how to monitor the network on node.js similar to chrome/firefox developer tools?

Use external HTTP Debugging tool. Your options include:

• node-http-proxy as seen in How do I use node.js http-proxy for logging HTTP traffic in a computer?
• middlefiddle written in node.js (but abandoned for 3 years now) https://github.com/mdp/middlefiddle
• mitmproxy - a CLI tool http://mitmproxy.org
• fiddler http://www.telerik.com/fiddler
• and many more - https://www.google.pl/search?q=HTTP+debugger

You fire up one of those, tell them where to route the traffic, and point your application at that debugging proxy instead of the real server.

If you only need to see URLs of outgoing traffic and what caused it, You can use debugging-aid

npm i -D debugging-aidnode --require debugging-aid/network app.js 

Resulting console output may look like this:

[aid] network, outgoing  to: http://example.com/ stack:     at Agent.createSocket (_http_agent.js:234:26)    at Agent.addRequest (_http_agent.js:193:10)    at new ClientRequest (_http_client.js:277:16)    at Object.request (http.js:44:10)    at Request.start (myapp-path/node_modules/request/request.js:751:32)    at Request.end (myapp-path/node_modules/request/request.js:1511:10)[aid] network, outgoing  to: http://example.com/ stack:     at Agent.createSocket (_http_agent.js:234:26)    at Agent.addRequest (_http_agent.js:193:10)    at new ClientRequest (_http_client.js:277:16)    at Object.request (http.js:44:10)    at get (myapp-path/node_modules/got/source/request-as-event-emitter.js:234:22)    at Immediate.<anonymous> (myapp-path/node_modules/got/source/request-as-event-emitter.js:305:10)

Disclaimer:

I'm the author of debugging-aid
This answer was written when debugging-aid was on version 0.2.1

I came to this question looking for something similar but I'm using the request package. In this case all you need to do is include this line in your code:

require('request-debug')(request);

(make sure request-debug package is installed)

This will print all the request data to the console.