Motif Discovery in Bipartite networks using Cytoscape
I have recently develop an R package (sorry not a Cytoscape solution) to deal with this kind of situations of something grouping other elements, like pathways and genes.
The package is based on GSEABase of Bioconductor to store this relationships. Basically you should store a gene set for each TF and genes it is linked. I would recommend to use the name of the TF as the name of the gene set and then create a GeneSetCollection to be able to use the package.

The package provides with functionalities that allow you to calculate the distribution of genes per gene set (using genesPerPathway), as well as, pathwaysPerGene to know in how many other TF regulate each gene. 

I am not sure of the biological inference you can take from this (I designed the package to test this) but you can also see if there is some specific preference for the TF to link to genes which are also regulated by other TF. This could be done by looking at the conditional probability (condPerPathways or sizesPerPathway).
Sorry the manual pages don't have examples and the vignettes are incomplete yet. 

Also you could use the package tidygraph to calculate the centrality of the TF or of the genes you want.