The Why, How, and When of Representations for Complex Systems

Complex systems, composed at the most basic level of units and their interactions, describe phenomena in a wide variety of domains, from neuroscience to computer science and economics.
The wide variety of applications has resulted in two key challenges: the generation of many domain-specific strategies for complex systems analyses that are seldom revisited, and the compartmentalization of representation and analysis ideas within a domain due to inconsistency in complex systems language.
This article by Leo Torres, Ann S. Blevins, Danielle Bassett, and Tina Eliassi-Rad proposes basic, domain-agnostic language in order to advance toward a more cohesive vocabulary. 

there is no perfect way to analyze a system

Updated analysis pipeline includes consideration of which computational methods to perform on the chosen representation, and what distinct or complementary perspectives these methods offer.
We note that each analysis provides its own perspective on the system representation. We recommend performing steps 1–4 with careful consideration in order to gain real insight into the system.

The main message of our work is that there is no perfect way to analyze a system, and that studying two dfferent systems may require two entirely different pipelines.
The modeling decisions made while studying one dataset compiled from a system will not necessarily carry over to another system or, indeed, not even to another dataset extracted from the same system. In contrast, many studies apply certain pipelines for seemingly no other reason than because they are common within a certain field.
Instead, we recommend that each new system and dataset be individually evaluated and investigated, and each assumption and pipeline decision be made in accordance with the concepts discussed here. More specically, we suggest designing pipelines based on the system and system dependencies, any external dependencies that may be induced by the data type or data collection method, and the limits of the system fragment under study. From there, we suggest choosing a framework that best fits the data, the research question, and the system itself, even if it requires using a new framework or extension that is outside of what is customary. Finally, we recommend choosing carefully the specic methods, measurements, and analyses performed on the chosen representation, and keeping in mind that their results may be biased by the choices made in the previous stages.
Different choices at each of these steps may ultimately yield results that are at odds with the results yielded by other choices. Only after respecting the system’s dependencies and unique qualities through proper representation and analysis methods will we uncover novel insights into the system under study.

Complex system analysis pipeline discussed in this paper. To begin, we suggest considering how the research question, data availability, and system dependencies may influence downstream analyses. We suggest choosing a framework (navy) that preserves and respects dependencies within the system and data. Frameworks themselves are mathematically related (light blue), but switching frameworks after the initial data encoding can result in making inaccurate assumptions or forgetting independent relations. Finally, choosing the appropriate analysis method for the system and representation (green) after all other steps have been performed carefully can offer insights into the system’s behavior, structure, or function.

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