Memories are represented by highly interconnected neural circuits in the brain and the spike-timing-dependent plasticity (STDP) is one of the most important neurochemical foundations of learning and memory. In this work, we diagram the behavior of a network in the cerebral cortex, where excitatory neurons have plasticity in the form of STDP, in its two varieties: long-term depression and long-term potentiation. These forms of plasticity trigger rewards or punishments, according to Skinner’s behavioral theory on which the network was based. We simulate a neural network with 1000 neurons, with axon conduction delay and following the rule of STDP plasticity. We found an explanation of the enigma of the distal reward, associated with a characteristic dopaminergic frequency whose value is around 25 Hz. For the analysis of the results, several tools of graph theory and information theory were implemented. We studied the dependence of the order parameter Fisher’s Information with the number of excitatory and inhibitory neurons. We found that the Closeness Centrality takes higher values for excitatory neurons, which is congruent with the generation of long-term plasticity. Finally, we observe how Fisher’s information decreases as the system evolves, which would be compatible with a phase transition. This system fulfills with a process of learning that combines the reward with the STDP, which reaches a maximum value of the estimator complexity in its temporal evolution compatible with a chaotic state.