The network scientist’s survival kit

Throughout the scientific disciplines, core values, methodologies, and worldviews vary to a frustrating degree. Network scientists are interdisciplinary. Through years of catching up with our disciplinary colleagues, we have learned to understand other disciplines better than many scientists of those disciplines understand us.

Such a fundamental thing as who a scientific result should benefit, and what this benefit could entail, can give otherwise open-minded academic colleagues tunnel vision. Therefore, explaining a network scientist’s role to scientists of other disciplines can be oh-so challenging. In this post, I’ll list some FAQs about network science that people have asked me at coffee breaks and conferences, in board meetings and job interviews, etc., etc.—and my short answers to them. I tried to write them in a journalist style—the essential things first, so they can be cut if the conversation gets interrupted by an earthquake, Instagram alert, or similar.

Two notes. i. Inspired by Wittgenstein’s TractatusI enumerate the paragraphs. ii. Obviously, there are other great answers to these questions. My answers have also changed with time and might do so in the future again.

1. What is network science? 

1.1. Well, it’s about networks—systems that we can understand via models based on graphs—and how to use networks to build scientific theories. Moreover, it is interdisciplinary at heart, integrating insights from diverse applications and theories and disseminating the results across many traditional academic fields.

1.2. The central idea in network science is that any node can influence other nodes, not only their direct connections. Such indirect influence happens through some external phenomenon—travel in a transportation network, information transfer in the Internet, vibrations in a spiderweb, etc.—and depends on how the network is connected. Thus, we can use the graph describing the interaction structure to understand how the system works, the roles of individual nodes, etc.

1.3. What I just described is somewhat at odds with how science usually works. Both science as a whole, and science applied to a specific problem, follows (what computer scientists would call) a divide-and-conquer algorithm—we divide the problem into more manageable subtasks and start by handling these. For science in its entirety, the subtasks are the traditional disciplines, and “handling” means letting people specialize in these fields. For concrete problems—understanding the evolutionary function of transposons, tone sandhi in Akan, or corruption in the GDR—would also start by breaking down the problem by identifying variables, subunits, factors, etc. Network science does not zoom in on any subunits but rather zooms out to take “a crude look at the whole” (in the words of Murray Gell-Mann). Coincidence or not, the role of network science within science is also to connect one side with the other—from space travel to protein folding, from literature critique to supply chains of the automotive industry.

1.4. As with all emerging scientific fields, it makes sense to take a social (autonymic) starting point and say that network science is the science done by people calling themselves network scientists. These are people connected by academic organizations—we go to the same conferences, publish in the same journals, are members of the same societies. Regarding contemporary research, such a definition would not wholly overlap with a topical / methodological one [1.2,1.3], but well enough, I think. However, looking back in time, there is a big difference as network science in the social sense was born around the year 2000.

Just as the trans-Arctic airplane traveler knows not to take shelter in the fuselage after a crash, the network scientist knows how to answer: “Is network science physics?”

2. Is network science a part of [discipline]?

Could be asked out of curiosity or implying that you don’t belong here. “Discipline” could be “physics,” “computer science,” or “(applied) mathematics.”

2.1. Network science is not a subdivision of [discipline] but overlaps with it. If you need to think of network science as a partition of science, the partitioning would be different from the traditional academic one (math, physics, chemistry, biology, etc.).

2.2. That much said, ideas from [discipline] are of fundamental importance to network science. Moreover, I think it is precious for a [discipline] department to have expertise in network science. It is a place for network scientists to be productive and feel intellectually at home. It also connects the department to the rest of the university and academia at large. In my experience, even traditional-minded students enjoy such a presence. It broadens their perspective and shows the width and versatility of [discipline].

3. What is the holy grail of network science?

3.1. There is none. Just like science itself, the overarching goal is to gather knowledge (within the scope outlined above [1]) and make it accessible.

3.2. This doesn’t mean that we have no direction. Ask any network scientist, and you’ll hear about current trends, both when it comes to theory and applications. It also doesn’t mean that we don’t know when network science is completed. Nowadays, the research frontier is slowly leaving models of simple graphs in favor of more information-rich frameworks. If this development continues, there might come a time when “network” feels too off, and we settle on a different descriptor.

4. Give me your best example of how network science has improved our lives

Or “what is the best achievement of network science?”

4.1. This is a loaded question. The main achievement of network science is to have empowered people with understanding, and tools to analyze, the networked world we live in. “Life improvement” or “achievement” typically refers to one invention or discovery, something we would credit to a person or team, not a scientific field.

4.2. Since name-dropping examples wouldn’t lead to a constructive discussion; I’m reluctant to do so. Probably it would be better to ask how we know network science has an external impact? Do network-science students quickly get hired by companies? Yes, they do. Why? Because methods from network science lie behind many of today’s information technologies. (Substitute “lie behind …” with “power business solutions” when appropriate.) Does network science inform the rest of science? According to citation analysis, for lack of better quantitative tools, network science is astoundingly successful, especially if one considers the field’s size.

5. Where will network science be in ten years from now?

Perhaps implying that young fields tend to disappear quickly.

5.1. If I knew, I would be there already. The prevailing trends are pretty evident, though. One is to forsake some generality of the methods for the benefit of more information-rich data representations. Nowadays, higher-order network models, and networks embedded in space and time, are popular. A second trend is network science gravitating towards data science and applied machine learning, away from the quest for universal laws in the spirit of physics. Third, there is a growing interest in applied network science, which I find essential to promote. There has been an understated and counterproductive rule that good network science should always present new methods, which I hope will disappear.

6. Do you think we should model everything as networks?

Perhaps between the lines, “You psycho probably think we should replace PDEs with graphs.”

6.1. No, but network science can give insights into surprisingly many problems. Systems colloquially known as networks (or similar)—computer networks, social networks, food webs, etc.—are safe bets for when you need network science approaches. They appear throughout almost every branch of science.

6.2. One can list some general criteria for network science to be helpful. I would say three requirements cover most of it: i. Nodes and edges should have concrete interpretations. ii. There should be self-evident mechanisms for how nodes can indirectly influence one another. iii. The number of edges should not be almost zero or almost maximal.

6.3. In addition to the ones described above, there are many other non-obvious examples. I’ve been somewhat doubtful of network studies where the nodes are regions of a spatial grid and links come from temporal correlations. Brain networks are the most prominent such example. By now, brain network methods are so well-established that I have to shrug to my skepticism. Another example is atmospheric teleconnections—distant areas on Earth linked by their weather patterns (and not necessarily because a contiguous zone of similarity (like the El Niño basin) connects them).

6.4. The list goes on, and it seems to pay off to have an open mind about what we could use networks for. A few years ago, Marián Boguñá et al. studied a network of numbers based on their prime factors, to the acclaim of card-carrying number theorists. Network theory goes into scalable 3D animations of crowds and bird-flocks. Developmental linguistics uses lexical networks. Birdsong grammar is another exotic application area, and so are collective memories of historical events.

PS “Survival kit” in the title obviously refers to those military survival guides of the cold war era. When your plane crashes in the High Arctic, remember to supplement your diet of rabbits with polar bears and seals, but don’t eat their liver.

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