How do I get the adjacency matrix from gene similarity network? I am exploring application of Graph convolution network on gene similarity network. I am trying to explore
genemania.org and https://string-db.org/

Please let me know where can I find the data for my research in gene interaction network, which allows me to download the data in the form of an adjacency matrix.
The STRING download page is here. I am not sure that they provide any data in the form of an adjacency matrix, as the number of nodes (rows/columns) would be quite large, and for this reason they are likely to represent the data as lists of links, for compactness. 

Their data will likely have to be cleaned for any purpose you are interested in. You will have to make some decisions on how to filter the data. For example, as suggested in the comments, you may want to filter on the quality of the evidence supporting interactions, or based on species of the protein, or other things.

It's possible that you may have better luck going with another database that has done some of these steps already. For example, there are relatively compact human interactome datasets here, or yeast interactome datasets here. In this case you will still need to convert from a list of links to an adjacency matrix, however this is not very difficult if you can use a scripting language. 

Notably, you may have to figure out how to distinguish missing data from tested non-interactions in these cases (or decide that missing data is ok). In most cases people will not have exhaustively tested every cell of the all-by-all interactome adjacency matrix.

Hope that helps.