## Probabilistic Graphical Models Course - Textbook Errata, Notes, and Explanations

This page lists errors in textbooks used for Cmput 651 (Sept-Dec, 2008).
### Koller & Friedman Text

- Ch. 2 - Section 2.3.4, Definition 2.3.13

The definition given for a *clique* is actually the definition of what we call a **maximal**
clique. The definition of *subclique* corresponds to what we call a *clique*.

So, the
way we use the words, a *clique* is any complete (i.e. fully connected) induced subgraph. For
example, any two nodes that are connected by an edge constitute a clique of size 2. A *maximal
clique* is a clique that is not a subgraph of any clique. That is, if you add any extra node to a
maximal clique, it stops being a clique. A **maximum** clique (note: that's
maxim**um** not maxim**al**) is a clique with the largest number of nodes of all
cliques in the graph. For example, in a lattice, any two nodes connected by an edge form i) a clique,
ii) a maximal clique, and iii) a maximum clique.

Also see
http://en.wikipedia.org/wiki/Clique_(graph_theory) and
http://en.wikipedia.org/wiki/Maximal_clique.