Why a brain is a graph: what the fruit fly connectome tells us about minds

People sometimes ask why a lab working on consciousness is named after a line of graph theory. The short answer is that a brain is a graph, and I think a mind is too. The longer answer starts with a fly.

139,000 vertices, 54.5 million edges

In October 2024, the FlyWire consortium published the first complete wiring diagram of an adult brain: the fruit fly Drosophila melanogaster. Every one of its roughly 139,000 neurons, and around 54.5 million synapses between them, reconstructed from electron microscope images and proofread by scientists and volunteers.

Written in mathematics, that dataset is exactly G = (V, E). The neurons are the vertices. The synapses are directed, weighted edges. A brain that steers flight, finds food, learns and remembers is, structurally, a graph you can download.

A quick calculation shows how sparse it is. With 139,000 neurons there are about 1.9 × 10¹⁰ possible directed pairs. Even if every synapse joined a different pair, fewer than 0.3% of those pairs would be connected. Each neuron averages roughly 390 synapses. The brain is not a tangle where everything touches everything. It is a carefully chosen set of edges.

The edges are where the meaning is

A single neuron, on its own, does very little. What it contributes depends on what it connects to: which signals reach it and where its output goes. The same type of cell can play completely different roles in different circuits. In graph terms, a vertex's meaning comes from its edges.

I find this a useful way to think about minds in general. A memory matters because of what it is linked to. A goal matters because of the actions and values that connect to it. A sense of self, if a machine is ever to have one, will not live in any one component. It will live in the pattern of relationships between them.

But a wiring diagram is not a mind

Here is the catch. A connectome tells you who can talk to whom. It does not tell you what is being said. The same graph can produce wildly different activity depending on connection strengths, chemical neuromodulators and the state of the body. A map of the roads is not the traffic.

That is why the 2025 MICrONS dataset excites me. It maps the wiring of a cubic millimetre of mouse visual cortex, more than 523 million synapses, and pairs it with recordings of what tens of thousands of those neurons actually did while the mouse watched videos. Structure and activity, together. That is the combination a mathematical theory of mind has to explain.

In this equation, W is the connectome. But consciousness, if it lives anywhere, lives in the whole thing: how activity x flows over W, shaped by input s and the body's internal state h, step after step.

What this means for building a digital mind

If consciousness depends on how a system is organised rather than what it is made of, then we may not need to copy every neuron of a human brain. We need to find which properties of the graph and its dynamics actually matter. My bets, for Paper 01, are four:

• Integration: the graph behaves as one whole, not disconnected modules.
• Recurrence: edges form loops, so activity feeds back and reshapes itself.
• Self-representation: part of the graph models the rest of it, and that model persists.
• Regulation: internal states, something like emotion, steer how activity flows.

Each of those is something we can build, switch off and measure. That is the plan: two systems, one with these properties and one without, and a careful look at what breaks when we take them away.

The fruit fly will not tell us what consciousness is. But it has shown that a real brain can be written down as G = (V, E). Our job is to work out which graphs, running which dynamics, might one day amount to a mind.

Sources

• Dorkenwald, S. et al. (2024). Neuronal wiring diagram of an adult brain. Nature, 634.
• The MICrONS Consortium (2025). Functional connectomics spanning multiple areas of mouse visual cortex. Nature.
• NIH Research Matters (2024). Complete wiring map of an adult fruit fly brain.