Generalized friendship paradox in networks with tunable degree-attribute correlation

Area of Science:

• Network Science
• Complex Systems Analysis
• Statistical Physics

Background:

• The friendship paradox describes how individuals' friends tend to have more connections than they do.
• The generalized friendship paradox (GFP) extends this concept to arbitrary node attributes.
• Network-level GFP is linked to positive correlations between node degrees and attributes.

Purpose of the Study:

• To investigate the conditions under which the generalized friendship paradox holds for individual nodes.
• To differentiate between network-level and individual-level phenomena of the GFP.
• To explore the influence of network topology and attribute correlations on the GFP.

Main Methods:

• Analysis of a solvable model to determine paradox holding probability in uncorrelated networks.
• Numerical simulations of correlated network models with adjustable degree-degree and degree-attribute correlations.
• Investigation of assortative and disassortative network structures.

Main Results:

• Characterization of paradox holding probability for individual nodes in uncorrelated networks.
• Demonstration that degree-attribute correlations impact individual GFP relevance differently based on network assortativity.
• Identification of interplay between network topology and node attributes in determining GFP at the individual level.

Conclusions:

• The generalized friendship paradox's manifestation at the individual node level is distinct from its network-level occurrence.
• Network assortativity plays a crucial role in modulating the effect of attribute correlations on individual GFP.
• Understanding these individual-level dynamics is key to comprehending complex network behavior.