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A bus topology was one of the first topologies used in that it consists of a single bus (aka: backbone). Typically this is a coaxial cable where nodes can connect via a T' connector which allows the bus to continue to the end of the cable. Due to the nature of this design when the data reaches the end of the cable if it's not properly terminated (which kills the signal) then we can receive what's called bounce back. This ricocheting of the data could severely hinder the communication pathing of the bus. As I recall there is a general rule of thumb for a bus topology which is the rule of 5-4-3-2-1. This means that you can have 5 data segments of which there can be 4 connectors (continuing connections) which link the 5 data segments. 3 of the segments must be populated. There must be 2 terminators on the bus (1 at each end of the cable) and 1 network connection out.
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A ring topology is similar to a bus topology except that the bus is in the form of a circle and every node on the ring can only connect to the neighboring node. There is no beginning and no end to a ring topology which gives it its name of ring topology. Since every device on the ring can only talk to its immediate neighboring node on the ring if that neighboring node is offline or cannot communicate then there is a break in the ring and data basically comes to a stop. A ring topology is also known as a token-ring which means that there is a token which is passed from node to node. A node can only put information on the ring if it has the token. Once a node places data on the ring and it's done sending the data then it passes the token on to the next node. It is possible for there to be multiple tokens flying around on the network at one time. Ring topologies can carry large payloads of data.
The last topology which seems to be more prevalent in today's small, medium and large network configurations is a Star topology. A star topology is where a group of computer nodes connect directly to a central point on the network. This central point can be a hub, switch, or a router. By this type of connection it creates an image of a star. A good point to this type of setup is that each computer is on its own hardware segment of the network. If something fails it's fairly easy to troubleshoot and the fault doesn't usually take down the entire network. This is true unless the central point of the network such as the hub, switch or router itself fails. In a star topology, many times there are multiple star segments which hang off of each other. This way it creates a form of a star but also a tree type effect of the smaller star networks. Hubs usually connect up to the switches and the switches usually connect up to other switches which connect to routers which join networks together.
Ethernet is the medium which connects computers together in a local area network configuration. Ethernet allows computers to communicate at the MAC address layers per the 7 layers of the OSI model. Ethernet uses twisted pair cabling (sometimes shielded) for the faster data transfer rates. Ethernet can carry bandwidths typically of 10/100 Base T and lately has been able to go upwards of 1000BaseT. Ethernet has grown to be the primary forms of linking computers in a LAN since 1990's. This is true over Token ring, FDDI, and ARCNET. (Wikipedia)
Token Ring is very similar to ring topologies in that every node on the network can only talk to the neighboring node directly next to it. This again is by the token being passed from one node to another. A draw back to Token Ring networks are the possibility of a broken network for a down server and the write access to the ring can only be granted if you have the token.
Fiber distributed data interface (aka: FDDI) is of the ring family of networking. Instead of the ring being made of copper wire it's made of fiber optics strands. Again each node talks directly to the neighboring nodes but unlike the copper lines of ring topologies. In a FDDI configuration each node has a smart link in that if the network node (aka computer, server, and workstation) is offline for any reason then it directs the data back around onto the other link. This is done by there being 2 actual rings in a FDDI configuration. So if one link goes down then ring A routes to Ring B and head back in the opposite direction. These 2 rings oppose each other in the direction of data flow.
A new comer to the world of networking is wireless connections. Wireless connections follow a general connection process much like the star topology. Only there is no actual hard connections from the central point to the remote network nodes. Instead the wireless network uses what's called an access point instead of a hub or switch. Remote nodes can link up to the wireless access point which would create a LAN situation. From the wireless access point it maybe connected to the rest of the corporate LAN via a hard LAN cable connection. There are different connection bandwidths and speed in the wireless networking configuration which vary from 11Mb/sec (802.11b) to 54Mb/sec (802.11g) and now we are starting to see upwards of 108Mb/sec which is basically 2 chipsets of the 802.11g tied together. Range and distance come into effect for wireless connection points.