Computational approaches to understanding the connectivity of biological neural networks using graph theory and dynamical systems have been recently gaining traction. I am wondering if there are any existing models for spiking neural networks that explicitly incorporate graph dynamical systems in their construction.

I've looked at simulation libraries like Brian 2, but they don't seem to emphasize the connectivity schemes found in the brain.

If I were to construct one myself, I am mainly interested in what the connectivity/geometry of the network would be like to create an adjacency matrix. I've been learning about ergodic Markov chains and wondering if their geometry could be somehow applied here.

I know that given an adjacency matrix, and a binary vector of initial conditions, one can describe state dynamics at time t by raising the adjacency matrix to the power of t and computing the product with the initial conditions vector. As a starting point it could be interesting to combine this with an "accurate" adjacency matrix, later incorporating inhibition and other parameters.


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