Planar Maximally Filtered Graphs (PMFG) are an important tool for filtering the most relevant information from correlation based networks such as stockmarket networks. One of themain characteristics of a PMFG is the number of its 3and 4-cliques. Recently in a few high impact papers it was stated that, based on heuristic evidence, the maximum number of 3and 4-cliques that can exist in a PMFGwith n vertices is 3n−8 and n−4 respectively. In this paper, we prove that this is indeed the case. © 2014 Elsevier B.V. All rights reserved.