Generalized friendship paradox in networks with tunable degree-attribute correlation

Hang-Hyun Jo, Young-Ho Eom

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

One of the interesting phenomena due to topological heterogeneities in complex networks is the friendship paradox: Your friends have on average more friends than you do. Recently, this paradox has been generalized for arbitrary node attributes, called the generalized friendship paradox (GFP). The origin of GFP at the network level has been shown to be rooted in positive correlations between degrees and attributes. However, how the GFP holds for individual nodes needs to be understood in more detail. For this, we first analyze a solvable model to characterize the paradox holding probability of nodes for the uncorrelated case. Then we numerically study the correlated model of networks with tunable degree-degree and degree-attribute correlations. In contrast to the network level, we find at the individual level that the relevance of degree-attribute correlation to the paradox holding probability may depend on whether the network is assortative or dissortative. These findings help us to understand the interplay between topological structure and node attributes in complex networks.
Original languageEnglish
Article number022809
Number of pages6
JournalPhysical Review E
Volume90
Issue number2
DOIs
Publication statusPublished - 21 Aug 2014

Fingerprint

paradoxes
Paradox
Attribute
Vertex of a graph
Complex Networks
Solvable Models
Topological Structure
Arbitrary

Keywords

  • friendship paradox
  • degree-attribute correlation
  • network models

Cite this

@article{8035a1da95414d67860b1e4a681cbb0a,
title = "Generalized friendship paradox in networks with tunable degree-attribute correlation",
abstract = "One of the interesting phenomena due to topological heterogeneities in complex networks is the friendship paradox: Your friends have on average more friends than you do. Recently, this paradox has been generalized for arbitrary node attributes, called the generalized friendship paradox (GFP). The origin of GFP at the network level has been shown to be rooted in positive correlations between degrees and attributes. However, how the GFP holds for individual nodes needs to be understood in more detail. For this, we first analyze a solvable model to characterize the paradox holding probability of nodes for the uncorrelated case. Then we numerically study the correlated model of networks with tunable degree-degree and degree-attribute correlations. In contrast to the network level, we find at the individual level that the relevance of degree-attribute correlation to the paradox holding probability may depend on whether the network is assortative or dissortative. These findings help us to understand the interplay between topological structure and node attributes in complex networks.",
keywords = "friendship paradox, degree-attribute correlation, network models",
author = "Hang-Hyun Jo and Young-Ho Eom",
year = "2014",
month = "8",
day = "21",
doi = "10.1103/PhysRevE.90.022809",
language = "English",
volume = "90",
journal = "Physical Review E",
issn = "1539-3755",
publisher = "American Physical Society",
number = "2",

}

Generalized friendship paradox in networks with tunable degree-attribute correlation. / Jo, Hang-Hyun; Eom, Young-Ho.

In: Physical Review E, Vol. 90, No. 2, 022809, 21.08.2014.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Generalized friendship paradox in networks with tunable degree-attribute correlation

AU - Jo, Hang-Hyun

AU - Eom, Young-Ho

PY - 2014/8/21

Y1 - 2014/8/21

N2 - One of the interesting phenomena due to topological heterogeneities in complex networks is the friendship paradox: Your friends have on average more friends than you do. Recently, this paradox has been generalized for arbitrary node attributes, called the generalized friendship paradox (GFP). The origin of GFP at the network level has been shown to be rooted in positive correlations between degrees and attributes. However, how the GFP holds for individual nodes needs to be understood in more detail. For this, we first analyze a solvable model to characterize the paradox holding probability of nodes for the uncorrelated case. Then we numerically study the correlated model of networks with tunable degree-degree and degree-attribute correlations. In contrast to the network level, we find at the individual level that the relevance of degree-attribute correlation to the paradox holding probability may depend on whether the network is assortative or dissortative. These findings help us to understand the interplay between topological structure and node attributes in complex networks.

AB - One of the interesting phenomena due to topological heterogeneities in complex networks is the friendship paradox: Your friends have on average more friends than you do. Recently, this paradox has been generalized for arbitrary node attributes, called the generalized friendship paradox (GFP). The origin of GFP at the network level has been shown to be rooted in positive correlations between degrees and attributes. However, how the GFP holds for individual nodes needs to be understood in more detail. For this, we first analyze a solvable model to characterize the paradox holding probability of nodes for the uncorrelated case. Then we numerically study the correlated model of networks with tunable degree-degree and degree-attribute correlations. In contrast to the network level, we find at the individual level that the relevance of degree-attribute correlation to the paradox holding probability may depend on whether the network is assortative or dissortative. These findings help us to understand the interplay between topological structure and node attributes in complex networks.

KW - friendship paradox

KW - degree-attribute correlation

KW - network models

UR - http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.022809

U2 - 10.1103/PhysRevE.90.022809

DO - 10.1103/PhysRevE.90.022809

M3 - Article

VL - 90

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 2

M1 - 022809

ER -