A Preliminary Analysis of Co-authorship Networks of a Community of Philippine Physics Researchers

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Our new research work got accepted in the journal Scientometrics: 

• K.M.A. Aguana and R.C. Batac, Emergence of power-law statistics in the co-authorship networks of Philippine physics researchers, Scientometrics (2025). 

Here are some thoughts and behind-the-scenes regarding the conceptualization, analyses, and delivery of the work. 

Laying the foundation. I started working on co-authorship networks of Filipino authors in physics in 2017 together with my student Jasmine Abella (Jas). We began with the set of papers from the National Institute of Physics (NIP), College of Science (CS), University of the Philippines Diliman (UPD) [1] and, in the following year, we extended it to the publications of UPD [2]. Our analyses focused on the occurrence of Zipf's law, an empirical observation wherein the rank \(r\) of an observation is inversely proportional to its occurrence \(C\), i.e.

\[\begin{equation}\label{eqn:zipf}C \propto 1/r = r^{-1} \end{equation}\]

In our work, we count the number of times an author has collaborated with other researchers, and found that these collaborations plotted by the rank of the author begin to show regimes that obey Eqn. (\(\ref{eqn:zipf}\)) over time. The transition from an exponential (suggesting a random process) to Zipfian (indicating complex, rich-getting-richer mechanisms) over time is an interesting storyline, one that we revisited in the most recent work. 

Fast forward to 2021, while working with Kiona Aguana, we revisited this co-authorship network research, this time for an extended “community” involving five higher education institutions (HEIs) in the Philippines (more on this later). We worked on the data from 2011-2020 (the last decade available at that time) for her undergraduate thesis, and even submitted the paper to Scientometrics. Our results not only show Zipfian statistics for individual authors, but also for connected clusters within the entire co-authorship network; i.e. if the giant connected cluster (GCC) with size \(N_1\) number of authors is set to be rank \(r=1\), the next separated cluster with size \(N_2\) authors for \(r=2\), and so on, we will also obtain regimes that obey power-law \(N\) vs. \(r\) plots, albeit with a slightly different negative exponent. Due to time constraints, however, we had to withdraw the submission. 

When Kiona came back for her masters, we revisited the topic and obtained an even larger data set. 

The data. We limited our data to the physics departments from five HEIs that were originally given a Center of Excellence (COE) in Physics accreditation by the Commission on Higher Education (CHED). This ensures that these departments have the most mature and productive undergraduate and graduate (especially doctoral) programs in physics in the country. The five HEIs considered, in alphabetical order, are: Ateneo de Manila University (ADMU), De La Salle University (DLSU), Mindanao State University-Iligan Institute of Physics (MSU-IIT), University of the Philippines Diliman (UPD), and University of San Carlos (USC).

Incidentally, we also noted that these five HEIs are the pioneers in the physics community in the Philippines (at least from academia). In an early work that collected papers from 1979 to 1980, Arunachalam and Garg reported that the Philippines had zero papers in the physical science and astronomy domain, in contrast with the dozens produced by its southeast Asian neighbors [3]. Our own analyses revealed a paper in 1963 from the Physics Department of USC, which we disregarded (because it will leave a long period without new papers from the community). The first few papers from the local community came in 1985 through UPD (it should be noted that the National Institute of Physics was established from the Physics Department of UPD in 1983). It was followed by papers from the physics departments of DLSU; and then USC; then ADMU; and, finally, MSU-IIT. From 1985 to 2009, the number of papers from this community accounted for around 52% of all the papers from the Philippines (using the results of a simple search for a broad category of physics and astronomy from Scopus). 

Key insights. One of the promising results is the recovery of faster-than-linear trends in the cumulative counts of the number of papers and the number of authors over the years. The author count trends are even “disrupted” over the last few years due to the papers borne out of very large collaborations (such as in particle physics joined by UPD researchers and atmospheric physics from ADMU), leading to sudden jumps in the number of co-authors even with just a few papers. On the other hand, the cumulative number of papers showed a slower exponential rate of increase over the last decade and a half, which we attribute to the limited community that we considered; we believe that the trends will follow the same or possibly even steeper exponential curve when all the other HEIs with physics degrees are added to the study. 

The growth of the community is also manifested in the number of distinct connected clusters, i.e. the independent subgroups that are being included in the system. We extended Kiona's original work on the subgroup count vs. rank, and obtained two trends: the first is the increase in the size of the GCC, indicating the connectedness of the previously disparate subgroups into the main cluster, and the second is the extension of the tails of the size vs. rank plot, indicating that new independent groups are continuously being added over time. Both results bode well for the community. 

Co-authorship network of Philippine physics researchers from the five HEIs.

The state of collaboration among researchers, institutions, and countries are also probed in the work. One of the striking results here is the fact that, at the institutional level, despite the small data set (only five HEIs), the within-community co-authorship network is not fully connected! There is no DLSU to MSU-IIT connection as of yet [maybe we could—and should—do something about that!]. This just highlights the fact that the local physics community has yet to evolve towards a more collaborative and inclusive network. In the paper, we noted how these observations are also noted in the national scientific agenda of the Philippines for the past two administrations. If the physics community is to grow and contribute to the national development, these early challenges need to be addressed. 

Finally, the title of the paper reflects the results that are particularly interesting (at least for us) from a scientific point of view. By all accounts, the community is still relatively young, even at forty years. But the emergence of robust statistical regularities are very prominent in our analyses. Both measures of co-author counts (the number of unique individuals an author has worked with) and co-authorships (the number of collaborations, i.e. the co-author count multiplied by the number of papers) reveal power-law statistics. Interestingly, the co-author distributions follow a power-law with exponent almost equal to 2; this value is revealed to be the lower limit of a model of a preferential attachment probability asymptotically close to linear [4]. This indicates that the number of co-authors follow preferential attachment mechanisms, a rich-getting-richer phenomenon. The fact that it deviates from the usual power-law with exponent of 3 (as in the Barabasi-Albert preferential attachment model) is due to the fact that the preference is not per individual, but for strongly-connected cliques. 

We also noted that the power-law distribution of the co-authorship measures directly leads to Zipf's law, as given by Eqn. (\(\ref{eqn:zipf}\)) [5]. In this case, the last two decades of data already show stable Zipfian rank-size plots. 

 

Oftentimes, when asked to discuss (for example, in class) a case of the emergence of complexity in human interactions, I cite other examples from older studies of well-represented groups. With this work, we are able to see how these emergent properties manifest in a local setting, with names and papers that are familiar to us. Now, when students ask for examples of complex systems, it's exciting just realizing that I can now use this work as a reference. ■

References:

[1] J.M.T. Abella and R.C. Batac, Temporal and social network analysis of the co-authorship networks from papers from the National Institute of Physics, Proceedings of the Samahang Pisika ng Pilipinas 35, SPP-2017-PB-35 (2017). URL:https://paperview.spp-online.org/proceedings/article/view/117. 

[2] J.M.T. Abella and R.C. Batac, Social network analysis of the co-authorship network of the University of the Philippines Diliman from 1996 to 2016, Proceedings of the Samahang Pisika ng Pilipinas 36, SPP-2018-PB-39 (2018). URL: https://paperview.spp-online.org/proceedings/article/view/SPP-2018-PB-39. 

[3] S. Arunachalam and K. C. Garg, Science on the periphery—A scientometric analysis of science in the ASEAN countries. Journal of Information Science 12(3), 105-117, https://doi.org/10.1177/016555158601200303 (1986). 

[4] P.L. Krapivsky, S. Redner, and F. Leyvraz, Connectivity of growing random networks. Physical Review Letters 85(21), 4629, https://doi.org/10.1103/PhysRevLett.85.4629, (2000).

[5] D.M.T. Ordoñez and R.C. Batac, Testing the validity of Zipf and Pareto laws: A multi-method approach. Physica A: Statistical Mechanics and its Applications 675, 130827. https://doi.org/10.1016/j.physa.2025.130827 (2025).