Title: Critical elements for connectivity analysis of brain networks

Abstract: In recent years, new and important perspectives were introduced in the field of neuroimaging with the emergence of the connectionist approach. In this new context, it is important to know not only which brain areas are activated by a particular stimulus but, mainly, how these areas are structurally and functionally connected, distributed, and organized in relation to other areas. Additionally, the arrangement of the network elements, i.e., its topology, and the dynamics they give rise to are also important. This new approach is called connectomics. It brings together a series of techniques and methodologies capable of systematizing, from the different types of signals and images of the nervous system, how neuronal units to brain areas are connected. Through this approach, the different patterns of connectivity can be graphically and mathematically represented by the so-called connectomes. The connectome uses quantitative metrics to evaluate structural and functional information from images of neural tracts and pathways or signals from the metabolic and/or electrophysiologic activity of cell populations or brain areas. Besides, with adequate treatment of this information, it is also possible to infer causal relationships. In this way, structural and functional evaluations are complementary descriptions which, together, represent the anatomic and physiologic neural properties, establishing a new paradigm for understanding how the brain functions by looking at brain connections. Here, we highlight five critical elements of a network that allows an integrative analysis, focusing mainly on a functional description. These elements include; (i) the properties of its nodes; (ii) the metrics for connectivity and coupling between nodes; (iii) the network topologies; (iv) the network dynamics and (v) the interconnections between different domains and scales of network representations.