New Tool Finds Critical Points in Everything from Cybersecurity to Ecological Conservation

[Vienna, 29.01.2025]—What if you could break apart a network like grating cheese—isolating its most crucial elements, fragmenting it into disconnected pieces to reveal where disruptions would be most devastating? That’s the power of fitness centrality, a new method introduced by researchers at the Complexity Science Hub (CSH) in a recent study published in Journal of Physics: Complexity.

By identifying the most vital nodes in any network—from social media and financial systems to transportation grids and ecological conservation—fitness centrality provides a faster and more efficient way to pinpoint weak points before they cause chaos. Unlike previous methods, which require costly recalculations, this approach streamlines the analysis, making it practical even for vast, complex networks.

"What makes this discovery particularly exciting is its universal applicability," explains first author Vito D.P. Servedio, a senior researcher at CSH. “It extends methods previously limited to economic analysis into a universal tool that works for all types of networks.”

This approach is particularly good at finding nodes that, if removed, would isolate many other parts of the network—similar to a server failure interrupting the connection of many users in a communication network or a pump failure in a water supply network paralyzing the supply of water to districts.

“This is a crucial capability for both protecting critical infrastructure and understanding how networks might fail,” explains Servedio.

The tool has practical applications that are far-reaching. According to co-author Giordano De Marzo, the concept of 'fitness centrality' could be used in supply chains to determine which companies are vital to the network's functioning, enabling better risk management and more resilient planning. “In ecological networks, it could help conservationists identify which species are most critical to maintaining ecosystem stability,” adds De Marzo, a postdoc researcher at the University of Konstanz and a research fellow at CSH. 

For cybersecurity experts, it provides a new way to identify vulnerable points in computer networks that need extra protection, explains co-author Emanuele Calò, a visiting student at CSH. “In transportation networks, such as airline or road systems, recognizing key nodes, such as airports, and intersections, helps maintain connectivity of poorly connected areas and optimize response strategies during disruptions. Additionally, identifying essential employees and teams in collaboration networks within companies helps prevent communication breakdowns and ensure workflow continuity,” adds Calò, a PhD student from the IMT School for Advanced Studies Lucca.

“A key advantage of this method is its computational efficiency. Unlike other approaches that require recalculating network quantities after each node removal, this method computes fitness values only once at the initialization phase. This makes it practical for analyzing large networks where alternative methods would be prohibitively slow. The method is particularly valuable when recalculating network properties after node removal is unfeasible, such as in law enforcement operations targeting organized criminal networks”, says Servedio.

In test cases, the novel approach consistently outperformed existing methods by about 15% in identifying crucial nodes whose removal would most disrupt the network. "One could say our method produces 15% more network splinters," explains the senior researcher.

"There are many ways to disrupt a network, depending on your goal. If you aim to split a network into large communities, betweenness centrality is a suitable method. In contrast, our fitness centrality approach disrupts networks like a grater does to cheese, breaking them into small splinters—tiny clusters or isolated nodes with no connections. For example, in a terrorist network, splitting it into large parts could result in losing oversight of those groups. Instead, the goal would be to isolate as many individuals as possible," adds Servedio. 

As often happens in science, methods originally developed for a specific discipline or question can also prove useful in other fields. In this case, this was also true. ‘Fitness centrality’ is based on the key concept of Economic Fitness Complexity (EFC), a measure originally developed to explain and predict the economic development trajectories of countries, cities, and regions.

However, the existing algorithm was limited to bipartite graphs, which are mathematical models for relationships between elements of two sets. “It became unusable even with the smallest deviations from this bipartite structure–which is problematic, as real-world networks typically do not consist of just two groups," points out co-author Alessandro Bellina, from Sapienza University and Centro Ricerche Enrico Fermi in Rome. 

"We've taken a method that was originally developed for economic analysis and transformed it into a tool that can be used to understand any type of network system."

The paper "Fitness centrality: a non-linear centrality measure for complex networks," by Vito D. P. Servedio, Alessandro Bellina, Emanuele Calò and Giordano De Marzo was published in Journal of Physics: Complexity and is available online.

The Complexity Science Hub (CSH) is Europe’s research center for the study of complex systems. We derive meaning from data from a range of disciplines—economics, medicine, ecology, and the social sciences—as a basis for actionable solutions for a better world. Established in 2015, we have grown to over 70 researchers, driven by the increasing demand to gain a genuine understanding of the networks that underlie society, from healthcare to supply chains. Through our complexity science approaches linking physics, mathematics, and computational modeling with data and network science, we develop the capacity to address today’s and tomorrow’s challenges.