The World as I See It

Our perception of the world is limited by our current understanding, i.e. the models and theories that explain and describe the fundamental behaviors and characteristics. With every new model or theory, we step outside of this worldview, capturing a bigger perspective from our original ones.

In network theory, one of the famous models before Strogatz and Barabasi’s is the random graphs by Erdos and Renyi in 1959. It posits that in a system, the nature of the interaction of two parts in the system is random. That is, all pairs of nodes in a network is connected by a certain probability. While this worldview fails to capture several important properties that many real-world networks exhibit, this model provides a rudimentary framework as to how we view the world. At the very least, it reinforces the systems thinking approach wherein it is not enough to look at the individual parts to understand how the whole system works. Four decades later, a new perspective on modeling real-world systems was found.

Two of the real-world properties that random graphs fail to account are the tendency of nodes to cluster together to form communities and the small-world effect, appropriately described by the six degrees of separation phenomenon. Watts and Strogatz addresses the clustering tendency property by forming a ring- like network wherein most of our connections are also connected among one another. As for the small- world effect, introducing a rewiring probability that connects different communities together addresses this. Using those nodes that bridge communities, the six degree of separation phenomenon is captured.

As with many models, it would be able to capture some of the properties, but not all. One property that the Watts-Strogatz model failed to account is the existence of hubs, as a consequence of preferential attachment. In social networks, there is a tendency for humans to attach to other humans with high number of connections, called hubs. This leads to a power law distribution of connections, with a few nodes having many connections and many nodes having few connections, forming what is called a scale-free network. Barabasi and Albert has modeled this behavior through a growing network model, based on preferential attachment i.e. it is likely for a new node to connect with another node with high number of connections. Effectively, they have simulated the power law distribution exhibited by real world networks, leading to a widespread adaptation of this model.

However, no model is truly complete due to the sheer complexity of a system and its ability to evolve, possibly leaving behind the models which were accurately describing it beforehand. In a few years or maybe even a few months, a fresh perspective may cause this view of power laws in real world to be changed. In fact, there have already been some articles expressing how some of the real-world systems believed to exhibit the power law distribution may only be due to a bias of expecting a power law. In many papers, a power law is usually observed by plotting the distribution in log-log scale and fitting a line there. This makes it easily susceptible to confirmation bias. As such, it is necessary to avoid making any preconceptions on the nature of a system in order to avoid falling into the said trap.

That is not to discount the power of power law. It has beautiful implications in comparison of systems across different fields. For example, from systems with similar exponents, we can generate insights based on our understanding of a different field. Also, while not universal, there are still systems which almost perfectly exhibits the power law. And so, depending on the system, it is a powerful tool to understand these systems.

Real-world systems are very diverse and is continuously evolving and adapting. And so, one conclusion that may be observed from these continuous changes in the models is that there may be no universal model that can accurately capture all real-world systems. That is powerful on its own as it provides an avenue to segment the systems into different classifications, whether they are random, scale-free, or some sort of hybrid. It would then be easier to make transfer of insights from one random network to another and from one scale-free network to another. It has only made the field of network science more interesting since it isn’t a rigid science that only has one solution that works for all. While a universal solution is indeed elegant, the diversity of real-world networks is beautiful and something worth looking into. However, as with any science, it is completely arrogant to assume that this is the final version of truth. New data may come in that may help in creating a universal model. That, however, will be left for us to see in the future, and perhaps even take a part of.