Network topology is the layout of the connections (links, nodes, etc.) of a computer network.

There are two main

The names used - such as ring or star -  are only rough descriptions. The computers on a home network can be arranged in a circle but it does not necessarily mean that it represents a ring network.

Basic topology types 
There are seven basic topologies:
 Point-to-point topology
 Bus (point) topology
 Star topology
 Ring topology
 Tree topology
 Full/partial Mesh topology
 Hybrid topology

Which of these is chosen depends on what devices need to be connected, how reliable it has to be, and the cost associated with cabling.

Physical topology
The shape of the cabling layout used to link devices is called the physical topology of the network. This refers to how the cables are laid out to connect many computers to one network. The physical topology you choose for your network depends on:
 Office Layout
 Troubleshooting Techniques
 Cost of Installation
 Type of cable used

Types of Physical topologies
The mapping of the nodes of the network and the physical connections between them – the layout of wiring, cables, the locations of nodes, and the interconnections between the nodes and the cabling or wiring system.

Point-to-point
The simplest topology is a permanent link between two endpoints (the line in the illustration above). Switched point-to-point topologies are the basic model of conventional telephony.  The value of a permanent point-to-point network is the value of guaranteed, or nearly so, communications between the two endpoints. The value of an on-demand point-to-point connection is proportional to the number of potential pairs of subscribers, and has been expressed as Metcalfe's Law.

Permanent (dedicated)
Easiest to understand, of the variations of point-to-point topology, is a point-to-point communications channel that appears, to the user, to be permanently associated with the two endpoints. A children's "tin-can telephone" is one example, with a microphone to a single public address speaker is another. These are examples of physical dedicated channels.

Within many switched telecommunications systems, it is possible to establish a permanent circuit. One example might be a telephone in the lobby of a public building, which is programmed to ring only the number of a telephone dispatcher. "Nailing down" a switched connection saves the cost of running a physical circuit between the two points. The resources in such a connection can be released when no longer needed, for example, a television circuit from a parade route back to the studio.

Switched:
Using circuit-switching or packet-switching technologies, a point-to-point circuit can be set up dynamically, and dropped when no longer needed. This is the basic mode of conventional telephony.

Bus

In local area networks where bus topology is used, each machine is connected to a single cable. Each computer or server is connected to the single bus cable through some kind of connector.  A terminator is required at each end of the bus cable to prevent the signal from bouncing back and forth on the bus cable. A signal from the source travels in both directions to all machines connected on the bus cable until it finds the MAC address or IP address on the network that is the intended recipient. If the machine address does not match the intended address for the data, the machine ignores the data. Alternatively, if the data does match the machine address, the data is accepted. Since the bus topology consists of only one wire, it is cheap to implement compared to other topologies. However, there is a higher cost of managing the network. Additionally, since only one cable is used, if the network cable breaks, the whole network will be shutdown.

Star

In local area networks with a star topology, each network host (for example a PC) is connected to a central hub with a point-to-point connection. All traffic on the network passes through the central hub. The hub acts as a signal booster or repeater. The star topology is considered the easiest topology to design and implement. An advantage of the star topology is the simplicity of adding additional nodes. The primary disadvantage of the star topology is that it may need a lot more cables, and if the hub breaks everything will stop working. And if the information is to be passed only to a single computer then it can't be done in this topology i.e. all the computers interact with each other and the information will be shared to all the computers. information cannot be shared to a single computer in this topology.

Ring

A network topology that is set up in a circular fashion in which data travels around the ring in one direction and each device on the right acts as a repeater to keep the signal strong as it travels. Each device incorporates a receiver for the incoming signal and a transmitter to send the data on to the next device in the ring. The network is dependent on the ability of the signal to travel around the ring.

Mesh 

Fully connected mesh topology
The number of connections in a full mesh network of n nodes is = n(n - 1) / 2. The fully connected mesh topology is generally too costly and complex for practical networks. It has been used on networks with only a small number of nodes.

Partially connected mesh topology
The type of network topology in which some of the nodes of the network are connected to more than one other node in the network with a point-to-point link – this makes it possible to take advantage of some of the redundancy that is provided by a physical fully connected mesh topology without the expense required for a connection between every node in the network.

In most practical networks that are based upon the partially connected mesh topology, all of the data that is transmitted between nodes in the network takes the shortest path between nodes. The network used a longer alternative path in the case of a failure or break in one of the links. This requires that the nodes of the network possess some type of logical 'routing' algorithm to determine the correct path to use at any particular time.

Tree

Also known as a hierarchy network.

The type of network topology in which a central 'root' node (the top level of the hierarchy) is connected to one or more other nodes that are one level lower in the hierarchy (i.e., the second level) with a point-to-point link between each of the second level nodes and the top level central 'root' node.  Each of the second level nodes that are connected to the top level central 'root' node will also have one or more other nodes that are one level lower in the hierarchy (i.e., the third level) connected to it, also with a point-to-point link, the top level central 'root' node being the only node that has no other node above it in the hierarchy (The hierarchy of the tree is symmetrical.) 

Each node in the network having a specific fixed number, of nodes connected to it at the next lower level in the hierarchy, the number, being referred to as the 'branching factor' of the hierarchical tree.  This tree has individual peripheral nodes.

Logical topology 
Logical topology describes the way in which a network transmits information from network/computer to another and not the way the network looks or how it is laid out. The logical layout also describes the different speeds of the cables being used from one network to another.

The logical topology, in contrast to the "physical", is the wignals act on the network media, or the way that the data passes through the network from one device to the next without regard to the physical interconnection of the devices. A network's logical topology is not necessarily the same as its physical topology. For example, twisted pair Ethernet is a logical bus topology in a physical star topology layout. While IBM's Token Ring is a logical ring topology, it is physically set up in a star topology.

The logical classification of network topologies generally follows the same classifications as those in the physical classifications of network topologies but describes the path that the data takes between nodes being used as opposed to the actual physical connections between nodes.

Notes:
 Logical topologies are often closely associated with Media Access Control methods and protocols.
 The logical topologies are generally determined by network protocols as opposed to being determined by the physical layout of cables, wires, and network devices or by the flow of the electrical signals, although in many cases the paths that the electrical signals take between nodes may closely match the logical flow of data, hence the convention of using the terms logical topology and signal topology interchangeably.
 Logical topologies are able to be dynamically reconfigured by special types of equipment such as routers and switches.

Daisy chains
Except for star-based networks, the easiest way to add more computers into a network is by daisy-chaining, or connecting each computer in series to the next.  If a message is intended for a computer partway down the line, each system bounces it along in sequence until it reaches the destination.  A daisy-chained network can take two basic forms: linear and ring.

Centralization
The star topology reduces the probability of a network failure by connecting all of the peripheral nodes (computers, etc.) to a central node.  When the physical star topology is applied to a logical bus network such as Ethernet, this central node (traditionally a hub) rebroadcasts all transmissions received from any peripheral node to all peripheral nodes on the network, sometimes including the originating node. All peripheral nodes may thus communicate with all others by transmitting to, and receiving from, the central node only.  The failure of a transmission line linking any peripheral node to the central node will result in the isolation of that peripheral node from all others, but the remaining peripheral nodes will be unaffected. However, the disadvantage is that the failure of the central node will cause the failure of all of the peripheral nodes also,

If the central node is passive, the originating node must be able to tolerate the reception of an echo of its own transmission, delayed by the two-way round trip transmission time  (i.e. to and from the central node) plus any delay generated in the central node. An active star network has an active central node that usually has the means to prevent echo-related problems.

A tree topology (a.k.a. hierarchical topology) can be viewed as a collection of star networks arranged in a hierarchy.  This tree has individual peripheral nodes (e.g. leaves) which are required to transmit to and receive from one other node only and are not required to act as repeaters or regenerators.  Unlike the star network, the functionality of the central node may be distributed.

As in the conventional star network, individual nodes may thus still be isolated from the network by a single-point failure of a transmission path to the node.
If a link connecting a leaf fails, that leaf is isolated; if a connection to a non-leaf node fails, an entire section of the network becomes isolated from the rest.

In order to alleviate the amount of network traffic that comes from broadcasting all signals to all nodes, more advanced central nodes were developed that are able to keep track of the identities of the nodes that are connected to the network.  These network switches will "learn" the layout of the network by "listening" on each port during normal data transmission, examining the data packets and recording the address/identifier of each connected node and which port it's connected to in a lookup table held in memory. This lookup table then allows future transmissions to be forwarded to the intended destination only.

Decentralization
In a mesh topology (i.e., a partially connected mesh topology), there are at least two nodes with two or more paths between them to provide redundant paths to be used in case the link providing one of the paths fails.  This decentralization is often used to advantage to compensate for the single-point-failure disadvantage that is present when using a single device as a central node (e.g., in star and tree networks). A special kind of mesh, limiting the number of hops between two nodes, is a hypercube. The number of arbitrary forks in mesh networks makes them more difficult to design and implement, but their decentralized nature makes them very useful.  This is similar in some ways to a grid network, where a linear or ring topology is used to connect systems in multiple directions.  A multi-dimensional ring has a toroidal topology, for instance.

A fully connected network, complete topology or full mesh topology is a network topology in which there is a direct link between all pairs of nodes. In a fully connected network with n nodes, there are n(n-1)/2 direct links. Networks designed with this topology are usually very expensive to set up, but provide a high degree of reliability due to the multiple paths for data that are provided by the large number of redundant links between nodes. This topology is mostly seen in military applications.  However, it can also be seen in the file sharing protocol BitTorrent in which users connect to other users in the "swarm" by allowing each user sharing the file to connect to other users also involved.  Often in actual usage of BitTorrent any given individual node is rarely connected to every single other node as in a true fully connected network but the protocol does allow for the possibility for any one node to connect to any other node when sharing files.

Hybrids
Hybrid networks use a combination of any two or more topologies in such a way that the resulting network does not exhibit one of the standard topologies (e.g., bus, star, ring, etc.).  For example, a tree network connected to a tree network is still a tree network, but two star networks connected together exhibit a hybrid network topology. A hybrid topology is always produced when two different basic network topologies are connected. Two common examples for Hybrid network are: star ring network and star bus network
 A Star ring network consists of two or more star topologies connected using a multistation access unit (MAU) as a centralized hub.
 A Star Bus network consists of two or more star topologies connected using a bus trunk (the bus trunk serves as the network's backbone).

References

Tendaishe Sigauke, (2007: 46) Explaining networking terms

Other websites

 A Guide to Network Topology
 Research network topology 
 Types of topology 
 Logical Topology Example
 8 Common Network Topologies & How to Use

Tendaishe Sigauke, (2007: 46) Explaining networking terms

Computer networking