Networks are everywhere, and they are beautiful

This is another popular-science post, for anyone out there who wants to see the light of network science! It could be considered a network sermon of sorts. This is also the way how I begin my course on complex networks and most of my pop science talks.

networks from genetic regulation to the Internet

So, why are networks so fundamentally important? Because they exist on all levels of the living universe.

Let’s begin by having a look at what’s inside our cells. First, there is some (messy) software written into double-stranded DNA, where the functional subunits are called genes. They like to talk to other genes, upregulating or downregulating their activity. This network of genetic regulation determines what happens inside our cells. In particular, it determines which proteins are to be built. Mirroring the genes that code for them, the proteins also like to interact, again forming a network (which is coupled to the network of genes…). To make all this happen, some fuel and some building blocks are needed, and this is taken care of by a network of chemical reactions: the metabolic network that is responsible for the logistics of energy and matter.

Our cells are full of networks. We are full of networks.

As it often happens in nature, similar kinds of structures emerge on multiple levels. If we now zoom out from inside the cells and look around, we again see networks. This time, the networks are those of cells talking to one another and influencing each other’s actions, the immune system being a most beautiful example (I’ll return to it in a later post). But there are no cells that are more fond of networking than neurons, the nerve cells. I am typing this paragraph because of spike trains transmitted by each of my ten billion neurons to about ten thousand other recipient neurons (this much can be said, but no-one knows how these spike trains actually encode the words that I am typing). These neurons are the fundamental building blocks of my brain, a network of enormous complexity (and by that I don’t mean my brain but any human brain).

Let us continue zooming out to get a broader view. Just like the neurons inside them, brains also like to network! Practically speaking, we do not even exist in isolation. Our brains have evolved into social supercomputers: most of the concepts inside our heads exist because larger networks of brains have agreed that they are meaningful, and developed a language to describe them. And boy have we come a long way from those times when these larger networks were of the size of a tribe (of about 150 members, it has been claimed). Now our connections transcend space and time through social media and the Internet, and we are all part of a gargatuan social network that spans the entire planet.  What is happening right here, right now, is a long-distance connection between two brains. One brain talks to another, mine to yours, across time and distance. Hi, brain!

But these networks of brains do not only exist for talking. We humans like to build things: systems of trade, structures of power, grids that transmit energy, webs that transmit information, organizations that exist for making things that didn’t exist before. We dig up raw materials and transform them into parts that are brought elsewhere and merged with other parts to make larger parts, over and over again, until this complex weave of logistics and manufactoring spits out cars and cloud servers. We connect cities with ships and trains and airlines; we connect minds with phones and computers.

We really, really like to build networks. But we cannot do it alone, so we connect with others. We form networks that build networks. The same thing that happens on all levels. From genes to cells, from brains to people. Networks building networks.

This is why networks are cool, essential, and beautiful.

(I’ll stop here to end on a high note. I’ll talk about applications and other earthly things in later posts).

Mobile phone calls in time

This is a popular-science post; I am giving a talk to science journalists at the Academy of Finland on 27.4., and this post provides background material if anyone wants to write a story. But you don’t have to be a science journalist to enjoy this, so please read on!

My research group has worked on mobile phone data for over a decade. How our research is called has evolved over this time span, from social network analysis to data science and computational social science. Within these fields, mobile phone data analysis has emerged as its own subfield. Whatever you choose to call what we do, we quantify the behavioural patterns of up to millions of individuals.

We use auto-recorded, anonymized, time-stamped call detail records, provided by teleoperators for purposes of science, or collected by other means, like smart-phone apps. These records (who called whom and when) allow us to reconstruct social networks and also to look at patterns in the times of calls. It turns out that a ton of useful information is contained in such patterns!

Let us first look at very short time scales – seconds or minutes. If we take an (anonymous) person, or a pair of persons, and for each call, draw a line on an axis that represents the flow of time, it will look like this:

Burstiness of phone calls

The pattern above is bursty – it is random but not uniformly so! Rather, there are bursts of mobile phone calls within very short times, and longer gaps between these bursts. It turns out that human activity patterns are very often bursty – and I think it’s safe to say that no-one really knows why. Interestingly, this is also how the firing patterns of nerve cells look like! So maybe we are just neurons in the great, self-aware social network that spans the entire planet… Well, let’s leave that idea for writers of science fiction!

Let us move to somewhat longer timescales (hours, days) from the rapid bursts. What we encounter next is something that is far better understood – and very naturally so: circadian rhythms, our daily patterns of activity that follow a 24-hour cycle. If we pick a few people, and count how many calls they make at each hour of day (averaging over longer periods), we see something like this:

Chronotypes and call rhythms

So even though people mostly sleep at night and are awake during the day, their rhythms are different, and this is clearly reflected in their calling behaviour too! There are individuals who are early birds, already making calls while others still sleep, and there are individuals who talk a lot at night with others like them. We are all different!

However, there’s much more to this story. Our rhythms differ not only in call frequencies: who we call also depends on the time of day, with evenings being often reserved to our closest ones. Further, it seems that our rhythms correlate with many other behavioural patterns  – but you’ll have to wait a bit to hear that story because we haven’t written it up yet, so consider this as a teaser trailer only. (Update: see this preprint)

Now move on to even longer time scales – months and years! Here, the times of single calls don’t really matter that much, so for every person, let’s sum up the number of calls to everyone they know and see how these patterns change in time! For each person (“ego”) that we look at, we’ll get something like this:

Social signature

This social signature measures what fraction of an ego’s communication is targeted at the person they call the most, 2nd most, and so on. So basically a signature measures how evenly or unevenly one’s communication is distributed – usually pretty unevenly: your top three gets up to 50% of your calls! This clearly reflects the way how we tend to shape our social networks: we keep only a handful of individuals very close to us, and have larger numbers of friends and acquaintances who do not belong to this restricted inner circle. Most of our links are weak, but the few strong ones are very important to us.

Social signatures are slightly different for everyone and that’s in fact why we decided to call them signatures. They are also very stable in time and their shapes tend to persist even when there is a lot of network turnover – if you are someone who likes to really focus on 1-2 best friends, you are likely to do that even if your old best friends are replaced by new ones because you move to another city, and if you maintain a more flat signature, you will probably do that in the future too.

The stability of one’s signature, and the rate of changes of one’s network have to do with personality. My coauthor Simone Centellegher has written an excellent blog post on this topic, so I won’t repeat our results here.

For further reading, here are some original publications (and their open-access versions if published behind paywall):

  • Small But Slow World [Phys. Rev. E | arXiv] (2011)
  • Daily Rhythms in Mobile Telephone Communication [PLoS One] (2015)
  • Persistence of Social Signatures in Human Communication [PNAS | arXiv] (2014)
  • Personality Traits and Ego-Network Dynamics [PLoS One] (2017)
  • Effects of time window size and placement on the structure of an aggregated communication network [EPJ Data Science] (2012)
  • From Seconds to Months: the Multi-scale Dynamics of Mobile Telephone Calls [EPJB | arXiv] (2015)

Great network analysis tutorial (iPython notebook)

A very short post: this Python network analysis tutorial by Vincent Traag, written as an iPython notebook and available on GitHub, is absolutely brilliant and I strongly recommend it to anyone interested in social networks and network analysis with Python. I’ll certainly use this in my teaching.

Interested in networks and network science? Click here to read more!