Understanding the world through networks

This is an introduction to the world of networks, a very powerful concept that has been the underpinning of many important innovations and structures in history and is even more important today, in our interconnected world. As the ones who know me are well aware of, I am a huge nerd about network effects. To understand them and their importance completely, gaining an understanding of a couple of foundational concepts is important, networks themselves being one of them. Below you can find an introduction into the world of networks, starting from 0. I will tend to use the scientific definitions of terms but will sometimes use my own terms to describe nuances that I have seen. This is a part of a multi-part series that I will work on for the foreseeable future. I often write about concepts that I simply find interesting. In this instance, I am actually qualified to write about it. I have been writing about network effects for some time, worked at Stripe on Marketplaces, gathered experience at Uber and was the expert for Masterplan.com on Platforms and Network effects.

The Basics

Let us start with a definition. A network can be defined as 'A pattern of interconnections amongst a set of things'. This can be the connections among humans in their circle of friends, the connections between different train stations or the connections of trading partners on a market. Here are two visual examples of very simple networks.

Figure 1: Small Social Network
Figure 2: Train network


Figure 1 shows a simple social network with 4 people. A connection between two people signals that those people are friends with each other. While Mary is friends with Jack and Peter, she is not friends with Anna. If you need something less fuzzy than the idea of a real-world friendship just assume that a connections signals that these people are connected with each other on a platform like Facebook.

Figure 2 shows a very similar form as figure 1 if you simply look at the number of circles and the lines between them. However, it describes a very different relationship. Figure 2 shows the 4 train stations on an island and connections between them. A line between two train stations implies that there is a direct train connection between the two stations without a stop at any of the other stations.

The goal of presenting two very similar graphs (need to define before or talk about using it later), that explain two different networks is to indicate how broadly the concept of networks can be applied. The world is increasingly interconnected. Supplier networks, communication networks, physical networks like electricity grids, they are everywhere. Understanding networks means obtaining a better understanding of the complex world we live in. To effectively communicate about such an all-encompassing concept, we need specific language to ensure that we are taliking about the same things. Let us give names to the 'circles' and 'lines' from the figures.

Nodes, edges and graphs.

In network theory, the things represented by the circles in the figures are called 'Nodes' and the lines symbolizing their connections are called 'edges'. For example, you could say that the Node 'Mary' had two edges. One with Peter and one with Jack, whereas the Node 'Anna' only had one edge with Jack.

A graph describes the graphical depictions of a network in the way we showed it above. I have actually used the word earlier in the text without defining it since it has an intuitive explanation to it.

Figure 3: Nodes and Edges in a Network

Networks can have a multitude of nodes and edges or just a handful as in our examples above. To think of a complex network, imagine the number of connections in social networks like facebook or the links between websites google is indexing. You can see an example of a more complex network graph with a vast number of nodes and edges below. Here is one example of Facebooks global network of connections built by a former intern in Facebook's data infrastructure engineering team.  As you can see, using some context, in this case the outline of the continents on our planet can sometimes greatly increase the expressiveness of a network graph. In this case, you cannot focus on individual nodes or edges anymore but just see the truly magnificent pattern these nodes and edges create.

https://www.facebook.com/notes/facebook-engineering/visualizing-friendships/469716398919


Network Theory, or more specifically the research into complex networks is also used to combat the spread of contagious diseases. You can find an interesting paper on the topic here and find a visualization below.

Complexity in global, network-driven contagion phenomena.


You might get a semblance of why I think this topic is very important based on the examples above. I actually think that it is one of the most important concepts to understand to prevail in our connected world and will give a short explanation of why below.

The Value of Network Theory

The theory of networks combines explanatory value and practical value like few others I know.

Network theory has very high practical value. There are many concepts that have theoretical value but do not really help you in everyday life. Network theory on the other hand can be of practical value for you, regardless of whether you want to analyze your social circle, build a startup or design a new transport system. Understanding it enables you to be a more effective manager, a more thoughtful friend and a better researcher.

In addition to practical value, it has very strong explanatory value. A concept is truly powerful if it either explains a lot of different things or if it explains specific things in a lot of detail. The explanatory value of something is the product of the number of things it explains and the specificity of how well it does so. Only the greatest concepts can combine explaining many things very well. This is why physics and mathematics are such powerful areas. They are very precise and their foundational concepts can be used to explain a lot of different phenomena. The theory of networks is less precise than physics but the best theory to explain very fundamental areas like social networks or network effects in products. It also explains a lot of different areas as we explored above. So the first reason why network theory is important is because it has a lot of explanatory value. It helps you to understand the world.

This is the first part in a multi-part series I have planned on network effects. Once I publish the next articles, I will publish them here. If you like the above, feel free to follow me on Medium for my writing or on Twitter for my irregular thought blurbs.