Are there any way/software to construct network with nodes and edges - (Apr/22/2020 )

Dear All, 

I am searching for a software or tool to construct a network of several nodes (variable) and edges (links) connecting them. Importantly I want this tool to give a weight for the edges meaning that edge length is corresponding to distance between nodes, so more length = more distance 

Please advice 

If you meant to build a tree you can try this website, though it's not really maintained and a bit slow: http://evolution.genetics.washington.edu/phylip/software.html

and as you already mentioned R surely has this possibility, but I'm not familiar with sophisticated graphics there. But you can find many forums specialised on help for R and helping with code etc.