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Epidemiological Models of Topic Propagation in Co-authorship Networks: Degree-Block Models Versus Homogeneous Mixing

This paper challenges the validity of using co-authorship networks as the substrate for epidemic models of topic propagation, demonstrating that degree-block models do not consistently outperform homogeneous mixing models because most topic adoptions occur without prior collaboration with active authors, suggesting that true contagion requires networks that include non-adopters and predate adoption.

Original authors: Ismael Robles-Martínez, Jorge Cruz-Trani, Daniela Aguirre-Guerrero, Ricardo Marcelín-Jiménez

Published 2026-10-26

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ismael Robles-Martínez, Jorge Cruz-Trani, Daniela Aguirre-Guerrero, Ricardo Marcelín-Jiménez

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

For decades, scientists have watched how new ideas spread through the research community, treating the process much like a virus moving through a population. When a researcher publishes their first paper on a new subject, they are considered "infected" with that idea. If they stop publishing on it, they are "recovered" or have moved on. For a long time, the standard way to model this spread assumed that every scientist had an equal chance of meeting every other scientist, a concept known as homogeneous mixing. It was a simple, clean picture: ideas float in the air, and anyone can catch them at any time. However, the real world of science is not a free-for-all. Researchers work in tight-knit groups, collaborating repeatedly with the same small circle of colleagues. This creates a complex web of connections, where some scientists are central hubs with hundreds of co-authors, while most have only a few. The question that has lingered is whether this specific web of connections is the true engine driving how ideas spread, or if the simpler, random-mixing model is actually sufficient to explain what we see.

A team of researchers from the Universidad Autónoma Metropolitana in Mexico City set out to test this question by looking at eight distinct fields within computer science, ranging from established topics like online data processing to emerging areas like tiny machine learning. They gathered data on every paper published in these fields up to 2024, identifying the authors and mapping out exactly who had worked with whom. Instead of assuming everyone could talk to everyone, they built a digital map of the actual co-authorship networks for each topic. On this map, they placed the "infection" of an idea onto the authors who first published on it and watched how the models predicted the spread compared to the real historical data. They ran two types of simulations: one that ignored the network structure and assumed random mixing, and another that respected the actual connections, accounting for the fact that some authors have many more collaborators than others.

The results challenged the assumption that the complex network structure is the primary driver of how ideas take hold. When the researchers compared the predictions of the network-based models against the real-world adoption curves, the more complex models did not perform better. In fact, in twenty-four separate comparisons across the different topics and models, the network-based approach only provided a better fit in three cases. The simpler model, which ignored the specific web of connections, was just as good at predicting how many authors would join a field over time. This suggests that the intricate details of who knows whom are not the main factor determining how fast a new topic spreads.

The researchers dug deeper to understand why the network structure seemed to matter so little. They discovered a fundamental flaw in using the co-authorship network of a specific topic to model the spread of that very topic. The network they built was constructed entirely from the people who had already adopted the idea. It was a map of the infected, not the susceptible. In many cases, between 64% and 95% of the authors who entered a new field did so without having co-authored a paper with anyone who was already active in that field. They arrived independently, perhaps reading a paper or attending a conference, rather than catching the idea through a direct collaboration. Because the network was built from the people who had already joined, it cannot be the substrate of the contagion. The network was a result of the spread, not the cause.

Furthermore, the researchers found that the mathematical properties used to predict the speed of an epidemic in a network were often unstable in this context. The models relied on a specific number derived from the network's structure to determine how contagious an idea was. However, for three of the four growing topics, this number was so sensitive that the model could not determine a unique value for it; the best fit was always pushed to the very edge of the possible range. This indicates that the data simply does not contain enough information to pin down the exact rate at which authors recover from a topic or abandon it. The growth of the field, however, was clear and measurable, but the internal mechanics of the network model were too fragile to explain it.

Ultimately, the study concludes that to truly understand how ideas spread through collaboration, we need a different kind of map. The network used in this study only included the people who eventually adopted the topic, missing the vast majority of researchers who never joined. To see the contagion in action, one would need a network that includes everyone, including those who never adopted the idea, and that exists before the idea spreads. Without a map of the susceptible population that precedes the infection, the complex network models cannot outperform the simple assumption that ideas spread through a general pool of researchers. The findings suggest that while collaboration is essential to science, the specific web of co-authorships within a single topic is not the hidden engine driving the adoption of new ideas.

Technical Summary: Epidemiological Models of Topic Propagation in Co-authorship Networks

Problem Statement
Since the 1960s, the spread of research topics has been modeled using compartmental epidemiological models (SI, SIS, SIR) under the assumption of homogeneous mixing. A previous conference version of this work fitted these homogeneous models to eight Computer Science topics and observed that the largest residuals occurred in topics with specific network structures, leading to the conjecture that co-authorship network topology significantly influences topic adoption. However, the conference version did not test this conjecture with network-based models. This paper addresses whether incorporating the empirical structure of co-authorship networks via degree-block (heterogeneous mean-field) approximations provides a better fit for topic propagation than homogeneous models, and investigates the validity of using the topic-specific co-authorship network as the substrate for contagion.

Methodology
The study analyzes eight Computer Science topics (ANFIS, BPEL, DHT, OLAP, GP, GNN, TinyML, QML) using data from the Scopus database up to 2024.

Data Construction:
- Networks: For each topic, a static, unweighted co-authorship network is constructed where nodes are authors and edges represent co-authorship on at least one record of the topic. Crucially, these networks contain only eventual adopters; edges are formed by publications that define adoption.
- Epidemiological States: Authors are classified into Susceptible (S), Infected (I), and Recovered (R) states based on their publication history:
  - SI: Infected from first publication onwards.
  - SIS: Infected only in years they publish; susceptible otherwise.
  - SIR: Infected from first to last publication; recovered thereafter.
- Degree-Block Approximation: The networks are partitioned into blocks based on degree $k$ . The contact matrix $C$ is derived from empirical degree correlations $P(k'|k)$ , capturing the probability that a node of degree $k$ connects to a node of degree $k'$ .
Model Fitting:
- Both homogeneous and degree-block SI, SIS, and SIR models are fitted to the same observed time series (cumulative adopters, active authors, or authors in their active period).
- Constraints: Both model families use the same initial conditions (observed proportion of infected authors in the first year) and the same number of parameters.
- Optimization: Parameters (transmission rate $\beta$ , recovery rate $\gamma$ ) are estimated via non-linear least squares using the Trust Region Reﬂective algorithm.
- Comparison: Goodness of fit is evaluated using Normalized Root Mean Square Error (NRMSE) and the Akaike Information Criterion (AIC).

Key Contributions and Results

Model Fit Comparison:
Contrary to the initial conjecture that network structure improves fit, degree-block models outperformed homogeneous models in only 3 out of 24 comparisons (8 topics $\times$ 3 models). In the majority of cases, the added complexity of the network structure did not yield a statistically significant improvement in fitting the adoption curves.
Network Substrate Validity:
The analysis reveals a fundamental flaw in using the topic co-authorship network as the substrate for contagion:
- Entry Mechanism: Between 64% and 95% of authors enter a topic without co-signing with an author already active in that topic. This implies that the network edges (co-authorships) are often formed after or independently of the initial adoption, rather than preceding it as a transmission vector.
- Spectral Radius and Localization: The spectral radius $\rho(C)$ , which determines the epidemic threshold and enters the basic reproduction number $R_0$ , is dominated by very small structures. Specifically, the leading eigenvector of the contact matrix is often localized on the authors of a single article. Consequently, the network reproduction number can be set by the author list of a single paper rather than the global network structure.
Parameter Identifiability:
- Recovery Rate ( $\gamma$ ): For three of the four growing topics, the fitted recovery rate (and consequently $R_0$ ) consistently hit the upper bound of the search interval ( $\gamma \in [10^{-2}, 10]$ ). This suggests the data cannot reliably identify the recovery rate or the network reproduction number.
- Growth Rates: In contrast, growth rates (including the adoption growth rate $\beta$ ) did not hit search bounds, indicating they are more robustly identifiable from the data.

Significance and Claims
The paper concludes that the topic co-authorship network, as constructed from adoption records, cannot be the substrate of the contagion because the majority of adoptions occur without prior collaboration with active authors in that specific field. The network is a consequence of adoption rather than its cause.

The authors assert that testing contagion through collaboration requires a network that:

Precedes adoption: It must exist before authors enter the topic.
Includes non-adopters: It must contain authors who are susceptible but have not yet adopted the topic.

The study refines the previous conference version by demonstrating that while degree-block models are theoretically superior for capturing heterogeneity, their application to topic propagation using post-hoc co-authorship networks fails to improve predictive accuracy due to the misalignment between the network structure and the actual mechanism of idea diffusion. The results highlight the limitations of inferring contagion dynamics solely from the network of adopters.

Technical Summary: Epidemiological Models of Topic Propagation in Co-authorship Networks

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