Uncovering information hidden within brain networks can be a daunting task, especially in the cases of abnormal, disrupted neural networks, such as epilepsy. Here, I present a multifaceted approach that combines signal processing, computational neuroscience, and theoretical and mathematical modeling to investigate the mechanisms and structure that underlie neuronal activity in both time and space. First, we show that there is a mathematical symmetry in the temporal and spatial domains if the spike-centered averages (a novel second-order metric of the action potential spike-LFP relationship) resemble sinc functions in human focal seizures. We then advance network analysis by presenting a novel approach to characterize neural networks using third-order motifs, which are sufficient to completely and uniquely characterize networks in both time and space. Furthermore, these third-order motifs are classified according to their sequencing depending on the combination of up to two lags in time and space, yielding fourteen qualitatively distinct motif classes that can embody well-studied neural network properties, such as synchrony, feedback, divergence, and convergence. Building from triple correlation, I then develop a novel quantitative metric that captures overall network activity: the 4D entropy based on the spatiotemporal lag distribution computed from triple correlation. Applying this metric to rat cortical cultures from microelectrode arrays, I demonstrate the enhanced value of 4D entropy, which is based on third-order structure, in that it captures the underlying dynamics in comparison to 2D, or pairwise, entropy. Lastly, I develop and implement a Hodgkin-Huxley simulation of excitatory-inhibitory population activity to model the first three stages of a focal seizure and use triple correlation to show that the network represented by the model is a good fit for the network of the patient data.