Snmp
 

How to know the status of network using snmp commands in linux

Your question is far too broad. Are you trying to monitor a switch, router, or another machine? Are you doing passive monitoring, or would you like to receive traps when certain events happen. I haven't played around with it much, but MRTG has a number of pre-rolled scripts for monitoring network bandwidth on various devices.

I agree with btmiller though I have recently come across (and finally got going), 'nagios' which can be used to monitor servers, printers, routers, modems etc. I'm really impressed with the kind of info it reports and to monitor bandwidth in a router/modem, you'll also need to install MRTG. Both packages should be easily installable depending on what distro you have.

some other items to look at.

netsnmp - tools relating to the Simple Network Management Protocol
rrdtool - RRDtool as a reimplementation of MRTGs graphing and logging features.
Cacti -RRD Front-end

NMS packages similar to Nagios.
openNMS
Zenoss
Zabbix
Hyperic

Also you might look at Zenoss though i really hated it. flashy on the front end but behind, its a total buff :p