communication with router

If you're looking for something built-in or an easy way to do this, then the short answer would be: No.

Every router is different and what you can do depends on what you're exporting as well. For instance there's differences in what you can do with an AIR executable versus a SWF embedded in a webpage.

Also each router is different and almost every one offers a https entry point and more top end units can support tcp as well.

Flash has TCP and UDP sockets. If you know your way around sending valid requests and handling responses to a HTTP server then depending on the types of protocols used by the routers HTTP or TCP interfaces you have a small shot at working your way through the requests necessary to pretend you're a browser or directly interface over sockets with its API.