A recently published paper, titled Network Cosmology (PDF format) has demonstrated remarkable similarities in the structure and dynamics of several large scale networks that you may have heard of: the human brain, The Internet, and universe. The paper is by six researchers including Dmitri Krioukov, perhaps best known as the scientist whose four page physics paper titled "Proof of Innocence" (PDF format) was presented to the judge in court, saving Dmitri from a $300 traffic ticket. Having avoided his traffic fine, Dmitri and friends went on to demonstrate that many complex networks from the brain to the entire universe seems to be governed by similar underlying laws. To do this, they looked at the math of causal sets a representation of the quantum gravity that underlies spacetime. From the paper:
"We show that the structure of these networks in de Sitter spacetime, such as our accelerating universe, is remarkably similar to the structure of complex networks -- the brain or the Internet, for example. [...] We show that as a consequence of a simple geometric duality, the growth dynamics of complex networks and de Sitter causal sets are asymptotically identical. These findings suggest that unexpectedly similar mechanisms may shape the large-scale structure and dynamics of complex systems as different as the brain, the Internet, and the universe."
According to the researchers, the probability of the equivalence between all these complex networks being pure coincidence is very low, so there's almost certainly some fundamental law at work. It would be very interesting to identify and understand a new law of physics that affects the emergence of four-dimensional space from the quantum vacuum, the development of our brains, and the dynamics of our social network of friends. The paper contains lots of math, so we recommend against reading it while you're driving.