Illustration of pairwise vs partial correlation networks.

Thicker edges represent stronger absolute correlations. Left: true network of partial correlations (blue), with 8 connections, no triangles. Middle: associated pairwise correlation network, with erroneous direct connections (red) that form 84 triangles. Right: pruned network of 8 strongest pairwise correlations, with two isolated nodes (yellow) and two erroneous connections (red) that form 2 triangles (2-3-8 and 3-7-8). Comparing the true partial correlation network on the left with the pruned pairwise correlation network on the right, which consists of the same number of edges as the underlying network, three differences stand out. Firstly, indirect connections may appear as direct connections (i.e., nodes 2–8 and nodes 3–7). This results in an excessive number of triangles, affecting network measures such as small-worldness. Secondly, while the true network is connected (i.e., there exists a path between each pair of nodes), pruned pairwise correlation networks tend to consist of isolated (groups of) nodes (i.e., nodes 1 and 9). Thirdly, the number of connections of a node may differ from the true number of connections (e.g., node 3 has four instead of three edges). In larger networks, hub nodes may emerge erroneously.