Researchers introduce “fitness centrality,” a faster, more efficient approach to identifying the most critical elements in networks – from social and financial systems to ecosystems
Networks are everywhere in our world – from social media connections to global supply chains, from financial systems to power grids. Understanding which elements in a network are most crucial for the whole network is ever more important in an increasingly interconnected world where disruptions in one part of a network can have widespread consequences.
Scientifically, it has been a long-standing challenge to capture the significance of individual elements within a dynamic network. Which firms have major influence on the economy of a country? Which roads are most vital to keep traffic flowing smoothly?
In a new study published in the Journal of Physics: Complexity, researchers from CSH present a powerful new mathematical tool called “fitness centrality” that can identify the most vital nodes, meaning elements, in any network. “What makes this discovery particularly exciting is its universal applicability,” explains first author Vito D.P. Servedio from CSH. “It extends methods previously limited to economic analysis into a universal tool that works for all types of networks.”
FAR-REACHING PRACTICAL APPLICATIONS
This new approach is particularly good at finding nodes that, if removed, would isolate many other parts of the network – much like a failure of a server in a communication network that would interrupt the connection of many users or the failure of a pump in a water supply network that would paralyze the water supply of districts.
“This is a crucial capability for both protecting critical infrastructure and understanding how networks might fail,” Servedio says.
The practical applications of this discovery are far-reaching. He provides several examples: In supply chains, ‘fitness centrality’ could help identify which companies are most crucial to keeping the network functioning, allowing better risk management and more resilient planning. In ecological networks, it could help conservationists identify which species are most critical to maintaining ecosystem stability. For cybersecurity experts, it provides a new way to identify vulnerable points in computer networks that need extra protection. In transportation networks, such as airline or road systems, recognizing key nodes (airports, intersections) helps maintain connectivity of poorly connected areas and optimize response strategies during disruptions. Similarly, in collaboration networks within companies, identifying essential employees or teams prevents communication breakdowns and ensures workflow continuity.
FASTER AND MORE EFFICIENT
“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, this new approach consistently outperformed existing methods by about 15% in identifying crucial nodes whose removal would most disrupt the network. What does this mean? “One could say our method produces 15% more network splinters,” explains Servedio.
He continues, “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.”
RE-PURPOSING AND EXTENSION
As often happens in science, methods originally developed for a specific discipline or question can also prove useful in other fields. This was the case here as well. ‘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,” Servedio says.
“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,” he explains.
About the study
The study “Fitness centrality: a non-linear centrality measure for complex networks,” by V. D.P. Servedio, A. Bellina, E. Calò and G. De Marzo, was published in Journal of Physics: Complexity veröffentlicht (doi: 10.1088/2632-072X/ada845).