commonly used are traceroute, ping, etc. maybe you even use nmap. But why not SSH?
$ ssh-keyscan 127.0.0.1 192.168.10.10 192.168.10.15 2>/dev/null 127.0.0.1 ssh-rsa AAAAB3NzaC1yc2EAAAABIwAAAIEAwSbacjbHnvKV9 192.168.10.10 ssh-rsa AAAAB3NzaC1yc2EAAAADAQABAAABAQDxZpTiS+QVMfhfyVbBBvN/mXDQ 192.168.10.15 ssh-rsa AAAAB3NzaC1yc2EAAAADAQABAAABAQDxZpTiS+QVMfhfyVbBBvN/mXDQ
=> this means that those last 2 IP's are running on the same server!