what do I need to use for protein protein interaction network
If you are asking solely about data structure, the two data formats that you have given are essentially the same. Each row represents a PPI, so in a network a line (edge) will link the proteins (nodes) given in columns one and two. Column three is an edge score, but it can indicate a few things,  confidence in the interaction or strength of the interaction. Your network will for a single central node with 5 nodes linked to it in a wheel shape.

PPI networks may also be represented in Proteomics Standards Initiative Molecular Interaction XML Format. This provides a controlled vocabulary for programmatic access to data. 

The choice of data structure, there are many, is yours but simple formats (as above) are often sufficient. It is important to be mindful of the meaning of the network, are the PPIs directional? Do you have estimates of interaction (edge) confidence? Do you have estimates of interaction (edge) strength?

Cytoscape will allow you to visualise a protein-protein interaction network (PPI) such as the two that you have given. The Bioconductor project provides a number of options for the visualisation and analysis of PPI networks in R. 

If you want to create or build a PPI network from a single protein or list of proteins then Cytoscape, and possibly plugins such as Genemania, can also do that.

String is also useful for building PPI networks. The developers have focussed on a wide-range of species and their data export options will allow you to see the same network in a variety of data formats.