Do you mean you want to know the degree of certain nodes/proteins in the graph ? If so, download the protein-protein interaction file then use a script to find and count all interactions containing your proteins of interest or use a software (e.g. cytoscape) or library (e.g. igraph) to get a table with the degree of all nodes then filter this table to retain only proteins you're interested in.

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If I understand correctly your question, you can use the multiple proteins input tool from stringDB.