Encyclopedia of Social Network Analysis and Mining

2018 Edition
| Editors: Reda Alhajj, Jon Rokne

Scale-Free Nature of Social Networks

  • Piotr Fronczak
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-7131-2_248




The degree of a node in a network is the number of edges or connections to that node

ER graph

The network model in which edges are set between nodes with equal probabilities

Fat-tailed distributions

Have tails that decay more slowly than exponentially. All power-law distributions are fat tailed, but not all fat-tailed distributions are power laws (e.g., the lognormal distribution is fat tailed but is not a power-law distribution)

Node degree distribution

The distribution function P(k) that gives the probability that a node selected at random has exactly k edges

Power-law distribution

Has a probability function of the form P(x) ~ x−a


Feature of objects or laws that does not change if length scale is multiplied by a common factor; also known as scale invariance

SF network

The network with power-law distribution of node degrees


The notion of scale-freeness...

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© Springer Science+Business Media LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of PhysicsWarsaw University of TechnologyWarsawPoland

Section editors and affiliations

  • Przemysław Kazienko
    • 1
  • Jaroslaw Jankowski
    • 2
  1. 1.Department of Computer Science and Management, Institute of InformaticsWrocław University of TechnologyWrocławPoland
  2. 2.Faculty of Computer Science and Information TechnologyWest Pomeranian University of TechnologySzczecinPoland