What in the heck is a linux network?
A network using only linux devices?
OpenLDAP provides a single user account system for multiple *nix machines, and when paired with Samba, can also extend to Windows machines the same as Active Directory (Since they are both based on x509 DAP). You only need it if you want centralized auth.
You can make a router using Linux (if you REALLY just mean ROUTER), use iptables for the firewall. Or just use pfSense (FreeBSD-based router distro with all the hard work already done). pfSense includes ability to use Snort for network intrusion detection. Or put Snort on linux.
An NFS server would be the file server for other *nix machines. Again paired with Samba, provide SMB file sharing for Windows. Or FreeNAS (a pre-rolled FreeBSD file server with ZFS capabilities). Or OpenFiler (A pre-rolled Linux file server.)
BIND for DNS. Samba for WINS.
Apache or nginx for web.
Nagios for monitoring.
NTPd for a time server.
DHCPd for ... uh... dhcp services.
SpamAssassin for mail filtering.
Postfix...Dovecot...Sendmail for MTA and MUA.
And the thing is, none of this makes something a "linux network". These just provide services to the network that already exists.
And the best part is, you could have this all on one machine. And more.