# Also in the Article

Multiplex network and clustering algorithm
This protocol is extracted from research article:
Multiplex gene and phenotype network to characterize shared genetic pathways of epilepsy and autism
Sci Rep, Jan 13, 2021;

Procedure

The multiplex network represents a multilayer network where the same nodes exist in each layer; the network encodes both the PPI relationships and phenotype relationships between the genes in the network. The gene-PPI-phenotype multiplex network was created by stacking the PPI network and gene-phenotype network layers, generated as detailed in the previous sections, such that each node in one layer is connected to itself in the other layer.

The Louvain algorithm is a modularity maximization approach that is commonly used to detect modules in a network and has been shown to perform well on biological networks68. For the individual PPI and phenotype layers, the Louvain algorithm was used to maximize the modularity, H, defined by:

Here, $ec$ is the total number of edges in community $c$, $m$ is the total number of edges in the network, and $Kc$ is the sum of the degree of the nodes in community $c$. To maximize modularity, which the Louvain algorithm is useful for, then is to maximize the difference between the actual number of edges and the expected number of edges in a community. In the equation, $γ$, is the resolution parameter which controls the size of the communities. The Louvain algorithm was applied 1000 times with different random seeds at a range of resolutions and the partition with the globally optimal modularity was chosen (Fig. S3). The Louvain algorithm can be easily extended to be applicable to a multiplex network. In this case the overall modularity, which the algorithm will try to maximize, is the sum of the modularity of each layer weighted by some constant:

We set both layers to have equal weights in order to have equal contribution from the PPI and phenotype layers. The louvain-igraph Python package was used to run the Louvain algorithm (https://louvain-igraph.readthedocs.io/).

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# Also in the Article

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