Practical Social Network Analysis with Python pp 203-232 | Cite as

# Power Law

## Abstract

A quantity *x* is said to obey a *power law* is it is drawn from a probability distribution given by \(p(x) \propto x^{-\alpha }\) where \(\alpha \) is a constant parameter known as *exponent*. In this chapter we will look at ways to determine whether or not a certain set of values follow a power law. We will learn graph models that can exhibit power-law, mainly focusing on the *preferential attachment* model that has power-law degree distribution. We will then look at the *rich-get-richer phenomenon* and how this is prevalent in citation networks and population growth of cities. Finally, we will cover *densification power laws* and *shrinking diameters* which are properties observed from temporal social networks, which have given rise to the *forest fire* model.

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