Which is the best mathematical model to describe the structure of a complex network?
Researchers of the University of Barcelona and the Universitat Politècnica de Catalunya have led a study published in the journal Nature Communications, which presents a scientific method to identify, compare and establish objective differences with high precision between large complex networks.
Researchers of the University of Barcelona and the Universitat Politècnica de Catalunya have led a study published in the journal Nature Communications, which presents a scientific method to identify, compare and establish objective differences with high precision between large complex networks.
The new technology will allow, for example, comparing and distinguishing the functioning of the neuronal network between drug-addicts and healthy people, and therefore, making advances in the study of symptomatology and the effects of addictions on the brain. It will also allow analyzing more properly the functioning of critical complex systems, such as networks of energy distribution, airport interconnections or even social networks such as Facebook and Twitter.
The research counts with the participation of Albert Díaz-Guilera, professor from the Department of Condensed Matter Physics and the Institute of Complex Systems of the University of Barcelona (UBICS); Laura Carpi, post-doctoral researcher from the Department of Physics of the UPC (Terrassa Campus), and Cristina Masoller, professor at the School of Industrial, Aeronautical and Audiovisual Engineering of Terrassa (ESEIAAT), among other scientists from American Universities.
According to the UB researcher Díaz-Guilera, “this method allows us to discover the specific formation of a topological structure. Thanks to the definition of distance between networks, we can create virtual ones out of specific mathematical models and see which one is more accurate. It is not the same to treat networks that grow with geographical approximation, such as transport ones, than the ones who do it by affinity, such as the social ones. By understanding the creation of the network, according to these mathematical models, we can identify their strengths and their weaknesses”.
Cristina Masoller gave an example: “Letʼs imagine we have a system of energy distribution made of two networks interconnected with the same number of links each, and one of them loses a link because of some damage”. “The methods we had so far -continued the expert- allowed us to establish a difference in this missing link. Our method, in addition, defines where the lost link is and which importance it has in relation to the system, that is, it shows whether the lack of this link complicates the distribution of energy”.
At this moment, it is very difficult to differentiate, distinguish and compare the functioning and structure of networks that have hundreds of thousands of nodes interconnected between them and that create the so-called complex systems. The same happens with neuronal networks and brain connections. Identifying the structures, establishing differences between connections and detecting dysfunctions is a hard task. So far, there wasnʼt any proper and precise way to identify the presence or absence of critical links that connect or disconnect the network because, without identifying them, it is hard to ensure the proper functioning in information transfer.
“This is the reason why out method is an important advancement in the study of complex systems, because it points out precisely the importance of connections that fail in relation to the activity of a complex system”, says the UPC researcher. Apart from identifying and naming different nodes in a network, “we can also calculate the distances between the parts that create it. Thanks to mathematics, we achieved it, so the scientists have now a useful tool to study complex systems with more guarantees”, she confirmed.
With the methodologies that were available so far in the scientific community, researchers could detect a difference between the number of connections in a network -even the number of connections that donʼt work out-, but these methods didnʼt allow them to discover the place of failed connections or if they were really interrupting the information flow in all the network.
This research also counts with the participation of Tiago A. Schieber and Martin G. Ravetti, from the Federal University of Minas Gerais (Belo Horizonte, Brazil), and Panos M. Pardalos of the University of Florida (United States).
Article Reference:
T. A. Schieber, L. Carpi, A. Díaz-Guilera, P. M. Pardalos, C. Masoller, M. G. Ravetti. «Quantification of network structural dissimilarities». Nature Communications, January, 2017. DOI: 10.1038/ncomms13928