The quiet revolution: When complex left networks

Soon after networks became all the rage among statistical physicists, the field turned away from the home turf of complex systems science. This blog post argues for considering network science as distinct from complexity science. All is sketchy and subjective (from the viewpoint of a statistical physicist jumping on the complex-networks bandwagon). I can think of many good counterarguments to what I write, so don’t be upset about it, but hopefully, it can give a new perspective.

The small-world network paper by Watts and Strogatz (Nature 1998) and scale-free ditto by Barabási and Albert (Science 1999) set off a once-in-a-lifetime boom of network research among statistical physicists. It certainly changed my life because I was one of the network boomers. Or maybe I should say “complex network boomers” because, at that time, it felt apparent that network science was a topic under the greater umbrella of complexity science: Small-world networks embodied the complexity maxim that interesting stuff, and the world itself, happen between order and randomness. Name-checking the then-buzzwords “power-laws,” “universality,” and emergent “self-similarity,” scale-free networks seemed to herald the second coming of self-organized criticality—one of complexity science’s hottest topics in the first half of the 1990s.

After some years, the “complex” prefix became less frequent. For me, a turning point was when I heard from Mark Newman (probably in early 2005, when I was a postdoc in his group) that his forthcoming book would be called “Networks” and not “Complex Networks.” OK, I thought, “it’s great if we can gather all network science into one field,” ditching “complex” seemed like a worthwhile sacrifice. I didn’t notice that the complexity-science mindset was complemented, almost replaced, by another of the big ideas of the 20th century—structuralism.

Just like network science, the development of structuralism didn’t follow an obvious path, and some of its components were independently discovered in different fields. To mention one such example, Swiss linguist Ferdinand de Saussure realized that the signs communicating meaning in a language are arbitrary. They get their function from social conventions expressed in their relations to other signs. The same can, of course, be said about the other signs, which give a recursive relation familiar to all network scientists—function comes not only from the neighbors of a node but indirectly from the entire network. Around the time Moreno and Jennings invented the mapping of the structure of social networks, this idea was widespread and reflected in, e.g., Kurt Lewin’s topological psychology and the kinship algebra of Claude Lévi-Strauss and co-workers.

Even today’s network science deals with collections of “a large number of parts that interact in a nonsimple way”—Herbert Simon’s definition of complex systems. However, traditionally, complexity science has specifically sought to explain how these interactions build up entire systems. Early complex-networks papers followed this recipe—self-similarity, fractal dimensions, universality, the onset of synchronization, emergent patterns, etc. But sometime in the mid-aughts, the structuralist questions took over, focusing on individual nodes, edges, or small groups of them. In 2011, Laszlo Barabási, the figurehead of complex networks, published their work on identifying “controller nodes,” which felt like the end of the complex-network era. Since then, it’s been “many are different” rather than “more is different.”

It puzzles me why this paradigm shift was so quiet. One explanation is that it was a time of a rapid flux of ideas. Everyone studying complex networks was new to the subject, on a learning curve, and open to seeing things from new perspectives. Even though this implies that the entire field was a group of novices in what they were supposed to be experts, such an open-minded atmosphere is something I would like to experience again.