Aims: The severity of sleep apnea is often assessed using the apnea/hypopnea index (AHI), which is known to be inaccurate in the phenotyping of apnea patients. Hence, better approaches are needed to characterize these patients and to allow cardiovascular risk stratification, and treatment selection. In this context, this work studies the cardiorespiratory interactions in patients suffering from both sleep apnea and apnea associated comorbidities by means of graph theory and kernel methods. Methods: Heart rate variability (HRV), respiration, and SpO2 signals recorded from 100 sleep apnea patients (AHI>15) were used to construct the cardiorespiratory graph. A subgroup of 50 (comorbidity) patients presented apnea associated comorbidities. From both the HRV and the respiration, the normalized powers in the classical LF and HF bands were computed using a moving-window approach (=60s, 50s overlap). The mean desaturation in the 60s window was used as feature for the SpO2 signal. In total, 5 time series, 2 for HRV, 2 for respiration, and 1 for SpO2, were obtained with a sampling period of 10s. These series correspond to the vertices of the cardiorespiratory graph and their degree and interactions during the full night were analyzed using the RBF kernel. The connectivity of the graph for each patient was estimated using the evolution of the graph algebraic connectivity. Results: The total connectivity of the graph is reduced with higher AHI and this reduction is significant (p<0.05) in the comorbidity group. Furthermore, in the comorbidity patients with AHI>35, the vertex degree of the LF band of HRV is significantly lower and the link between the respiration vertices and SpO2 is significantly weaker. Conclusions: These results are in line with studies that report stronger oxygen desaturations in patients with apnea associated comorbidities, and more unstable control systems, which could be used for a better characterization of apnea patients.