  In spiking neural networks an action potential could in principle trigger
subsequent spikes in the neighbourhood of the initial neuron. A successful
spike is that which trigger subsequent spikes giving rise to cascading
behaviour within the system. In this study we introduce a metric to assess the
success of spikes emitted by integrate-and-fire neurons arranged in complex
topologies and whose collective behaviour is undergoing a phase transition that
is identified by neuronal avalanches that become clusters of activation whose
distribution of sizes can be approximated by a power-law. In numerical
simulations we report that scale-free networks with the small-world property is
the structure in which neurons possess more successful spikes. As well, we
conclude both analytically and in numerical simulations that fully-connected
networks are structures in which neurons perform worse. Additionally, we study
how the small-world property affects spiking behaviour and its success in
scale-free networks.
