A network topology is like a framework, although purely in virtual terms. A topology is a layout of how computers should connect, not how they are physically arranged in a space.
The most common network topologies include the bus topology, which connects all the computers with a single cable. The computers are all able to see when a machines taps into the wire to connect to another machine, however privacy is assured as only the connecting units can access the data. This arrangement work well with less devices, it’s easy enough to set up (10Base-2 ("ThinNet") and 10Base-5 ("ThickNet") cables work well). However the downside is that if the connecting cable fails all the units attached cannot interact.
The second one is the ring topology, typically used in schools; the arrangement is such that each unit is connected to two other units, hence like a ring. If one of the units crashes however the whole network ceases to function properly (FDDI, SONET, or Token Ring technology are good for implementing this topology).
Next, the star topology typically has a hub (hub, router or switch) to which all units are connecting using a unshielded twisted pair cable. The benefits of this type are that if a unit crashes, the network still continues to function. The downside is that more cable is required.
The tree topology consists of a number of star topologies connected through a bus topology. Confusing? It’s actually quite simple; we simple connect the central hubs of the star networks in the form of a bus topology. This type of network is easy to expand.
The mesh topology uses routes, therefore any messages transferred can take a number of routes to get to their destination, in a full mesh network, every device connects to every other device.
The type of topology you choose to implement really depends on you requirements, so look carefully at the number of units involved and how complicated your network is expected to be.