Generalized friendship paradox in complex networks: The case of scientific collaboration

Abstract

The friendship paradox states that your friends have on average more friends than you have. Does the paradox “hold” for other individual characteristics like income or happiness? To address this question, we generalize the friendship paradox for arbitrary node characteristics in complex networks. By analyzing two coauthorship networks of Physical Review journals and Google Scholar profiles, we find that the generalized friendship paradox (GFP) holds at the individual and network levels for various characteristics, including the number of coauthors, the number of citations, and the number of publications. The origin of the GFP is shown to be rooted in positive correlations between degree and characteristics. As a fruitful application of the GFP, we suggest effective and efficient sampling methods for identifying high characteristic nodes in large-scale networks. Our study on the GFP can shed lights on understanding the interplay between network structure and node characteristics in complex networks.

Generalized friendship paradox in networks with tunable degree-attribute correlation

“…The origin of the GFP at the network level has been clearly shown to be rooted in positive degree-attribute correlations [18]. In other words, high-attribute individuals are more likely to be observed by their friends as high-attribute individuals have more friends.…”

“…The GFP holds for a node if the node has a lower attribute than the average attribute of its neighbors. The GFP at both levels has been observed in the coauthorship networks [18]. While the GFP at the network level accounts for the average behavior of the network, the GFP at the individual level can provide more detailed understanding of the centrality of individuals, and of their subjective evaluations of attributes.…”

“…This requires us to study the interplay between topological structure and node attributes of social networks. The friendship paradox has been also considered for arbitrary node attributes [17][18][19], which is called the generalized friendship paradox (GFP) [18]. Note that if the degree of node is considered as the attribute, the GFP reduces to the FP.…”

“…The paradox has been shown to hold in both offline and online social networks [15][16][17][18][19][20]. Examples include friendship networks of middle and high school students [15,20] and of university students [6], scientific collaboration networks [18], and Facebook and Twitter user networks [16,17,19]. The paradox can be understood as a sampling bias in which individuals having more friends are more likely to be observed by their friends.…”

Resilience of Core-Periphery Networks in the Case of Rich-Club

“…This is because the clustering coefficient, the efficiency, and the average path length are measures averaged over all the network nodes (while the diameter is a more extremal measure) and are thus affected by the centrality values retained by the richclub. This bias is especially evident in scale-free networks whose heterogeneity in the degree distribution contributes to phenomena like the friendship paradox, which holds if the average degree of nodes in the network is smaller than the average degree of their neighbors [39]. The origin of the paradox is attributed to the existence of hub nodes and to the variance of the degree that contributes to altering the mean values of the degree over the neighborhoods of the nodes.…”