We study the effects of reshulling of connections on collective dynamics. We start from a leaky Integrate-and-Fire model whose connectivity was initially designed in such a manner as to favor the spontaneous emergence of collective oscillatory spatiotemporal patterns of spikes and we reshuffle all the connections. For each chosen connection we change the presynaptic neuron, choosing as the new presynaptic neuron a random neuron of the network. After reshuffling the connections, not only the number of excitatory and inhibitory connections is the same as before, but also all the strengths of the connections are the same, and only the topology is changed. We observe that reshuffling the connections changes the features of the dynamics dramatically. Before reshuffling the system has a transition from a regime of Poissonian noisy activity to a regime of spontaneous persistent collective replay, and at the transition point the network dynamics shows an intermittent reactivation of the stored patterns, with alternation of up and down states, and bimodal distribution of spiking rate. Reshuffling all the connections we observe that the transition region with bimodal distribution disappears, and the dynamics is Poissonian with unimodal rate distribution for all the parameters investigated. These results show the role of topology in dictating the emerging collective dynamics of neural circuits.