How to Predict a System Collapse: Find the K-Core
In a new study, a team of physicists from The City College of New York found a way to predict the collapse of a mutualistic system. In a mutualistic system, participants cooperate and benefit from one another. The concept can apply to many types of networks, from microbial ecosystems to banking to social groups.
The paper, authored by research associates Flaviano Morone and Gino Del Ferraro, and Professor Hernán Makse (CCNY and The Graduate Center, CUNY), appears in Nature Physics.
The key to foreseeing a breakdown is a metric called the “k-core.” In a mutualistic system, the k-core is an inner group of members with many connections to rest of the network. If the connections within the network start to weaken to the point where the members of the k-core go extinct, the paper says, the entire network will collapse.
You can find the k-core by first removing all participants with less than one connection, then removing those with less than two connections, and so on, to the point where if you continued, there would be none left. In biology, k-core members are analogous to keystone species. These species have a large influence on their ecosystem, such as gray wolves in Yellowstone National Park. Because their results are true for a large class of systems, the researchers say, these ideas could also extend to social networks, neural circuitry, and gene regulatory networks.
One way to keep a system stable is to protect those k-core species. Cooperation between members, the authors say, also strengthens the system. On the other hand, a rise in the number of commensalists — members that benefit from the network but neither harm nor benefit others in return — is a sign that the network is approaching its tipping point.