In today’s society, the word ‘network’ is used often and in numerous contexts: social, neural, financial, transportation... But what exactly is a network and what makes it complex? From a more abstract point of view, a network is simply a structure comprised of several interconnected nodes. And it becomes complex when these connections are not simple, linear or random, but when both order and disorder exist in the same network, resulting in, for example, groups of nodes in the form of communities or nuclei of influence.

Over the past three decades, one particular method for analysing complex networks became particularly popular and was applied in numerous fields (neuroscience, technology, chemistry, biology, social studies, transportation networks, telecommunications, etc.). Yet the universal and cross-cutting application of this analysis model has been called into question by researchers at the UPF Center for Brain and Cognition (CBC), the Institut des Neurosciences de la Timone (INT) and the Institut des Neurosciences des Systeme (INS), both in the French city of Marseille.

The most common method fails to take the distinctive features of each network sufficiently into account

In essence, the research considers the most common scientific methodology for studying complex networks overly homogeneous and simplistic, claiming that it fails to take the distinctive features of each network sufficiently into account, and proposes a new approach that overcomes these limitations. The results of the study are presented in a scientific article, recently published in the journal Chaos: An Interdisciplinary Journal of Nonlinear Science. The study's co-authors are Gorka Zamora-López, researcher in the UPF Center for Brain and Cognition’s Computational Neuroscience Research Group; and Matthieu Gilson, currently linked to INT and INS in Marseille and who was formerly a member of the CBC-UPF.

The new analysis tool factors in differences in networks’ information propagation dynamics

One of the key aspects of the new paradigm is that it increases the focus on the differences in each network’s information propagation dynamics. To illustrate these differences, Gorka Zamora-López (CBC-UPF) uses the following example: in social networks, a message posted on one profile may be shared by one or more users, an action which may in turn be replicated by others, facilitating the distribution of the content and rapidly spreading it to an increasing number of users. This propagation model bears no resemblance to, for instance, travel in a transportation network. A person who uses the underground to commute from home to work passes several stations on their journey and may have to change lines or hop on a bus at one of these stations. In this case, we are not talking about information that replicates, but rather one person travelling on a network, who begins and ends their journey at different stations (nodes).

The analysis method that has been most widely used up until now is based on graph theory and serves to produce a simplified representation of a network’s nodes and connections. This paradigm proved popular because it makes it possible to analyse networks based on a simple view of their structure and because, within the same analytical framework, it was the first to enable comparative research between different fields. Nonetheless, the traditional method’s simplicity is at the same time its major limitation, as, according to the study, it discards much of the information needed to understand networks. It is a method whose metrics for measuring the connections between network nodes employ combinatorial and probabilistic properties. For instance, with regard to social networks, these metrics could help us calculate the probability that one “friend” is also a contact of other “friends”.

By shifting the perspective towards a dynamical view, the study shows that these traditional metrics are only compatible with cascade propagation models, which would suit the previous example regarding the propagation of content on social media, but would be incompatible with the way a user travels in a transportation network. This is why the researchers questioned the universal nature of the metrics employed thus far. According to Matthieu Gilson (INS/INT), “the major limitation of the traditional method is that it excludes forms of propagation that exist in networks. However, jointly studying the structure and propagation dynamics –appropriate to each case– would substantially improve our interpretation of the results.”

The researchers have therefore proposed a paradigm shift in the analysis of complex networks. They call for an approach based on a model that adapts to the specific features of each network, developing 5 prototypical models (which may be adjusted to match each network’s specific attributes). The new method serves to adjust the metrics to the specific characteristics of each network, making it possible to move beyond a combinatorial and probabilistic perspective.

Gorka Zamora-López (CBC-UPF): “Beyond neuroscience, this paradigm shift also presents the opportunity to make similar corrections and design specific methodologies for analysing complex networks in numerous other fields of knowledge”

In the field of neuroscience, this new analysis model may help draw distinctions between healthy brains and brains with some sort of disorder. In healthy individuals, nerve signal propagation initially follows a cascade model, until the chain of transmission is interrupted to prevent the brain from becoming overloaded with information. In patients with disorders of consciousness, this interruption occurs almost immediately, impeding the information from reaching the regions it is supposed to reach.

While the study was developed in the field of neuroscience, Gorka Zamora-López concludes that, “beyond neuroscience, this paradigm shift also presents the opportunity to make similar corrections and design specific methodologies for analysing complex networks in numerous other fields of knowledge.”

Reference article: 

Gorka Zamora-López, Matthieu Gilson; An integrative dynamical perspective for graph theory and the analysis of complex networks. Chaos 1 April 2024; 34 (4): 041501. https://doi.org/10.1063/5.0202241