PPI-Network igraph for tissue-specific data

I am new to bioinformatics in general and would really appreciate some help with the project Im working on.

My data of protein-protein interactions is constructed in a table (stored in MySQL) with binary information about tissue-specificity. Now I am trying to create an undirected graph with igraph in R, but could not understand what type of data structure I should use without losing the tissue-information (Adjacency matrix, edge list…).

Thank you in advance!