Classification of Logical Topologies

The logical classification of network topologies
generally follows the same classifications as those in
the physical classifications of network topologies, the
path that the data takes between nodes being used to
determine the topology as opposed to the actual physical
connections being used to determine the topology.
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.A linear topology puts a two-way link between one
computer and the next. However, this was expensive in
the early days of computing, since each computer (except
for the ones at each end) required two receivers and two
transmitters.By connecting the computers at each end, a ring topology
can be formed. An advantage of the ring is that the
number of transmitters and receivers can be cut in half,
since a message will eventually loop all of the way
around. When a node sends a message, the message is
processed by each computer in the ring. If a computer is
not the destination node, it will pass the message to
the next node, until the message arrives at its
destination. If the message is not accepted by any node
on the network, it will travel around the entire ring
and return to the sender. This potentially results in a
doubling of travel time for data, but since it is
traveling at a fairly insignificant multiple of the
speed of light, the loss is usually negligible.

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.

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.

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 networkA 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).While grid networks have found popularity in
high-performance computing applications, some systems
have used genetic algorithms0 to design custom networks
that have the fewest possible hops in between different
nodes. Some of the resulting layouts are nearly
incomprehensible, although they function quite well.