🕸 Using Networks Science Models in Art and Design

Putting Network Effects to Use!

Introduction

Here, we will see a few Network Behaviours and Network Effects, and understand how they could be useful tools in Art and Design!

Small Worlds

“It’s a Small World” is a aphorism you must have heard before. Most times, it is uttered when you claim to know someone who knows someone you have just met! This seeming “leap of a connection” bridges across communities that may otherwise be isolated. That one small link jumping across “vast distances” seemingly compresses the network into a "Small World"!

Implications

• Target audiences that may seem inaccessible, and very far, may suddenly be not far at all due to one “random link” that bridges communities
• The World becomes smaller than you had thought

Why it matters in Art/Design?

• Try a very tenuous-looking, unlikely location to access a new community of users / artists / designers / collaborators?
• Put yourself / your art/design enterprise in dangerous positions?
• Try meeting communities or people very unlike yourself.

Figure 1: Increasing Random Links ( L to R )

Figure 2: "Network Distance" and "Clustering"

Figure 3: Small World Construction (Emergent)

Preferential Attachment

If you were signing up for a new social media platform, would you rather follow a random user or the most popular user? Most people would choose the latter. This is the essence of preferential attachment, a concept that explains how networks grow and evolve over time.

(a) Preferential Attachment Emerging

(b) Resulting Network

Figure 4

When new nodes are added to a growing network (like web pages or people joining social media), they are more likely to connect to existing nodes that already have many connections. This creates a “rich get richer” effect. This is akin to the [Matthew Effect] from the Bible:

Figure 5: Matthew Effect

Some examples:

• Imagine a school where kids form friendships.The kid who has the most friends is always invited to more parties (gets more invitations). A new student joins and wants to make friends—instead of randomly picking someone, they choose the kid with the biggest social circle because that’s where the “buzz” is.
• The Internet topology (where some servers are connected to thousands of others)
• Social media networks (a few influencers have millions of followers)
• Biological protein interaction networks (some proteins interact with far more partners than most)

The model is a simplified abstraction, but it provides critical insight into why real-world complex systems exhibit such specific statistical properties. It also serves as the foundation for models like the Barabási–Albert model, which uses preferential attachment to simulate network growth and predict system behavior under various conditions.

Implications

• Power-law degree distribution: The probability \(P(k)\) that a node has k connections follows a power law: \(P(k) ∝ k^{-γ}\). This means most nodes have very few connections, but a small number of “hubs” dominate.

Figure 6: Power Law for Node Degree with Preferential Attachment

• Self-reinforcing growth: As the network grows, hubs become even larger because they attract more connections.
• Emergence of scale-free structure: Over time, this process creates networks with an infinite number of possible connection paths and robustness against random failures.

Why It Matters in Art/Design

• The robustness of infrastructure networks (many small links can fail, but hubs remain). OTOH, if these hubs fail, the network comes to a halt. So more money, typically, would be spent in protecting hubs.
• The spread of information or disease through a population is controlled by hubs. Innoculate them, and you are better off.
• If one is on a fund-raising platform, add some seed funds to each new user, and they will be more likely to attract more funds. This is a preferential attachment effect.

Metcalfe’s Law

Discussion Questions

Conclusions

References

1. The Network Effects Bible. https://www.nfx.com/post/network-effects-bible
2. Duncan Watts and Steven Strogatz. (1998). Collective dynamics of ‘small-world’ networks. Nature 393, 440–442. https://snap.stanford.edu/class/cs224w-readings/watts98smallworld.pdf
3. Mark Granovetter. (1973). The Strength of Weak Ties. American Journal of Sociology 78(6): 1360–1380. https://snap.stanford.edu/class/cs224w-readings/granovetter73weakties.pdf
4. The Startup Junkie.* How to be a Connector*. https://startupjunkie.org/2021-12-1-the-power-of-weak-ties-tips-on-how-to-become-the-connector/
5. Ran Katzir. Experience Network Science through Play. https://medium.com/@ran_katzir/teaching-network-science-using-board-games-f78489a3b3bd ( Describes an in-design board game.)
6. Mitchell Resnick. Beyond the Centralized Mindset. https://web.media.mit.edu/~mres/papers/JLS/JLS-1.0.html
7. Thomas W. Valente.(2012). Network Interventions. Science(337) 49. Available here https://sci-hub.se/10.1126/science.1217330. The term “network interventions” describes the process of using social network data to accelerate behavior change or improve organizational performance. In this Review, four strategies for network interventions are described, each of which has multiple tactical alternatives.
8. Nicholas Christakis. (May 3, 2024). To exploit social contagion, tools are needed to efficiently identify individuals who are better able to initiate cascades. To be maximally useful, such tools should be deployable without having to actually map face-to-face social network interactions. https://t.co/DHCKxXeGYg. This is a paper that presents design tools that exploit the “Friendship Paradox” to create Social Contagion. A quick summary of the paper is available here. https://www.science.org/doi/10.1126/science.adi5147
9. David Pinsoff. (Dec 2025).Everything is Bullshit Substack. https://www.everythingisbullshit.blog/p/a-big-misunderstanding
10. fee.org.(Wednesday, September 19, 2018 )How Can Game Theory Prevent Disease Outbreaks.https://fee.org/articles/how-game-theory-can-help-prevent-disease-outbreaks/

Important Papers in Network Science

1. Watts and Strogatz on Small Worlds

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2. Vespigniani on Hubs

3. Mark Newman, The Physics of Networks. Good intro Power Laws and examples of many networks.

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