There are a few different topology types used. Which type is used depends on what the computer network is being used for as well as how old the network is. For example, your cable company uses a different topology than your phone company to provide Internet service. The most predominant network topology in the 1970s was different than the topologies used today. Each topology provides advantages and disadvantages from the others. The purpose of this post is to give you a general overview of each topology. For the most part, if you are concern about which topology to use at your house, don’t be. You have only one practical choice to pick, anyways
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The most redundant, reliable but least scalable topology is called a mesh topology. The idea in a mesh topology is that every computer is connected to every other computer on your network. If you have six computers, computer 1 has a cable for computer 2, another cable for computer 3… so on and so on. If every computer has a cable for every other computer, this is called a full mesh. If there is a mesh that does not have all cables for all computers, this is called a partial mesh. If computer 1 does not have a cable for computer 3, but there is a cable from computer 1 to computer 2 and from computer 2 to computer 3, computer 1 has to go through computer 2 to communicate with computer 3.

Partial Mesh. Even though there is not a cable between every other computer, there is still some redundancy.
The advantage of meshes is that there is no central point that will take down the network. If the line from computer 1 to computer 5 goes down, traffic can be rerouted through any of the other computers in order for computer 1 and computer 5 to communicate. However, if you add a computer to a network with 7 computers in order to make 8, you will need to run 7 cables to add the computer in a full mesh topology. This is expensive and not convenient at all. Another advantage is performance. Think about it. In a full mesh, when one computer talks to another computer, they communicate on a cable directly connected to each other (does not have to go through another device) on a dedicated line (not shared with other devices.) Mesh networks (at least today) are not commonly used to create LANs, but are used in WANs (such as the Internet) in order to connect switches together.
Token ring (ring topology) is another topology. The purpose of a ring topology is to connect computers together in a circle, like a ring. A token is then passed along from one computer to the next in the circle. Along with the token is the data that is being sent over the network. When a computer has the token, it has control of the network. It reads the data to see if any of the data is for that computer. Then, it transmits the data it wants to send, any of the data that was attended for another computer, along with the token to the next computer.
An advantage of token rings is that there are no collisions (explained later.) This also means that when another computer is connected to the network, the performance degrades ‘gracefully.’ A disadvantage of token ring is if a computer is down, the computer can alter the whole entire network. And, what if a computer is connected to two computers that are both down? This can be a problem… To overcome this, a hub can be used in a ring topology. Using a hub, all the computers are connected to a central point. The token is still passed from one computer to the next. However, if a computer goes down, the hub can bypass the port of the down computer and go on to the next computer.
FDDI (Fiber Distributed Data Interface) is a type of ring topology. Computers using FDDI is connected together in two rings instead of one, using fiber optic cables. The advantage FDDI has over a normal token ring is that since there are two rings, one ring can be used as a backup if the other ring goes down.
Spanding-Tree is another topology used for switches and bridges. The devices are connected in a tree-like structure. Usually, you would have a device on top of the tree, with everything spanding underneath it. For example, device A is at the top connected to device B and device C. Device D and E are on device B, while device F and G are on device C. Confusing? Absolutely. In order to prevent loops or sending data to dead-ends due to device failure, the devices need to communicate with each other. They use a layer 2 protocol called STP (Spanding-Tree Protocol). Since you will not worry about this at home, I will not say anything else about this topology. If you really want more spanding-tree, you can find more information here.
The most popular topology out there is called Ethernet. Ethernet is so popular because it is cheap, it supports many cable (and wireless) mediums and it is easy to implement. The difference between Ethernet and all the other topologies is every device shares the same medium. This is a problem because collisions can occur. A collision is when more than one device transmits at the same time over the same medium, causing data corruption. A section on your network where a collision can occur is called a collision domain.
To address the problems of collisions, Ethernet uses a layer 2 protocol called CSMA/CD (Carrier Sense Multiple Access with Collision Detection). Using this protocol, a device listens to the medium to see if the medium is free before transmitting the data. Even though a device checks first before transmitting, it is still possible for two devices to transmit at the same time, thus causing a collision. Thankfully, it is very easy to detect a collision. If two devices transmit at the same time, the voltage on the cable will double to what it is supposed to be. When a collision is detected, all devices in the collision will keep on transmitting the data a few more moments in order to make sure that every device on the medium has a chance to detect it. Then, every device generates a random number to countdown from. When the first device reaches its countdown timer, it starts to retransmit. Because of collisions, Ethernet networks degrade exponentially. This means that adding another device on the network dramatically slows the network down. However, with 100MB or gigabit transmission speeds, Ethernet can still be very, very fast with a lot of devices connected to it.

Bus Topology. The thicker line is the backbone cable. The red lines represent terminators. Blue circles are the devices.
There are two ways to wire an Ethernet network. The old legacy way to wire Ethernet is a bus topology. First, you would start with one coaxial cable. This cable is usually referred to as the backbone. Each end of the cable is not connected to anything. A problem with this is that data can reach to the end of the cable and then bounce back. So, a terminator is connected to each end of the cable in order to absorb the signal. Then, each device is connected to the backbone cable with its own cable. In order to connect the cables to the backbone, the backbone is punctured with the cable connected to the device. Usually, the backbone uses thicknet and the cables that connect the devices to the backbone uses thinnet.
The bus topology concept is used to deliver almost every utility to your house (all except LAN line.) Your water, sewer, gas, electric and cable is all bused to your house. The backbone cable and everything connected to it is all part of the same collision domain. A bridge can be used to divide the backbone into two, thus dividing the collision domain into two. A bridge can also be used to connect two different topologies together, such as a token ring and a bus topology. A disadvantage of bus is if the backbone cable fails, the network fails.
Star is another Ethernet topology. In a star topology, all devices connect to a central point. The central point can be a hub, switch or router. Multiple central points can then be connected together. For example, a hub might go to a router, which then can go to another hub. This is called an extended star topology. Even though star and extended star is the most common topology used today, it has one big flaw: if the point fails, the whole network fails!

Extended Star. In this diagram, the three red circles are the center points. The blue circles are the devices.
Hubs are layer 1 devices. They only connect devices together. They do not make any intelligent decisions. So, collisions can still occur in a star topology when hubs are used. A switch is considered a multi-port bridge. A switch will learn every devices’ MAC addresses that is attached to it. Then, a circuit is created in transmission for the source and destination. Because of this, devices are given their own designated line to transmit on, eliminating collisions. This is called micro segmentation.
There is a topology hybrid that combines the use of using a token along with connecting everything in a bus or a star. This is called ARCnet (Attached Resource Computer Network). The advantage of ARCnet is that there are no collisions. This means that an ARCnet network does not degrade greatly when more devices are added to the network. Segment sizes (data chunks) are also bigger on an ARCnet, compared to Ethernet. However, the disadvantage in ARCnet is that only one computer can transmit on the network at any time and must wait for the token in order to start transmitting. This gives ARCnet slower initialization than Ethernet. ARCnet was very popular as a LAN network back in the 1980s, mostly because the cost of ARCnet network cards were much cheaper than Ethernet network cards. However, with faster bandwidth, micro segmentation using switches along with much cheaper costs nowadays, Ethernet is the more dominant choice over ARCnet (or any other topology, for that matter.)
Most home networks nowadays use a combination of wired and wireless Ethernet in a star topology. Wireless networks, as far as computer networks are concerned, usually use the star or extended star topology. The device used at home are wireless routers. Routers will be explained in another post. Another device used is an access point. An access point gets connected to a port on a router, hub or switch in order to create a wireless access point for the network. Access points are considered a layer 2 device because data gets forward from one wireless device to another wireless device based on MAC addressing, just like a switch.
Out of all the different topologies, Ethernet definitely won the race. That is, to set up a LAN. However, the Internet uses a more reliable redundant option, such as spanding-tree and mesh.
Resources
http://learn-networking.com/network-design/a-guide-to-network-topology
http://www.datacottage.com/nch/troperation.htm
http://www.cisco.com/en/US/tech/tk389/tk621/technologies_tech_note09186a0080094797.shtml
http://ecommercetechnology.org/english/data/57.htm
http://area72.ro/general-it/the-bus-topology.html
http://www.arcnet.com/
http://wiki.answers.com/Q/What_is_ARCnet
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