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Connected networks are a fundamental structure of neurobiology. Understandingthese networks will help us elucidate the neural mechanisms of computation.Mathematically speaking these networks are `graphs' - structures containingobjects that are connected. In neuroscience, the objects could be regions ofthe brain, e.g. fMRI data, or be individual neurons, e.g. calcium imaging withfluorescence microscopy. The formal study of graphs, graph theory, can provideneuroscientists with a large bank of algorithms for exploring networks. Graphtheory has already been applied in a variety of ways to fMRI data but, morerecently, has begun to be applied at the scales of neurons, e.g. fromfunctional calcium imaging. In this primer we explain the basics of graphtheory and relate them to features of microscopic functional networks ofneurons from calcium imaging - neuronal graphs. We explore recent examples ofgraph theory applied to calcium imaging and we highlight some areas whereresearchers new to the field could go awry.

Neuronal graphs: a graph theory primer for microscopic, functional networks of neurons recorded by Calcium imaging