You can open a netlink socket and send route update messages. There is an article about how to do this.
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You can also run "strace route add ..." to see how the route command does it.
On my system, it uses ioctl with SIOCADDRT. A little searching turns up some
sample code.
Oddly, the best documentation I have found is from IBM's AS400 man pages.
If you just want to read the routing table, you can open and read /proc/net/route. (Again,
strace shows that this is how the route command does it.) The hex numbers are 32-bit IP addresses in machine-endian form. Try
cat /proc/net/route.
