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}. Sparse and complex topologies like this are usually 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 properties and 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 afforded 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 as a network. In both pairwise and global dynamics, the system's components will be represented as nodes or vertices. Further, interactions and relations between nodes will be depicted by edges or connections (MAKE explicative FIGURE A). These connections can be of directed (i.e. known directionality) or undirected (i.e. bidirectional or unknown directionality) nature (MAKE explicative FIGURE B). Therefore, 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

Given that any system could be potentially understood by the appropriate modeling of its local structure, component rankings, global connectivity, and other properties \cite{degenne1999introducing,wasserman1994social}, 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}. As mentioned before, 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}\\) or \(\longleftrightarrow{x_i x_j}\)). Thus, directed on undirected pairwise relations can be quantified. Once the mechanism has been represented as a network, researchers can proceed to apply the plethora of tools anchored in graph theory \cite{Bullmore_2009} and/or algebraic topology \cite{Horak_2009}. Graph theory allows the quantification of different properties of the system and its mechanisms, such as modularity, hierarchy, or centrality \cite{Girvan_2002,Ravasz_2003,Barth_lemy_2004}. Complementarily, network topology allows the exploration of higher-order interactions -rather than pairwise relations- as well as non-trivial features of the mechanism's intrinsic structure \cite{Horak_2009,Carlsson_2009,Curto_2016}. Applying these techniques would allow a better understanding of the structure and function of complex systems' mechanisms. [Quizás incluir un mini tutorial o introducción a estas medidas?]
Taking into account the classic emblem “nothing in biology makes sense except in the light of evolution” \cite{Dobzhansky_1973}, we should expect most systems -and therefore their mechanisms- would present highly conserved aspects across different levels, scales, species, and types of measurements. Hence, in the light of evolution, most systems could be thought of as the result
phylo
- and ontogenic processes, time-and-space-locked to the physical world's regularities \cite{Parada_2018}. Many real-world complex networks indeed present topological and geometrical properties, such as short path length, high clustering, high-degree nodes, modularity, among others \cite{Bullmore_2009}. An evolutionary perspective would suggest that such pervasive properties provide functional advantages such as effective information transfer, robustness, and metabolical economy. Experimental evidence suggests this is actually the case, for example, \citet{Buzs_ki_2013} found that despite relevant brain size differences across mammalian species, the hierarchical organization of functional brain dynamics is surprisingly well preserved. In other words,
regardless
brain size, neural interactions unfold over similar time-scales within and across brain networks. Hence, a reasonable hypothesis would predict that such properties would also be found in graphs representing mechanisms. 

Studying body-world links