# 6.11. Glossary¶

**Barabási-Albert Model:** The Barabási–Albert (BA) model is an algorithm for generating random scale-free networks using a preferential attachment mechanism.

**Complementary CDF:** \(CCDF(x) ≡ 1 − CDF(x)\)

**Cumulative Distribution Function (CDF)** A function which maps from a value, \(x\), to the fraction of values less than or equal to \(x\).

**Explanatory Model:** Is a model that gives a useful description of why and how a phenomenon is the way it is.

**Growth:** Instead of starting with a fixed number of vertices, the BA model starts with a small graph and adds vertices one at a time.

**Heavy-tailed Distributions:** In probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded.

**Preferential Attachment:** Is any of a class of processes in which some quantity is distributed among a number of individuals according to what they already have.

**Probability Mass Function (PmF):** A function that maps from each value to it’s probabilities.

**Power Law:** A distribution follows this law if \(PMF(k) ∼ k−α\) where `PMF(k)`

is the fraction of nodes with degree `k`

, `α`

is a parameter, and the symbol ∼ indicates that the `PMF`

is asymptotic to `k−α`

as `k`

increases.

**Scale-Free Network:** A network whose degree distribution follows a power law, at least asymptotically.

**Standard Deviation:** A quantity calculated to indicate the extent of deviation for a group as a whole.

**WS Model:** A model that has characteristics of a small world network, like the data, but it has low variability in the number of neighbors from node to node, unlike the data.