This thesis proposes a novel approach for functional connectivity studies of neuronal signal recordings based on statistical signal processing analysis in the frequency domain using Multivariate Partial Coherence (MVPC) combined with network theory measures. MVPC is applied to spike trains signals to make inferences about the underlying network structure. The presence of connections between single unit spike trains is estimated using both coherence and MVPC analysis. Scalability of MVPC analysis is investigated through application to simulated spike train data with up to 100 simultaneous spike trains generated from a network of excitatory and inhibitory cortical neurons. Stable MVPC estimates were obtained with up to 198 predictors in partial coherence estimates, using a combination of simulated cortical neuron data and additional Poisson spike train predictors. MVPC provides higher order partial coherence analysis for multi-channel spike trains signals, removing effects of common influences in pairwise connectivity estimates. Network measures applied to binary and weighted adjacency measures derived from coherence and partial coherence are compared to determine the differences in unconditional and conditional networks of spike train interactions. A combination of MVPC analysis along with network theory analysis provides a systematic approach for multi-channel spike train signals. The proposed method is applied to simulated and multi-electrode array (MEA) spike train data. The MEA data consists of 19 single unit channels recorded from a study of connectivity in a model of kainic acid (KA) induced epileptiform activity for mesial temporal lobe epilepsy (mTLE) in a rat. The network theory analysis uses basic measures on both conditional and unconditional network, which highlights the differences in network structure and characteristics between the two representations. Complex analysis on conditional networks is useful in describing the properties of integration and segregation in the network
