# Clique-Percolation Algorithm's "corner cases"

I'm programming an implementation of the Clique-Percolation algorithm, but I have many doubts about some corner cases.

Imagine we want to find the communities of a graph using $k=4$. We are lucky and every node in the graph belongs at least to one k-clique (with $k \geq 4$). So it's trivial to apply the algorithm by hand (slow, but trivial).

Now imagine we add three more nodes to the graph, creating a 3-clique, and connecting this clique to the previous existing nodes with only 1 edge.

It's here where I have problems to understand what's expected of the Clique Percolation algorithm.

I have to add a new community for each new node? Only a new non-overlapping community matching the 3-clique? Nothing (not considering the new nodes in any community)?

Example initial graph: $$A \leftrightarrow B \\ A \leftrightarrow C \\ A \leftrightarrow D \\ B \leftrightarrow C \\ B \leftrightarrow D \\ C \leftrightarrow D \\$$

Modified graph: $$A \leftrightarrow B \\ A \leftrightarrow C \\ A \leftrightarrow D \\ B \leftrightarrow C \\ B \leftrightarrow D \\ C \leftrightarrow D \\ D \leftrightarrow E \\ E \leftrightarrow F \\ E \leftrightarrow G \\ F \leftrightarrow G$$

thanks for your time.