Encyclopedia of Social Network Analysis and Mining

2014 Edition
| Editors: Reda Alhajj, Jon Rokne

Scale-Free Nature of Social Networks

  • Piotr Fronczak
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-6170-8_248




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

Node Degree Distribution

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

Power-Law Distribution

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

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 log-normal distribution is fat tailed but is not a power-law distribution)

SF Network

The network with power-law distribution of node degrees

ER Graph

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


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


The notion of scale-freeness and...

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© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Piotr Fronczak
    • 1
  1. 1.Faculty of PhysicsWarsaw University of TechnologyWarsawPoland