A simple illustration of the extraction of the k -clique-communities at k = 4 using the clique-clique overlap matrix. Top left picture shows the graph in which the different cliques are marked by different colors. The according clique-clique overlap matrix is shown in the top right corner. To obtain the k-clique-communities at k = 4, algorithm CPM delete the off-diagonal elements that are smaller than 3 and also the diagonal elements that are smaller than 4, resulting in the matrix shown in the bottom left of the figure. The connected components (the k-clique-communities) corresponding to this matrix are shown in the bottom right.