I write tools that do it by pulling all types of info via SNMP. Anything from list of VLANs, STP info, CDP info, port characteristics, optical db loss levels, routing tables, etc. Dump info into a SQL database. Some things such as list of vlans and there descriptions (and relative root bridges) can easily just be displayed via a webpage table. Other things, such as the physical connectivity between devices, I use HTML5 canvas javascript API (e.g.: http://gojs.net/latest/samples/index.html) to draw the node relationships using CDP data I pulled.
If you do it yourself, you can automate it exactly as you like. It's also free.
If you have the time and/or motivation, try running through the lessons on HTML, CSS and Javascript on this site W3School. It's a pretty good site to give you the basics, and none of it requires more than notepad and a browser. Once you're comfortable, you can move onto things like this or even these
You'll find this data type more often referred to as a 'directed graph', so if you substitute this term for 'tree', you'll likely find more matches for the techniques you're looking for.
Angular contains nothing that will directly help you build a visualization of a directed graph. And in fact libraries like d3 are best suited for generating these visualizations. [1]
Angular can help you build the framework around it, for example if you wish to update the data source regularly, or provide the user methods to modify the graph's layout or styles.
There also exists d3 'meta-libraries' that provide easy to use interfaces for basic d3 charts[2]. To integrate a chart like this with Angular, create a directive that uses a data service to pass options and data to a d3 chart.
[1] That's not to say some have tried - here's a tutorial on replacing some d3 charts with angular+svg: http://alexandros.resin.io/angular-d3-svg/
[2] This is a particularly nice one: http://gojs.net/latest/index.html
You have 0 JS exp and want to do diagrams? Ok, this isn't going to teach you much about javascript. It will teach you how to use a javascript library.
To answer your question, yes that looks like it does what you want. The decision tree (expanded) might be closer to what you want though.
http://gojs.net/latest/samples/decisionTree.html
or entity relationship : http://gojs.net/latest/samples/entityRelationship.html