The difference between alter-based and ego-based friendship paradox means equals the degree-degree covariance normalized by the mean degree.
Friendship-paradox paradox: Do most people's friends really have more friends than they do?
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abstract
The classical friendship paradox asserts that, on average, an individual's neighbors have a higher degree than the individual. This statement concerns network-level means and does not describe how often a typical node is locally dominated by its neighbors. Motivated by this distinction, we develop a framework that separates mean-based friendship paradox inequalities from two majority-type quantities: a global fraction measuring how many nodes have a degree smaller than the mean degree of their neighbors, and a local fraction based on hub centrality that measures how many nodes are dominated in a median-based sense. We show that neither fraction is constrained by the classical friendship paradox and that they can behave independently of each other. A simple example and two empirical networks illustrate how quadrant patterns in the joint distribution of a node's degree and its neighbors' degree determine the signs and magnitudes of the two fractions, and how left- or right-skewed degree distributions of neighboring nodes can yield opposite conclusions for mean-based and median-based comparisons. The resulting framework offers a clearer distinction between population averages and local majority relations and provides a foundation for future analyses of local advantage, disadvantage, and perception asymmetry in complex networks.
fields
physics.soc-ph 1years
2025 1verdicts
ACCEPT 1representative citing papers
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Two variants of the friendship paradox: The condition for inequality between them
The difference between alter-based and ego-based friendship paradox means equals the degree-degree covariance normalized by the mean degree.