By default all your graphs and data are private and only visible to you.
If you would like to share them (via a URL) or embed (adding an interactive graph to another site), you will have to make the public first.
In order to do that, open your graph and then click on the share icon in the left menu:
Once you do that, the graph will reload and you’ll see:
A URL link to share the graph (selected on the image below)
A field with an embed code (copy and paste it into the code of your blog or a website).
If you want to make the graph private again, click that share button again.
Of course, you can also share your graph as a picture or as a .gexf file (for further processing in Gephi or other software like Pajek or Python NetworkX tools).
Learn how to do that in this article: