Centrality-friendship paradoxes: when our friends are more important than us

Desmond J Higham

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)
21 Downloads (Pure)


The friendship paradox states that, on average, our friends have more friends than we do. In network terms, the average degree over the nodes can never exceed the average degree over the neighbours of nodes. This effect, which is a classic example of sampling bias, has attracted much attention in the social science and network science literature, with variations and extensions of the paradox being defined, tested and interpreted. Here, we show that a version of the paradox holds rigorously for eigenvector centrality: on average, our friends are more important than us. We then consider general matrix-function centrality, including Katz centrality, and give sufficient conditions for the paradox to hold. We also discuss which results can be generalized to the cases of directed and weighted edges. In this way, we add theoretical support for a field that has largely been evolving through empirical testing.
Original languageEnglish
Pages (from-to)515-528
Number of pages14
JournalJournal of Complex Networks
Issue number4
Early online date23 Nov 2018
Publication statusE-pub ahead of print - 23 Nov 2018


  • friendship paradox
  • centrality
  • sampling bias
  • matrix-function centrality


Dive into the research topics of 'Centrality-friendship paradoxes: when our friends are more important than us'. Together they form a unique fingerprint.

Cite this