Abnormalities in schizophrenia are thought to be associated with functional disconnections between different brain regions. Most previous studies on schizophrenia have considered high-band connectivity in preference to the Alpha band, as there has been some uncertainty correlating the latter to the condition. In this paper we attempt to clarify this correlation using an Electroencephalogram (EEG) analysis of the Alpha band from schizophrenic patients. Global, regional Omega and dimensional complexity and local Omega complexity differentials (LCD) of single channel are calculated using 16 channels of resting EEG data from 31 adult patients with schizophrenia and 31 age/sex matched control subjects. It was found that, compared to the controls, anterior alpha Omega and dimensional complexity are higher in schizophrenia patients (p<0.05) with the single channel LCD also increasing at FP1, FP2, F7 and F8 electrodes. Furthermore, higher left hemisphere dimensional complexity and LCD at T3 point was also found. The results suggest there is lower connectivity in the pre-frontal and left temporal regions with respect to the alpha band in schizophrenia patients.