News ID: 217180
Published: 1223 GMT June 24, 2018

How community structure affects resilience of a network

How community structure affects resilience of a network
Demonstration of two interconnected modules from the coauthor collaboration network (dblp). Nodes are authors, and a link between two nodes exists if two authors have published at least one paper together.

Network theory is a method for analyzing the connections between nodes in a system.

One of the most compelling aspects of network theory is that discoveries related to one field, such as cellular biology, can be abstracted to a form that applies directly to a completely different field, like interstate traffic patterns, according to  

The most well-known application of network theory is social networking. In a social network, each person is a node connected to other nodes.

Additionally, a fraction of nodes within one network, so-called interlinks, will connect to nodes in neighboring networks.

This type of complex, overlapping network is referred to as a community structure. Characterizing these structures is fundamental in the study of networked systems, but researchers haven't fully understood how community structure affects the resilience of the network.

An international collaborative of researchers has developed the first theoretical framework demonstrating that community structure significantly affects the resilience of a system; their findings have wide ranging applications in social, technological, biological and climatic systems.

They have published their new theoretical framework in the Proceedings of the National Academy of Sciences.

System resilience is a way of describing the robustness of a network. To explore the effects of community structure on resilience, the researchers applied a theory called percolation.

Basically, percolation theory seeks the probability of an open path across a network. Percolation is strongly influenced by the number of interlinked nodes within a network.

It is not possible for all nodes in a network to become interlinks.

As an example, the authors cite international airports, "Only some airports have the longer runways, customs administration, and passport control required for international flights, and when an airport node already has interconnections, the costs of adding additional interconnections is significantly lower."

By contrast, a smaller airport without these infrastructural advantages would not be able to connect to airports in other countries.

This is analogous to people who possess the social facility to interlink different network neighborhoods, or brain cells that have the morphological capacity to interlink brain structures.

The researchers found that the interlinks between different communities deeply affect the percolation phase transition — they liken the fraction of nodes with interconnections to an external field in a physical phase transition.

They report that systems become more stable and resilient as the fraction of nodes with interconnections increases.

In terms of social networks, the greater the number of popular, cross-community people within a network, the more resilient the network will be to external forces like political upheaval or natural disasters.

The authors emphasize that their results apply to other types of networks.

They wrote, "Although our theory is applied here to study the resilience of modules within a single network, it can be extended to study resilience of interdependent networks and multiplex networks."


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