Networks robustness. A complex network is a mathematical structure composed of nodes and links, capable of representing a wide range of real-world systems. A central aspect of the Networks Unit’s research is the study of the robustness of real-world complex networks with respect to the removal of nodes and links. The robustness of a network represents its ability to maintain its functionality in the presence of failures, attacks or intentional removals of elements. Understanding the robustness of complex networks is essential to analyze and improve the functioning and resilience of real-world systems. This type of analysis is useful in many real-world problems. Ensure that critical networks, such as energy or transport, continue to operate even in the presence of failures or targeted attacks. Optimize the design of networks, balancing efficiency and robustness, while taking into account the limited resources available. Mitigate the impact of events that can propagate through a network, such as power grid outages, crises in financial systems, the spread of epidemics or fake news in social networks. Identify nodes and links that are critical to the correct functioning of the system. Understanding which attack strategy causes the most damage allows us to identify the crucial nodes and links for the system.
Ecological networks. Food webs are ecological networks that serve as representations of predator-prey relationships in an ecosystem. Food webs are modeled as directed graphs, where nodes correspond to species and links indicate who eats what. The extinction of a species can be studied as the removal of a node, with cascading effects on the entire network. If a key node, such as an apex predator or a primary species, is removed, it can cause the disappearance of other dependent species, leading to a trophic cascade and ecosystem instability.
The Networks Unit analyzed primary extinction in food webs by introducing a criterion based on minimum energy thresholds necessary for the survival of the species. If, following the primary extinction, one or more species see their resources fall below the critical threshold, they too must be extinct. Our simulations show that as the energy threshold required for the survival of the species increases, the robustness of food webs decreases significantly, making the ecosystem very vulnerable to resource loss. A small increase in the energy threshold causes a significant increase in secondary extinction, highlighting the fragility of food webs under energy stress. Structural analysis of these webs helps to identify the most critical species for ecological resilience and to predict the impact of factors such as climate change and human activity on biodiversity.
Biological networks. Biological networks can be of various nature. Nodes can represent proteins, genes, chromophores, or organisms, while links indicate biochemical interactions, genetic regulation, energy transfer, or matter flow. Their analysis helps to understand disease evolution, develop drugs, explain energy transfer mechanisms in plants, and study biological processes of various nature. The Networks Unit modeled the excitation energy transfer (EET) in the photosystem I (PSI) of Pisum sativum as a complex network of interactions, using the Förster Resonance Energy Transfer (FRET) to calculate the energy transfer between chromophores. In this network, nodes represent chromophores, while links indicate the amount of FRET between them. The efficiency of the PSI was analyzed using classical indicators of network science and a specific measure developed ad hoc: the number of chromophores connected to the P700 reaction center. The results indicate that PSI is a resilient system, in which the efficiency gradually decreases with the removal of FRET links, maintaining a significant overall energy transfer even after the loss of numerous interactions between chromophores.
Gastronomical networks. Network science has recently joined food science in food research. Gastronomical networks can be modeled in different ways, with nodes identifying ingredients, dishes, recipes, or nutrients, with links representing culinary combinations, flavor affinities, recipe similarities, or nutritional connections. Studying these networks allows us to create new recipes, improve nutrition, and analyze culinary traditions. Our lab, combining network science and intersection graph theory, analyzed the structural properties of recipe networks in Catalan cuisine. Using three different cookbooks, two traditional and one haute cuisine, we constructed recipe similarity networks by linking them based on shared ingredients, with link weights reflecting similarity between ingredients. Our analysis reveals that recipe networks exhibit structural differences across cuisines, particularly haute cuisine, which features more specialized recipes. Node centrality metrics then identify key recipes that define culinary traditions, such as “Allioli” in traditional Catalan cuisine and “Becada con brioche de su salmis” in haute cuisine. This study contributes to the field of computational gastronomy and provides a methodological foundation that can be integrated with AI techniques to support recipe personalization, food recommendations, and gastronomic innovation.
Social networks. In network science, social networks are represented as graphs, where nodes correspond to individuals (or entities) and links represent connections between them, such as friendships, collaborations or online interactions. These networks are often very complex, characterized by properties such as high connectivity between nodes, modular structure (communities of individuals preferentially connected to each other) and power-law distribution of the number of links, where a few highly connected nodes act as hubs.
The study of social networks allows us to analyze phenomena such as the diffusion of information, the formation of opinions, and the emergence of fake news and social dynamics related to these phenomena. The analysis of social networks finds applications in various fields of priority importance, including epidemiology, allowing the study and prediction of the spread of diseases. In this field, the Networks Unit has analyzed the role of the structure of social networks in the spread of epidemics and in the effectiveness of containment measures. Nodes represent individuals, while links indicate social contacts, considered potential channels of infection. Social link removal therefore describes the implementation of social distancing to reduce the spread of the epidemic. We found that the targeted removal of the most central social interactions, compared to their random removal, was more effective in slowing the spread of the epidemic. However, the timing of the interventions is crucial: delays greater than 20 days compromise the ability to contain the peak of infection. We then modeled vaccination in social networks in order to understand which vaccination strategy was more effective in stopping the epidemic spread. We simulated and compared different vaccination strategies, from the random one, to the one targeted to the most connected nodes in the network, showing how a semi-adaptive approach, which recalculates the centrality of the nodes after a certain number of vaccinations, increases the effectiveness of the vaccination strategy by up to 80%, thus demonstrating that the optimal choice depends on the availability of vaccines and the structure of the network.
Road networks. Road networks are graphical representations of road transport infrastructure, where nodes correspond to intersections or key points (such as junctions and roundabouts) and links represent the roads that connect them. Road networks have many applications, such as traffic flow analysis and congestion reduction, design of more efficient infrastructure, calculation of the shortest or fastest route, simulation of the impact of accidents or natural disasters on traffic. Our laboratory, in collaboration with Prof. Zhe-Ming Lu of the School of Aeronautics and Astronautics, Zhejiang University (China), studied the response of the Beijing road network to the removal of nodes to evaluate the robustness of the system with respect to local failures. The network, composed of nodes-intersections and links-roads, is a weighted network in which the weight of the links represents the number of vehicles passing through weekly. The damage was measured using both topological and weighted metrics. The results of our study show that weighted strategies, which take into account the weight of the links, cause the greatest damage to the transport capacity of the road system, highlighting the importance of the intersections where the highest traffic flows. Interestingly, a significant fraction of random node removals can generate damage comparable to or greater than that of targeted strategies. This suggests that extensive simulations of random failures could be useful to identify critical nodes and increase the robustness of transport infrastructures.