  We study reaction-diffusion processes on graphs through an extension of the
standard reaction-diffusion equation starting from first principles. We focus
on reaction spreading, i.e. on the time evolution of the reaction product,
M(t). At variance with pure diffusive processes, characterized by the spectral
dimension, d_s, for reaction spreading the important quantity is found to be
the connectivity dimension, d_l. Numerical data, in agreement with analytical
estimates based on the features of n independent random walkers on the graph,
show that M(t) ~ t^{d_l}. In the case of Erdos-Renyi random graphs, the
reaction-product is characterized by an exponential growth M(t) ~ e^{a t} with
a proportional to ln<k>, where <k> is the average degree of the graph.
