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.

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