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

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 maximum not maximal) 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.