## 1 Introduction  
Parkinson's Disease (PD) is the second most common neurodegenerative disorder with a prevalence of 0.3% of the total population and is one of the most frequent causes of physical disability [1]. The pathophysiology of this disease is the degeneration in selectively vulnerable neuronal populations of the _substantia nigra_ with dopaminergic dieneration of the striatum and formation of Lewy bodies composed of aggregated \(\alpha\)-synuclein [2]. The denervation has been described to be typically asymmetric lateralization in functional studies [3] and the cardinal clinical manifestations such as bradykinesia, rest tremor, or rigidity also show asymmetry [4]. This lateralized vulnerability and the hemispheric dominance interaction remains yet to be fully explained [5, 6]. The described functional impairments in PD are largely restored by levodopa administration [7] and also by deep brain stimulation. The nature of this effect has been related to changes in connectivity with both treatments [8; 9]. Thus, changes in brain connectivity have been considered as key characteristics of the disease and thoroughly studied using Electroencephalography (EEG), Magnetic Resonance Imaging (MRI), and Magnetoencephalography (MEG). Surface recordings have demonstrated that PD subjects have an increased resting-state cortico-cortical functional connectivity in several frequency bands [10; 11]. This increased connectivity has also been correlated with clinical manifestations as tremor severity and dementia [12]. In clinical applications of EEG, the single-channel EEG time series has been interpreted up to date using the concept of signal. This includes the denomination of waves or rhythms characteristic of different physiological states and topographies by visual inspection [13]. Connectivity changes cannot be studied by visually identifiable diagnostic EEG features and several signal analysis methods have been used to solve this question. Coherence has been widely used to analyze the connectivity of EEG [14]. It provides a measure of linear association and is a relatively straightforward approach to functional network interdependencies at first glance [15]. One of the characteristics of the EEG signals is their irregularity, and thus, analyses that provide a measure that summarizes frequency changes over a wide range are very helpful for this purpose. Considering that most physiological signals are nonlinear, entropy is ideal to study neural signals [16] and has been previously used to study EEG signals, especially in epilepsy [17]. Spectral entropy (SE) is a measure of signal irregularity [18]. The advantage of using spectral entropy for EEG analysis is that the contributions to entropy from any particular frequency range can be explicitly separated [19]. Connectivity can be addressed by means of the correlation coefficient among the electrodes' entropy in the frequency space, whose values indicate the degree of similarity between the information captured by the electrodes, quantifying the amount of dependence between them. Both measurements, coherence and spectral entropy, provide complimentary as well as global information on the EEG signals. Given this, this study aims to explore the usefulness of time series analysis techniques, such as spectral entropy and signal coherence, to determine differences in EEG connectivity in PD patients compared to controls both at rest and during motor activation. Scalp EEG connectivity is usually characterized as a graph, being the electrodes, the graph nodes, and the pairwise connectivity measures the edge weights [20]. From this graph, some graph-theoretical features describing the global and local graph topography are usually extracted [21], such as efficiency, clustering coefficient, or centrality, to mention a few among the most popular. In the present study we focus in the assortativity coefficient [22], which is an indirect measure of the resilience of the network, i.e., the vulnerability to insult.