The big picture
To understand how a big, complex system works as a whole, you need to zoom out and look from a distance. This is not only true for blind girls examining an elephant as in the cartoon, but for any large-scale, complex system in society or nature. The society itself is just such a complex system built by people and organizations with different abilities, interests and objectives. Our bodies are another example. Genes code proteins, proteins build cells, cells build tissues, tissues build organs—that seems relatively simple and hierarchical—if it wasn’t that the proteins interact with each other, so do cells, etc. To understand such lateral connections, we need to find the right level of modeling (or the right distance to look at the elephant). The bigger datasets we can gather, the more critical it will be to simplify the right amount. Representing a system as a network is one way of consistently discarding some details, to simplify and zoom out, while still being able to see how the whole system hangs together.
Everything is connected
…well almost. There are so many systems around us that could be modeled as networks, and so many questions we could try to answer: How to stop diseases spreading in the network of contacts between people. How to make power-grids robust against cascading failures. How to maintain biodiversity in ecosystems facing a changing climate. How to find inconsistencies in a narrative of historical events. Networks are mathematical abstractions, but much more alive than other such. The thing that got me interested in networks in the first place was how great they are to help one’s thinking about how a system works, and how easy it is to use them to explain this for other people. Computational network research is not so technically challenging either—one can stay close to the actual questions without going too much astray into advanced numerical methods.
Adding time
Sometimes a static network of just nodes connected by links would be an oversimplification. Sometimes one has information about when interactions happen, not only which nodes that interact, and it increases the accuracy of prediction, and our understanding of mechanisms, to integrate this temporal information with the network. Much of my recent research has been about this topic. I currently study how to understand temporal effects in the disease spreading and how that can be exploited for preventing epidemic outbreaks. Another current project concerns temporal networks of suspected criminals. A big challenge for temporal networks is that the great intuitiveness of regular, static networks is gone when one includes time. Sure, we are used to the concept of time and can think of a network evolving like a film clip, but then not all information is there at the same time, which makes it hard to use the temporal network to reason about e.g., disease spreading. The best one can do is usually time-line plots like in the cartoon, but for a network of hundreds of nodes … well, you can imagine.
Petter Holme 