Temporal networks and the extraordinary fluidity of effortless abstractions

This is a semi-grumpy post about the many ambiguities and reinventions in the field of temporal networks. Cheerful posts are more fun, so do consider browsing away. Also, I’m not always contributing to clarity myself, so maybe I’m not entitled to whine about this.

Many types of data consist of discrete interaction events, where we know what units interact and when the interaction happens. Such data could record emails, phone calls, people meeting people, penguins meeting penguins, people meeting penguins, public transport, etc. It is not difficult to construct mathematical or computational representations of such systems. However—more peculiarly—these representations are typically neither system-specific nor obvious (in the sense that people independently reach the same model). The science of such temporal networks* could:
A) Have a unified terminology and consistently use the same conventions, symbols, and notations.
B) Be in a perpetual state of confusion, where everyone talks in their own language, uses misaligned concepts, and keeps reinventing the field.
C) Be anywhere between A and B.
Over time, my impression of the field keeps swinging between B and midway between A and B.

* That’s what I usually call them and will keep calling them, at least for the remainder of this post.

The linguistic side

Different words, same thing

Rewind to the first few days of summer 2010 and the lazy Swedish coastal town of Öregrund. There I was attending an applied math workshop with a peculiarly uninvolved feel. Usually, not even a vacation around the corner would stop scientific discussions. Still, at this workshop, speakers dropped out from presenting. Some talks were cut short by FIFA 2010 games. It was more beer than coffee and more vuvuzelas than eigenvalues.

At that workshop, I ran into Jari Saramäki, and we started discussing data sets of binary contacts at discrete times. We had recently put a manuscript on the arxiv simulating disease spreading on empirical sexual contacts, and Jari’s group had another preprint with similar analyzes of phone-call data posted four days earlier. We decided to write a review paper on the topic, but what to call it? Already then, there were a bunch of names of this type of data around—dynamic networks, temporal graphs, blinking networks, time-stamped networks, etc. We settled for “temporal networks” by analogy to “spatial networks,” and because of Kempe, Kumar, and Kleinberg’s seminal paper “Connectivity and inference problems for temporal networks.” But, even though our review, to some extent, defined the research field, it failed to unify the name—people kept using their favorite phrases. I thought time and communication would iron out such wrinkles, but it remains a hurdle more than a decade later.

Same words, different things

Maybe even more confusing is that people use the same phrases slightly differently. “Temporal networks” could refer to a growing network, instantaneous events on a static graph, a flow network with changing link capacities, etc. For some authors, “temporal networks” generalizes “dynamic networks;” for others, “dynamic networks” generalizes “temporal networks.” For every paper, one needs to understand the definitions of the authors. It’s so confusing that I probably managed to have inconsistent terminology even within the same article, but let’s forget about that.

Explanation #1 for this imprecise language is that if everyone else makes up their own vocabularies, then why shouldn’t I? It doesn’t simplify anything to follow another dictionary if there are dozens of others.

Explanation #2 is that everyone has concrete data sets or real-world systems in mind behind the mathematical abstractions. (For me, it is usually proximity networks—describing who is close to whom, at what time.) Even if one can fit a multitude of systems into the same mathematical framework, peculiarities could influence its precise formulation and the choice of names of its variables and components.

Early temporal network visualization of Czechoslovakian air routes from 1933. From Edward Tufte’s Envisioning Information.

The social side

Bad excuses to not read the literature

There are explanations beyond the pure dynamics of language for why the temporal-networks terminology is so confusing. Reason #3 might look like laziness—people ignore the earlier literature—but it is really a systemic attitude problem. Excuses I’ve heard fall into two categories:

  1. It’s better to think for oneself. In two subcategories:
    1. The literature is just too vast. It’s impossible to read up on everything.
    2. Other people’s ideas disturb my thoughts. I need to focus on my own ideas to produce greatness.
  2. In our field, we don’t cite papers from other disciplines.

1a, is to some extent true, but learning the basic terminology does not need more than an hour or so, and you’d anyway need to convince yourself that your research idea is original . . Unless, of course, you’ve sworn allegiance to 1b. But 1b is almost a rejection of science itself and thus madness. Ironically (or maybe, obviously), the ideas of the people professing 1b never feel very fresh.

Point 2 is provokingly stupid, but something I’ve heard from people of various backgrounds. It’s completely missing the point of the division of labor in science—we specialize in order to make deep understanding accessible to everyone, not to create a group of specialists eo ipso.

A few early citations missing are not such a big deal, especially if they are from other disciplines. The literature further away from home is, of course, less accessible. (It took me two papers to learn about Lamport’s work on vector clocks from the ’70s.) Furthermore, at some point, it makes more sense to cite survey papers or textbooks rather than the original research. But the problem with the field of temporal networks is that articles wholly disconnected from the literature (not even citing textbooks) keep popping up.

Publication pressure or pure evil

The final explanation, #4, will make you think that I suffer from the latter stages of paranoia: Could it be that people, though aware of some of the literature, deliberately use their own descriptors to make their contribution sound more unique?

It happened to me that I spent a lot of effort building a computational or mathematical model to solve a problem but eventually never really reached a solution. In such situations, it feels like one still deserves a publication for the effort—like selling the cotton candy machines to minimize the losses of one’s failing Paul Erdős theme park—and the only thing of potential value is the model itself. This is how I imagine the backstory of some articles “proposing a framework” for temporal networks without fully crediting existing theory.

An illustration from a temporal network classic: Leslie Lamport’s “Time, clocks, and the ordering of events in a distributed system.”

What to do

How can we make the field of temporal networks more user-friendly and welcoming? Most importantly, articles need more context than usual—not just starting where another left off but explaining the whole situation. This has the positive side effect that your reference list will look cooler and more eclectic than your across-the-corridor neighbor’s. Second, choose the terminology that seems most adopted throughout the literature, not only in your field, and give precise definitions of all terms. Third, don’t propose any more unifying frameworks—even if unification is what we dream of, that won’t happen by writing an article. Finally, write more cheerful blog posts.

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