Speaker:

Scott Feld, Professor of Sociology, Purdue University

Title:

Finding Highly Connected Nodes in Networks: The Power of Common Friends

Abstract:

This paper extends the Friendship Paradox – where friends have more friends than random people do, on average – to the more general phenomenon that mutual friends have more friends than friends do, on average. We show that we can find people who who are friends of multiple people in practical sized random samples in one regional Facebook network of 63,392 people with an average of 24 friends each, where people with two friends in a random sample have an average of 212 friends overall, with three friends have an average of 391 friends, etc. We further illustrate this general network phenomenon by taking random samples of citations from 79,034 journal articles. We find that a source cited by two articles in a random sample has an average of 461 citations, placing it in the top 0.01% in numbers of citations among all sources cited by these articles. We provide a general expression for the expected overall number of friends of a person found to have k friends in a random sample from a population with a given distribution of numbers of friends. We show that the effectiveness of using common friends among random samples for finding highly connected nodes is most pronounced when there are nodes with a great disproportion of the ties, as seems to be both typical and important for many types of social and other networks, such as where there are superspreaders of diseases, mega-influencers on the Internet, and highly connected central nodes in centralized neural networks. We discuss further implications, applications, and directions for further research.

Speaker Bio:

Scott Feld served as Assistant to Full Professor of Sociology at the State University of New York at Stony Brook from 1975-1991. He then served as Professor of Sociology at Louisiana State University from 1991 until 2004, and joined the faculty at Purdue University in 2004. He has published over sixty articles, including twelve published in the most prestigious journals in the fields of Sociology and Political Science. His ongoing research interests involve 1) causes and consequences of patterns in social networks, 2) processes of individual and collective decision making, and 3) applications of sociology, most recently including innovations in marriage and divorce laws (covenant marriage). He regularly teaches undergraduate and graduate courses on social networks, research methods, and statistics.