No, nothing like that.
I got a router, the neighbors on each side have the password to it.
Some routers allow you to enable a "Guest" mode (as illustrated in the
Linksys example). This Guest mode is intended to keep guests off your local network, but still allow them to access the internet through your router/gateway. This separation is intended to help protect your computer(s) from sniffing-attacks and man-in-the-middle attacks.
If you have this type of feature, then I would recommend that you change your primary network's password and don't share it with anyone. Then also set-up the guest-network and share its password with only trusted neighbors as you wish. If your router doesn't have this type of feature, then you might want to get one that does have it. (Of course, to avoid the risks of wireless networks, you can also connect your computer to your router using an Ethernet cable, and turn off your computer's wireless NIC, and just use the wired NIC.)
There are other steps you can take to secure your wireless router--turn off the SSID broadcast, disallow admin-password changes except from local wired connections, use a long complex passphrase, allow only known MAC addresses (you would need to get your neighbor's and add them to the list). Some routers are dual-band a/b/g/n/ac. If yours is, you could put a passphrase on the b/g/n (2.4 GHz) that's different from the a/n (5 GHz).
The above steps help secure your computer's outer-perimeter (i.e. your network). To help secure your computer itself, be sure to keep the updates/patches current, and use a reputable security-suite that protects in multiple-ways, as anti-virus, and firewall, etc. for complete protection. Also, only install software you trust and that you have directly downloaded from a trusted source.
Hope this helps,
