Topology refers to the way in which the network of computers is connected. Each topology is suited to specific tasks and has its own advantages and disadvantages.

Network topologies are categorized into the following basic types:

* bus
* ring
* star
* tree
* mesh

The choice of topology is dependent upon

* type and number of equipment being used
* planned applications and rate of data transfers
* required response times
* cost

Ethernet bus topologies are relatively easy to install and don't require much cabling compared to the alternatives. 10Base-2 ('ThinNet') and 10Base-5 ('ThickNet') both were popular Ethernet cabling options many years ago for bus topologies. However, bus networks work best with a limited number of devices. If more than a few dozen computers are added to a network bus, performance problems will likely result. In addition, if the backbone cable fails, the entire network effectively becomes unusable.

In a ring network, every device has exactly two neighbors for communication purposes. All messages travel through a ring in the same direction (either 'clockwise' or 'counterclockwise'). A failure in any cable or device breaks the loop and can take down the entire network.

To implement a ring network, one typically uses FDDI, SONET, or Token Ring technology. Ring topologies are found in some office buildings or school campuses.

star network features a central connection point called a 'hub' that may be a hub, switch or router. Devices typically connect to the hub with Unshielded Twisted Pair (UTP) Ethernet.

Compared to the bus topology, a star network generally requires more cable, but a failure in any star network cable will only take down one computer's network access and not the entire LAN. (If the hub fails, however, the entire network also fails.)

Tree topologies integrate multiple star topologies together onto a bus. In its simplest form, only hub devices connect directly to the tree bus, and each hub functions as the 'root' of a tree of devices. This bus/star hybrid approach supports future expandability of the network much better than a bus (limited in the number of devices due to the broadcast traffic it generates) or a star (limited by the number of hub connection points) alone.

Mesh topologies involve the concept of routes. Unlike each of the previous topologies, messages sent on a mesh network can take any of several possible paths from source to destination. (Recall that even in a ring, although two cable paths exist, messages can only travel in one direction.) Some WANs, most notably the Internet, employ mesh routing.

Mesh topologies involve the concept of routes. Unlike each of the previous topologies, messages sent on a mesh network can take any of several possible paths from source to destination. (Recall that even in a ring, although two cable paths exist, messages can only travel in one direction.) Some WANs, most notably the Internet, employ mesh routing.

Source: about.com

For more information about topologies check out this articles:

http://en.wikipedia.org/wiki/Network_topology
http://www.webopedia.com/quick_ref/topologies.asp
http://www.homenethelp.com/network/

For a comparison between wired and wireless LAN go to this article here.