What does "lines vector file" refer to ? 

refers to vector data, that you can create, modify and so on with a GIS, and what I was wondering was if there's the possibility to deal with a graph at the same way than with a vector file.

If I understand correctly what GIS is, it seems like your dataset is a set of Euclidian vectors. Therefore your dataset somehow 'corresponds' to a planar graph where nodes correspond to the intersection of (at least) two vectors and edges connects any two nodes that belong to (at least) one same vector. Also edges could have weight that would represent the corresponding euclidean distance in the plane. You can also take a look at "embedding planar graph in 2-dimensional euclidean space" if you need more precise information.

However, any graph cannot be embedded into a 2-dimensional euclidean space if that was your second question. For this particular point you can have a look to "minor exclusion" and to particular graphs called K_5 and K_{3,3} that are respectively a clique of 5 nodes and a bipartite graph of 3x3 nodes.

These can be found on Wikipedia: 

Dear Annalisa,

Haider Al-Ani is right. Else you may create a .JPG (or other image/raster) of the graph and link it with an attribute in the attribute table. This is how you may display the graph along with the GIS data.

I hope, you find it useful.

P.K. Litoria

well, in fact, a graph is a vector of lines, but not vice versa!

 Ciao

Thanks all for the explainations, my initial doubt was confirmed in the end by Gabriele.. in fact I totally agree with you. Thanks Christian for the wide explaination/documentation about graphs, I'm quite new to the graph concept so I'll have a look at them. Thank you too Haider and Pradeep Kumar - I had no idea that a graph is intended as origin as a raster file - ant it seems quite crazy for me, since from the very first time I saw a graph I thought "oh, what a nice vector file!" is it really true? the graphs produced by the greater part of graph-softwares are images (=raster)? in an optic of "data treatment" seems quite unreasonable to me. ps. yes, my "graph" has coordinates and attribute table as well.. so it is, in the end, a vector file :)