A PROPOSAL FOR EMPIRICAL RESEARCH

The common purpose of scientific action is the understanding of complex systems' emergent processes. These systems are composed of a large -in some cases perhaps intractable- number of interacting components or entities. A common property of components within systems is that they can influence each other directly or indirectly. Evidence collected over the past few decades indicates these interactions often depend on the topology of such components \cite{Watts_1998,Newman_2003}. Furthermore, real-world systems' components often affect each other indirectly, with only few components exerting direct influence \citep{Watts_1998}. This sparse and complex topology is characterized by global indirect influence implemented by multiple local direct interactions \cite{Watts_1998,Newman_2003,Bullmore_2009}. This kind of systems can be better understood in the form of networks or graphs; mathematical objects allowing the quantification and prediction of a system's dynamics. Studying these graphs is Network Science's goal, with far reaching implications for genetics \cite{Alon2007}, physics \cite{papadopoulos2017network}, biology \cite{rolland2014proteome}, medicine \cite{Barab_si_2011}, sociology \cite{wasserman1994social}, ecology \cite{Hobson_2016}, and -of course- neuroscience \cite{Sporns_2018}. The seemingly universal usage of networks is made possible by the abstraction allowed by the branch of mathematics focusing on formal descriptions and analyses of graphs known as graph theory \cite{west2001introduction}. Thus, network-based applications -with a deeply rooted theoretical framework and its companion mathematical toolbox- allows the analysis of systems and their mechanisms with an unprecedentedly finesse. The components of a system, whose activity can be described in pairwise relations or -in more complex cases- global interactions (e.g.. all components perform similar processes), can be represented in a network. In both pairwise and global dynamics, the system's components will be represented as nodes or vertices. Likewise, interactions and relations between nodes will be represented by edges or connections. These connections can be of directed (i.e. known directionality) or undirected (i.e. bidirectional or unknown directionality) nature. Real-world systems can be mathematically represented by networks, providing an abstraction of the system's components and their interactions -in other words- its mechanisms.

Networks analysis of mechanisms

The seminal work by \citet{Watts_1998} introduced the "small-world" network model with deep implications for the study of a system's dynamic behavior. Given that any system could be potentially understood by its local structure, component rankings, global connectivity, among others \cite{degenne1999introducing,wasserman1994social}. Therefore, understanding a systems' topology and dynamics in the form of graphs is considered the main goal of network science \cite{Sporns_2018,Breakspear_2017,Avena_Koenigsberger_2017}. All system's components can be represented by nodes (\(x_i\)\(x_j\), etc.) while their interactions can be represented by edges (\(\vec{x_i x_j}\\)).