Figure 2.

The formation of triangles in a multilayer network. On the right side of the figure are two rows of triangles, each representing one case. For the first case, the sides of the triangle are made up of two layers. Taking nodes A, B, and C as examples, node B and node C in layer 1 belong to the neighbor nodes of node A, but there is no connecting edge between node B and node C. The connection edge between them is detected in layer 2. In this case, the nodes A, B, and C form a closed triangle in the multilayer network. A similar phenomenon can be observed for other triangles of the first type. In the second case, the sides of the triangle span three different layers. Taking nodes B, D, and E as an example, nodes B and D are connected at layer 1 but not at other layers, nodes B and E are connected at layer 2 but not at other layers, and nodes D and E are connected at layer 3 but not at other layers. In this case, the nodes B, D, and E form a closed triangle in the multilayer network. A similar phenomenon can be observed for other triangles of the second type.