Network science for philosophers

Max Noichl

Utrecht University

2025-07-4

To follow along, visit www.maxnoichl.eu/talk

About Me

• Promovendus at Utrecht University
• Interested in computational methods for philosophy.
• Background in HPS, education in comp. methods via GESIS, CompSciHub Vienna, SFI.
• Working on cognitive dynamics of philosophy, scientific model transfer, scientific information flow…

Goals of this talk

• Introduce key concepts of network science
• Show some examples from philosophy
• Share resources

What are networks?

1. Networks are graphs: Network Vocabulary
2. Networks are a data structure: Networks as data
   • Many things can be understood as networks that we don’t immediately think of as such. E. g. bimodal word – document networks, similarity based networks based on embedding models, networks of collocations, etc.
3. Networks are Matrices: Adjacency Matrix

Some exciting results!

Some exciting results!

• Scale free networks.
• Strength of weak ties.

Degree distributions

• Let’s generate simple random graph: Erdős–Rényi model
• Let’s look at the degree distribution: ER-degrees
• But it turns out, many real world networks don’t look like this! Example: Citations in philosophy

Scale free networks

• Let’s try Preferential attachement: Barabási-Albert Model
• The distribution now follows a power-law \(m * k^{- \alpha}\): Degree distribution BA-model
• It’s common to look at these distributions on log-log plot: Let’s compare!
• The powerlaw exhibits scale-freeness: However you zoom around the graph, it looks the same.
• Also, power-law distributions are heavy-tailed: Tail-comparison
• They are to robust to random, but fragile to targeted attacks: The average node doesn’t predict behaviour.
• These distributions are very common, and suggest rich-get-richer processes: The Matthew effect

For to everyone who has, more will be given, and he will have abundance; but from him who does not have, even what he has will be taken away.

— Matthew 25:29

Barabasi and Albert (1999);

Scale free networks

• These distributions are also common in social networks in philosophy: Petrovich, 2021
• And historically: Collins, 1998 (p. 56/80)
• Also useful to philosophy of science: Rubin & Schneider, 2021

Collins (1998); Petrovich (2022); Rubin and Schneider (2021)

Small worlds & weak ties

• We start with a simple random geometric graph.
• A signal takes quite a while to propagate: Signal propagation.
• But if we add just very few long connections: ‘weak’ ties:
• The signal now propagates much faster: Strength of weak ties.
• Weak, very distant ties are crucial for information spread in real communities. Many real world networks exhibit “small world effects”. (Formally: High clustering and small shortest path length.)
• These properties are highly relevant to network epistemology: Zollman, 2009

Zollman (2009), Granovetter (1983); Watts and Strogatz (1998)

Exploring networks!

Visualization

• Force directed networks: Explore in gephi-lite
• Some guidelines, by Mathieu Jacomy.
• UMAP/t-SNE: Flattening mammoths
• Edge bundling: Helpful, but handle with caution.

Clustering, Community-detection

• What’s a good clustering?
• One idea: Maximize Modularity (more edges within cluster than expected by a null-model)
• Louvain-algorithm: First Iteration.
• We then merge clusters & repeat: Second iteration.
• Leiden-algorithm (slightly improved version of Louvain)
• Stochastic Blockmodel: Explicit statistical model of communities.

• Null = configuration model, preserves degree
• Each node in its own cluster.
• Greedy algo: Does modularity improve? keep, else reject.

Some general thoughts

• Hairballs are the start of an analysis, not the end.
• Are you interested in network effects? Or do you want to control for them?
• Don’t accidentally rediscover random graph theory!
• (Null models are important!)

ERGMS

• How to incorporate null-models into graph-analysis? – There are so many possible graphs!
• One option: Exponential Random Graph Models fitted using MCMC to the adequate graph-category.
• Are features like density, star-patterns, homophilic connections, etc. more common than expected under chance?
• Used to investigate Philosophy of Science itself: McLevey et al., 2018
• Hard to make work in practice, identifiability problems.

Tools

Software

• Network analysis in Python: networkx
• Advanced network modelling in python: graph-tool
• Network-analysis in R (also includes ERGMs): statnet
• Interactive network-visualisation: Gephi
• Easy exploration of scientometrics: Vos-Viewer
• Prettier network-plots in python: Pylabeladjust

Data sources

Citation data

• Web-of-Science
• CrossRef (Great to fix bad citations.)
• Open-Alex (also great for abstracts, OA-literature)

Text-parsing

• Jstor
• Preprint servers (See ArxivHTML)
• Texts can be network-data! Malaterre & Lareau, 2022

Malaterre and Lareau (2022)

Some of my own work

Modeling Model-transfer

• OpenAlex Mapper: A huggingface space.
• Useful to investigate model-transfer, concept-spread, scientific cultures.

Cognitive Dynamics of philosophy

• Philosophical literature, uniform sample, 1950-2015
• We parse positions & examples: Some initial visualizations.
• Some first results (very wip ): Predicting Citation counts

Thank you!

Literature

Barabasi, Albert-Laszlo, and Reka Albert. 1999. “Emergence of Scaling in Random Networks.” Science (New York, N.Y.) 286 (5439): 509–12. https://doi.org/10.1126/science.286.5439.509.

Collins, Randall. 1998. The Sociology of Philosophies: A Global Theory of Intellectual Change. Cambridge, Mass: Belknap Press of Harvard University Press.

Granovetter, Mark. 1983. “The Strength of Weak Ties: A Network Theory Revisited.” Sociological Theory 1: 201–33. https://doi.org/10.2307/202051.

Malaterre, Christophe, and Francis Lareau. 2022. “The Early Days of Contemporary Philosophy of Science: Novel Insights from Machine Translation and Topic-Modeling of Non-Parallel Multilingual Corpora.” Synthese 200 (3): 242. https://doi.org/10.1007/s11229-022-03722-x.

Petrovich, Eugenio. 2022. “Acknowledgments-Based Networks for Mapping the Social Structure of Research Fields. A Case Study on Recent Analytic Philosophy.” Synthese 200 (3): 204. https://doi.org/10.1007/s11229-022-03515-2.

Rubin, Hannah, and Mike D. Schneider. 2021. “Priority and Privilege in Scientific Discovery.” Studies in History and Philosophy of Science Part A 89 (October): 202–11. https://doi.org/10.1016/j.shpsa.2021.08.005.

Watts, Duncan J., and Steven H. Strogatz. 1998. “Collective Dynamics of ‘Small-World’ Networks.” Nature 393 (6684): 440–42. https://doi.org/10.1038/30918.

Zollman, Kevin J. S. 2009. “The Epistemic Benefit of Transient Diversity.” Erkenntnis 72 (1): 17. https://doi.org/10.1007/s10670-009-9194-6.