To investigate genes through a network based approach you can use several tools. I don't know which level of programming you have or which tool you prefer but here is a brief overview of the possibilities you have.
You can look into established databases containing information about interactions like, for instance, STRING. Or, you can build networks using the wgcna method with R.
Then, once you have your network you can analyse its properties and here you also have several tools available such as standalone, java-base software like cytoscape, R libraries such as igraph, python libraries such as networkX online tools like centiserver...
Also you can perform gene set enrichment analsysis, which means adding a further layer of biological information to you set of genes like metabolic pathways (from KEGG, for example) and molecular functions (from GeneOntology, for instance) (gsea) as here, here, and here.
Here there is also a nice tutorial about network analysis with R.