# Association analysis

Association analysis (*Since version 7.16*) measures the strengths of associations between sets of nodes or variables **X** and **Y**.

For example, it can be used to measure the strength of links in a network.

Supported for discrete, continuous, hybrid (discrete - continuous) and multi-variate nodes.

## Mutual information

Mutual information quantifies the amount of information that can be gained from one variable through the other. Often denoted `I(X;Y)`

.

## Entropy

The Entropy for **X** and **Y**, denoted `H(X)`

and `H(Y)`

respectively, are reported for convenience, as the normalized forms of the mutual information require them.

## Symmetric mutual information

The symmetric mutual information (symmetric uncertainty) is a normalized version of the mutual information. It tells us the strength of the association given the level of uncertainty present in X and Y.

It equals `2 * I(X;Y) / (H(X) + H(Y))`

## Proficiency

The proficiency (uncertainty coefficient) normalizes the mutual information for either X or Y. For example, the proficiency of X given Y tells us how strong the relationship is given that we know Y.

The proficiency of X given Y, denoted `U(X|Y)`

equals `I(X;Y)/H(X)`

, and
`U(Y|X)`

equals `I(X;Y)/H(Y)`

.