Multilayer Graphs

A multilayer graph consists of multiple layers and is represented by a supra-adjacency matrix, where the off-diagonal matrices are the connections between layers (inter-layer) and the diagonal matrices are the intra-layer matrices containing the connections of the corresponding layer.

There are different types of multilayer graphs and they can be, like to the single-layer graphs, weighted or binary, and directed or undirected.

A visual representation of the different multilayer graph types available in BRAPH 2 is shown below:


A multiplex graph is a type of multilayer graph where only interlayer edges are allowed between homologous nodes. In this case, the layers follow a categorical architecture, which means that all layers are interconnected.

Ordered Multiplex

An ordered multiplex is a type of multiplex graph that consists of a sequence of layers with ordinal edges between corresponding nodes in subsequent layers.


A multilayer network allows connections between any nodes across the multiple layers, where all layers are interconnected following a categorical fashion.

Ordered Multilayer

An ordered multilayer consists of a sequence of layers with ordinal edges between any nodes in subsequent layers.