Reigniting complex networks at Cambridge

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Cambridge has loads of interesting research going on. A suprising amount touches on complex networks, but usually within specific areas like mathematics, statistics, physics, biology, neuroscience and even history. A while ago, Petra Vértes started a community that brought together all of these different researchers. It quickly expanded and became a prominent name for complexity research.

Enter Corona, and things were forced to a halt. And like with other pre-covid phenomena, this marked a turning point in the momentum that it had built up for nearly a decade prior.

Then, a newer community of individuals working on networks appeared to be spawning across Cambridge, and this seemed like the right opportunity to rekindle everything. Together with Kayson Fakhar and the Sourdough, we undertook the task of not only reviving the community, but actually giving it a proper sense of identity. After all, academic communities are really nothing more than a group name and the imagery assigned to a couple of researchers.

Petra talking about brains during the first reignition event.

Graphs seem like the obvious representation, but perhaps we could do something more involved than random squiggles. So, we came up with a parameterised design. We wanted something that could be automatically assigned to members or events, which led us to representations of the alphabet.

The rule is as follows. You pick a symbol, say the letter , and look at its -bit binary representation

which gives us a unique quantity to work with. We then perform the following operation

This gives us a graph representing the original symbol. Likewise, we can also use the adjacency matrix itself as a symbol.

The letter as an adjacency matrix (left) and a graph (right).