In this first part, I am explaining the Barabási-Albert model, which shows that in social, economic, biological, ecological, and electronic networks the elements which already have more connections are preferred.
Networks are everywhere: social networks, the Internet, human networks, protein interaction networks, citation networks, ecological networks... Unless we are part of a machine, we are surrounded by complex systems, including ourselves. These complex systems are made up of networks in which every element is connected to others via complex relationships. Understanding these networks is crucial for effective decision-making in the unpredictable and uncertain sea of relationships that surrounds us.
One of the researchers who set out to study these networks is Albert-László Barabási. A pioneer in the field of network science, Barabási has made significant contributions to our understanding of complex systems through his research on the structure and dynamics of networks. His work sheds light on the fundamental principles that determine the behavior of networked systems such as social networks, the Internet, populations, or corporate structures.
In 1999, Barabási mapped the World Wide Web and realized that the distribution of connections there did not demonstrate a Poisson distribution as expected for random networks, but rather a scale-free power law distribution[1]. Together with his colleague Réka Albert, he then analyzed other natural networks showing that, universally, gradual growth and 'preferential attachment' caused emergence of scale-free behavior in these networks. This is called the Barabási-Albert (BA) model of scale-free networks. Characterized by very few highly connected nodes and many nodes with fewer connections, this model reflects the natural growth and evolution of networks in contexts ranging from social networks, living bodies and the internet to corporate structures and supply chains.
At the heart of the BA model is a predisposition to 'preferential attachment', defined by the fact that new nodes entering the system are more likely to be connected to existing highly connected (high degree) nodes. This phenomenon explains the 'rich gets richer' observation seen in many real natural networks, where these higher-ranked nodes increase their connections at a faster rate. These nodes are called hubs. These hubs attract connection traffic to themselves causing very few highly connected ones at one end while the majority of nodes cluster in a corner with fewer connections. In this way, the network demonstrates a power law distribution or Pareto distribution rather than a distribution with stable mean (Figure 1). This emerges as a product of preferential attachment.
A typical example of this phenomenon can be found in online social networks. Platforms such as Facebook, Twitter and Instagram are structured in such a way that popular posts - those that have already received a significant number of likes, shares or comments - are more likely to be shown to other users. This increases their visibility and therefore the likelihood if greater engagement.
The startup ecosystem is another area where preferential connections are common. Venture investors often prefer to invest in companies that have already received funding from reputable investors. Previous funding is seen as a sign of a startup's potential and reduces perceived risk. As a result, startups that successfully raise initial funding are more likely to attract additional investment, creating an increasing cycle of financial support. This leads to a small number of fresh start-ups rapidly gaining traction and value, while the majority fail to break through.
In academia, new researchers or papers tend to cite well-known and frequently cited works. This creates a network in which a small number of influential papers collect many citations and become hubs. Similarly, leading researchers often collaborate more with those who are better known, leading to highly connected individuals within academic networks.
We can observe and replicate these examples in protein interactions, socio-cultural networks, fashion, music, the development of languages, and animal interactions. The concept of scale-free networks and the BA model of preferential attachment is not only an academic endeavor, as it guides our understanding of complex systems, but it can also provide us with very useful insights in our daily work life, as it affects decision-making processes, strategic planning and the identification of potential pitfalls. In the second part of this article, we will examine the insights, strategies and pitfalls of this model for decision making, especially decision making in business.
References
- Barabási, A. L., & Albert, R. (1999). Emergence of scaling in random networks.Science
- Holme, P. (Ed.). (2021). Networks with growth and preferential attachment: modelling and applications. Journal of Complex Networks, 9(1), cnab008
- Barabási, A. L.,Network Science, (2015) (networksciencebook.com)
[1] See my previous article: Liberation from the bell: power to outliers | Cognitive Workshop (afifsay.org)