In a new study, a research team from the Institute of Complex Systems of the University of Barcelona (UBICS) has analyzed the temporal evolution of real complex networks and has developed a model in which the appearance of new nodes can be related to pre-existing nodes , similar to the evolution of species in biology.
This study analyzes the temporal evolution of the network of citations in scientific journals and the international trade network over a period of more than one hundred years. As explained by M. Ángeles Serrano, ICREA researcher at UBICS, “what is observed in these real networks is that both grow in a self-similar way, that is, their connectivity properties remain unchanged over time, so the structure of the network is always the same, while the number of nodes is increasing ».
Researchers have been able to explain this surprising self-similarity in growth using a model called geometric branching growth (GBG). In this model, the new nodes come from pre-existing nodes, similar to family trees. For example, in the world trade network, the countries are the nodes, and therefore the forks, and the transactions correspond to the links. The key property that characterizes the evolution of the systems under study, and therefore the model, is inheritance. In the example, when a country is divided, the new sovereign countries inherit the wealth and trading partners of the original state.
This model is related to a previous work that allowed to produce self-similar reduced versions of complex networks through a process of geometric renormalization. In these previous works, it was found that connectivity in complex networks at different spatial scales is regulated by the same principles. “What we see in the new article – emphasizes the researcher – is that these same principles are also maintained over time.”
In this new model, the appearance of new nodes can be related to pre-existing nodes, similar to the evolution of species in biology. (Image: UB)
When the two models — GBG and geometric renormalization — are combined, replicas of the original network can be created in a very wide range of sizes, larger or smaller than the original. “In this way, descending nodes or ascending nodes could be predicted, or phenomena that depend on the size of the network could be studied,” emphasizes Serrano. “Networks therefore present a fractal structure in space and time,” he adds.
These branching processes are the basis for the complex evolution of many real systems. “In summary, the two models allow us to understand the interactions in real systems at different scales, one of the keys to understanding and predicting how their evolution will be”, concludes the expert.
The study is titled “Scaling up real networks by geometric branching growth.” And it has been published in the academic journal PNAS (Proceedings of the National Academy of Sciences). (Source: UB)