Network topology
The topology of a computer network defines how that network is "laid out." Topologies can be either physical (meaning how the actual hardware is interconnected) or logical (meaning how that network is implemented by protocols in software).
There are numerous different basic network topologies (and many variations). Here are several examples, with diagrams:
Star topology
A star network has nodes surrounding a central point, so that it resembles a star when drawn.
Most wired networks, including those over optical fiber, are physical stars. It is far easier to install star cabling, with the simplicity of only needing to find a physical path from the computer to the center of the star. For the same reasons, it is much easier to troubleshoot a star: in the crudest case, one can keep disconnecting individual devices until the communications system starts to work again.
Bus topology
A "bus network" is hooked together like stops on a Public Bus route, one after the other. Bus networks usually require terminators at each end of the network, to prevent echo of the signal.
The original pre-IEEE Ethernet was a physical bus, as were the first two variants of IEEE 802.3 running over coaxial cable, 10BASE2 and 10BASE5. All modern 802.3 variants, however, are logical buses over physical stars. In the central device of the star, there is usually additional electronics to minimize bus contention (i.e., multiple devices trying to use the bus at once); microsegmentation and full duplex on the box at the center of the star further minimize contention.
Today's most common physical buses are wireless, where the common medium is a given radio frequency.
Ring topology
A "ring network" is literally in the shape of a ring; devices reach each other by passing data around in a ring. Physical ring networks often use two or more rings to add a level of redundancy if one of the rings should fail.
The obsolete IEEE 802.5 token ring networks were always implemented as a logical ring over a physical star, or set of stars. Fiber distributed data interface, obsolete in new installations but still in some production networks, originally was a dual ring topology: one working and one protection/backup ring. FDDI evolved to stars that contained logical rings, or "rings of stars", in which the physical rings interconnect only the star concentrators.
Physical rings are principally used today in the optical transmission systems of telephone companies and Internet Service Providers. These systems use first or second generation SONET or SDH. Especially in "next generation SONET", there is a wide range of failover modes. Basic SONET/SDH, like basic FDDI, started out as dual ring, and, in the original version, what is called 1+1: one working ring and one idle protection ring. For very critical networks, 1:1 was introduced, where the same data flows simultaneously over both rings, and the connected equipment ignores one.
Continuing evolution, recognizing that optical networks are extremely reliable, would use N:1, where 1 protection ring covers several working rings. N:M implementations have M protection rings, where M is less than N, to cover N working rings.
Even with all these ring refinements, it still is extremely common to see physical stars feeding into concentrators, which contain the logical ring. Even for installations that have protection rings, there still can be physical star cabling, with two cables running between the concentrator and the end equipment.
Mesh topology
A meshed network can be fully meshed, where every device connects to every other device, or partially meshed, where devices connect only to some other devices. Since these devices may be communications interconnects rather than computers, it can be seen that a branching star one case of a partial mesh.