New Model Emphasizes Social Network Communities Rather Than Connections

Carnegie Mellon University Electrical and Computer Engineering Professor Radu Marculescu has co-authored a paper in Nature Scientific Reports outlining a new model for how social networks change and develop over time. The research was conducted in collaboration with Mihai Udrescu and Alex Topirceanu of the Computer Science Department of the Politehnica University of Timişoara, Romania.

While their research focused specifically on social networks, the Weighted Betweenness Preferential Attachment (WBPA) model could have interesting applications in everything from modeling microbiomes to predicting the properties of new drugs and medications.

In modeling social networks, a node represents a single individual, and connections between nodes represent relationships between individuals. Prior models have focused on the amount of connections an individual has, also called the node degree, as the driving force behind a node acquiring new connections.

Nodes with high betweenness attract new links, before gradually losing their betweenness to neighboring nodes as a result of the node betweenness redistribution process.

In contrast, the core of the authors' WBPA model centers around the notion of "node betweenness." They discovered that this quality of being between communities is actually a greater attractor and driver for the formation of social ties than other measures of centrality like node degree. In the WBPA, rather than examining purely the amount of connections a single node has, researchers place more emphasis on the communities a node connects and the quality of those connections.

"When individuals make assessments of social attractiveness in real-world situations, they do not rely on executing algorithms or other types of complex quantitative evaluations," Marculescu said. "Instead, individuals make decisions based on their qualitative perceptions. As such, the quality of being 'in between' can be easily and quickly perceived."

(a) A non-influential individual (grey) initiates social contact (link) with other individuals equal or more influential than himself. (b) This action leads to a natural increase of the individual’s influence (betweenness). (c) Other nodes with less influence start connecting to the initial individual. At this point, the initial node has become a predominant receiver of new ties, as emphasized by the new violet links.

The WBPA model overcomes another limitation found in previous degree-driven models, which allow for individual node degree to grow indefinitely. This would equate to an individual being able to develop an unlimited number of friendships.

"The new model builds on the idea that humans are better at observing qualitative aspects than quantitative ones, which is why people typically favor investing in fewer qualitative social ties rather than numerous lower quality ties," Marculescu said. "This is why there's a node betweenness redistribution process at play in the WBPA, which limits the number of new links for high-degree nodes."

This redistribution process accounts for the real-world physical and mental limitations that constrain the amount of relationships a given individual can develop and maintain throughout their lifetime.

Finally, the Weighted Betweenness Preferential Attachment model can offer insight into an individual's possible means for improving their social status. An individual can increase their personal influence by broadening their neighborhood to influential agents, which can, in turn, trigger an increase in the strength of their connections with others.

Marculescu and his collaborators' next goal is to use findings from the WBPA model to investigate how opinions spread through social networks, and how robust these networks can act in the face of adversarial attacks.

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