Also, do consider using a heatmap for visualising the fold-change values. For example the ggplot package in R does this, though there may be Cytoscape modules available if you definitely want to present your data as a network.
That figure looks like something made by IPA network explorer. It will look up all of your genes/molecules and assign different shapes based on known function (receptor/kinase/etc). You will need a license to use this software, if you want a free alternative you can use Cytoscape. Both software have a bit of a learning curve. What IPA can do is show all up regulated genes in one color (such as green) and all down regulated genes in another color (often red) and form connections between genes based on literature, it is often useful for hypothesis generation after a genome wide expression study. This is an example