The relation between electroencephalography (EEG) rhythms, brain functions, and behavioral correlates is well-established. Some physiological mechanisms underlying rhythm generation are understood, enabling the replication of brain rhythms in silico. This offers a pathway to explore connections between neural oscillations and specific neuronal circuits, potentially yielding fundamental insights into the functional properties of brain waves. Information theory frameworks, such as Integrated information Decomposition (Φ-ID), relate dynamical regimes with informational properties, providing deeper insights into neuronal dynamic functions. Here, we investigate wave emergence in an excitatory/inhibitory (E/I) balanced network of integrate and fire neurons with short-term synaptic plasticity. This model produces a diverse range of EEG-like rhythms, from low δ waves to high-frequency oscillations. Through Φ-ID, we analyze the network's information dynamics and its relation with different emergent rhythms, elucidating the system's suitability for functions such as robust information transfer, storage, and parallel operation. Furthermore, our study helps to identify regimes that may resemble pathological states due to poor informational properties and high randomness. We found, e.g., that in silicoβ and δ waves are associated with maximum information transfer in inhibitory and excitatory neuron populations, respectively, and that the coexistence of excitatory θ, α, and β waves is associated to information storage. Additionally, we observed that high-frequency oscillations can exhibit either high or poor informational properties, potentially shedding light on ongoing discussions regarding physiological versus pathological high-frequency oscillations. In summary, our study demonstrates that dynamical regimes with similar oscillations may exhibit vastly different information dynamics. Characterizing information dynamics within these regimes serves as a potent tool for gaining insights into the functions of complex neuronal networks. Finally, our findings suggest that the use of information dynamics in both model and experimental data analysis, could help discriminate between oscillations associated with cognitive functions and those linked to neuronal disorders. Author summary: Electroencephalography (EEG) records cortical brain activity and is widely used in neuroscience for identifying cognitive states and diagnosing brain pathologies. However, the relationship between functional brain states and specific rhythms is sometimes unclear. Traditional methods combined with computational models often fail to link dynamical regimes to their possible functions. To address this, we used a computational model that generates in silico EEG-like signals in a neuron population. Instead of only analyzing spectral features, we focused our study on information flow in the neuron population between small groups of inhibitory and excitatory neurons during the emergence of different rhythms. We found that in some regimes, the system exhibits enhanced computational properties, with excitatory neurons maintaining parallel processing capacities, inhibitory neurons showing high robustness, or populations maximizing information transfer. In other regimes, low information flow results in more random behavior. Our work highlights the utility of informational dynamic analysis for understanding the relationship between emerging neuronal waves and functions in in silico neuronal populations, a fact that stimulates extending the present study to neuronal cultures and in vivo EEG time series. [ABSTRACT FROM AUTHOR]