk sets are expanded to incorporate discrete interaction types—specifically replies, retweets, and user mentions—alongside analyst-supplied stance labels categorized as support, denial, or questioning. The software facilitates descriptive role profiling, calculating actor transmission volumes, interaction reach, echo-chamber mixing metrics, and prospective next-event candidate rankings. Furthermore, the framework incorporates an experimental blocking simulation that evaluates immediate changes in communication probabilities when a specific actor is removed from the active system; in the worked demonstration, isolating account u5 eliminated 33.5 percent of the immediate next-event probability mass prior to renormalisation. Crucially, because this illustrative toy workflow included only five sequential events, the underlying numerical estimation naturally failed to achieve statistical convergence, serving as an explicit instructional reminder that descriptive diagnostic functions must not be misconstrued as asymptotic causal effects or comprehensive long-term contagion forecasts.

Hardware benchmarking on an NVIDIA GeForce RTX 4070 Laptop GPU highlighted substantial acceleration for isolated mathematical operations, alongside practical computational trade-offs inherent in complete analytical pipelines. For repetitive float64 likelihood and gradient calculations across one thousand events, transitioning from single-threaded NumPy CPU execution to compiled JAX GPU kernels reduced evaluation durations from 176.330 milliseconds to 5.734 milliseconds for fifty actors, and from 419.867 milliseconds to 11.055 milliseconds for one hundred actors, representing respective kernel speedup factors of 30.75 and 37.98 while maintaining numerical agreement to within 2.49 × 10⁻¹⁴. Nevertheless, full end-to-end fitting benchmarks conducted on Windows 11 revealed that complete execution times were overwhelmingly dominated by CPU-based risk-set and statistic construction rather than iterative numerical optimization, with data preparation consuming over 85 seconds of an 88-second total workflow. As REMFlow advances toward future releases targeting streaming statistic construction and multi-mode relational hyperevents, the package already provides an open, rigorous, and inspectable foundation for continuous-time interaction research across the wider scientific computing community.

Subject of Research: Computational social network analysis and software engineering for relational event models

Article Title: REMFlow: a python library for relational event modelling

Article References: Frąszczak, D. (2026). REMFlow: a python library for relational event modelling. SoftwareX, 36, Article 103216. https://doi.org/10.1016/j.softx.2026.103216

Image Credits: AI Generated

DOI: 10.1016/j.softx.2026.103216

Keywords: REMFlow, relational event modelling, Python, social network analysis, point processes, event history analysis, dynamic networks, risk sets, tie-oriented models, actor-oriented models, JAX acceleration, statistical computing, maximum likelihood estimation, survival analysis, open source software, interaction networks, software validation