## 1 Introduction  
A wide range of biological phenomena are characterized by synchronization of systems whose complex cooperation and integration explain the emergence of vital functions [1]. Several synchronization metrics have been introduced to quantify the coupling behavior of interacting dynamic systems [2, 3]. In particular, there has been a growing body of literature addressing the application of complex network analysis for the characterization of dynamical systems based on time series. These combined approaches have clarified fundamental issues about the organization of nonlinear dynamics in different fields. As an example, the complex and nonlinear nature of brain dynamics is widely discussed in the literature [4, 5, 6]. The human brain is modeled as a complex network composed of anatomical and functional sub-systems whose interactions allow the performance of both high- and low-level cognitive functions. Such interactions have been extensively modeledthrough the mathematical framework of the complex networks, which allows the treating of each subsystem as a node of a network and to identify specific topological properties of nodes and links in the network [7; 8]. Topological data analysis have been largely applied to investigate the architecture of brain networks and connectivity differences between individuals at several levels of the data hierarchy [9; 10; 11]. These techniques can be applied both to functional data, which describe the dynamic brain activity through functional magnetic resonance imaging (fMRI) or electrophysiological acquisitions [12; 13]. In particular, over the past decade, there has been an increasing interest in inferring connectivity properties from fMRI data [14; 15]. Functional connectivity (FC) analysis aims at assessing the strength of functional coupling between the signal responses in distinct brain areas [16]. According to the complex network framework, the anatomical regions of interest are modeled as the nodes of the network, linked by edges resulting from the selected synchronization metric. Pairwise Blood oxygenation level dependent (BOLD) time series connections can be estimated through different metrics including cross-correlation, cross-coherence and causal modeling [17]. Each FC metric quantifies different forms of dependency between the BOLD signals: zero-lag correlation metrics quantify the statistical similarity between pairs of region, other metrics assess synchronization at frequency band of interest [18; 19], others capture direct coupling between time series [20; 21]. Recently, new metrics to assess the coupling behavior of BOLD time series have been introduced to capture both linear and nonlinear interactions in human brain. In particular, a generalized synchronization index (SYNC) has been proposed to assess the functional connectivity with fMRI data [22; 23]. Such metric has been proven effective in detecting active sub-networks during a high-level cognitive process, describing age-related functional patterns [24] and identifying and quantifying pathological states [25]. The analyses of functional brain connectivity in the state of rest have revealed different modular configurations of the brain activity, which reflect specific functions and varied spatial topologies [26]. Moreover, the role of specific regions acting as network hubs for the efficient functioning of the human brain has been extensively documented [27; 28]. Brain hubs facilitate the integration of functionally specialized neural systems by supporting long-range connections [29; 30] and by routing a large amount of neural information [31]. The dysfunction of some brain hubs has been also related to pathological conditions and psychiatric disorders [32; 33]. In this work, we performed a comparison of the synchronization connectivity pattern derived from the SYNC metric, statistical Pearson correlation and spectral coherence functional connectivity.