The word topology can be thought of as "the study of location." Topology is a subject of study in mathematics, where maps of nodes (dots) and links (lines) often contain patterns. In this chapter, you will examine the various topologies used in networking from a mathematical perspective. Then, you will learn how a physical topology describes the plan for wiring the physical devices. Finally, you will use a logical topology to learn how information flows through a network to determine where collisions may occur.

A network may have one type of physical topology , and a completely different type of logical topology. For example, Ethernet 10BASE-T uses an extended-star physical topology, but acts as though it uses a logical bus topology. Token Ring uses a physical star, and a logical ring. FDDI uses a physical and a logical ring.

Mathematical Perspective
The bus topology has all of its nodes connected directly to one link, and has no other connections between nodes

Physical Perspective
Each host is wired to a common wire. In this topology, the key devices are those that allow the host to join or tap into the single shared medium. One advantage of this topology is that all hosts are connected to each other, and thus, can communicate directly. One disadvantage of this topology is that a break in the cable disconnects hosts from each other.

Logical Perspective
A bus topology enables every networking device to see all signals from all other devices. This can be an advantage if you want all information to go to every device.

Mathematical Perspective
A ring topology is a single closed ring consisting of nodes and links, with each node connected to only two adjacent nodes.

Physical Perspective 
The topology shows all devices wired directly to each other in what is called a daisy-chain. This is similar to the manner in which a mouse on an Apple PC plugs into the keyboard and then into the PC.

Logical Perspective
In order for information to flow, each station must pass the information to its adjacent station.

Mathematical Perspective
A dual ring topology consists of two concentric rings, each of which is linked only to its adjacent ring neighbor. The two rings are not connected.

Physical Perspective
A dual ring topology is the same as a ring topology, except that there is a second, redundant ring, that connects the same devices. In other words, in order to provide reliability and flexibility in the network, each networking device is part of two independent ring topologies.

Logical Perspective
A dual ring topology acts like two independent rings, of which, only one at a time is used.

Mathematical Perspective
A star topology has a central node with all links to other nodes radiating from it and allows no other links.

Physical Perspective
A star topology has a central node with all links radiating from it. Its primary advantage is that it allows all other nodes to communicate with each other, conveniently. Its primary disadvantage is that if the central node fails, the whole network becomes disconnected. Depending on the type of networking device used at the center of the star network, collisions can be a problem.

Logical Perspective
The flow of all information would go through one device. This might be desirable for security or restricted access reasons, but it would be very susceptible to any problems in the star's central node.

Mathematical Perspective
An extended star topology repeats a star topology, except that each node that links to the center node is, also, the center of another star.

Physical Perspective
An extended star topology has a core star topology, with each of the end nodes of the core topology acting as the center of its own star topology. The advantage of this is that it keeps wiring runs shorter, and limits the number of devices that need to interconnect to any one central node.

Logical Perspective
An extended star topology is very hierarchical, and information is encouraged to stay local. This is how the phone system is currently structured.

Mathematical Perspective
The tree topology is similar to the extended star topology, the primary difference is that it does not use one central node. Instead, it uses a trunk node from which it branches to other nodes. There are two types of tree topologies: the binary tree (each node splits into two links); and the backbone tree (a backbone trunk has branch nodes with links hanging from it).

Physical Perspective
The trunk is a wire that has several layers of branches.

Logical Perspective
The flow of  information is hierarchical.

Mathematical Perspective
In the irregular network topology there is no obvious pattern to the links and nodes.

Physical Perspective
The wiring is inconsistent; the nodes have varying numbers of wires leading from them. This is how networks that are in the early stages of construction, or poorly planned, are often wired.

Logical Perspective
There is no obvious pattern to the links and nodes.

Mathematical Perspective
In a complete, or mesh topology, every node is linked directly to every other node.

Physical Perspective
This wiring has very distinct advantages and disadvantages. One advantage is every node is physically connected to every other node (creating a redundant connection). Should any link fail to function, information can flow through any number of other links to reach its destination. Another advantage of this topology is that it allows information to flow along many paths on its way back through the network. The primary physical disadvantage is that for anything more than a small number of nodes, the amount of media for the links, and the amount of connections to the links becomes overwhelming.

Logical  Perspective
The behavior of a complete, or mesh topology depends greatly on the devices used.

Mathematical Perspective
The cellular topology consists of circular or hexagonal areas, each of which has an individual node at its center.

Physical Perspective
The cellular topology is a geographic area that is divided into regions (cells) for the purposes of wireless technology – a technology that becomes increasingly more important each day. There are no physical links in a cellular topology, only electromagnetic waves. Sometimes the receiving nodes move (e.g. car cell phone), and sometimes the sending nodes move (e.g. satellite communication links).

The obvious advantage of a cellular (wireless) topology is that there are no tangible media other than the earth's atmosphere or the vacuum of off-planet space (and satellites). The disadvantages are that signals are present everywhere in a cell and, thus, are susceptible to disruptions (man-made and environmental) and to security violations (i.e. electronic monitoring and theft of service).

Logical Perspective
Cellular technologies communicate with each other directly (though distance limitations and interference sometimes make it extremely difficult), or communicate only with their adjacent cells, which is  extremely inefficient. As a rule, cellular-based topologies are integrated with other topologies, whether they use the atmosphere or satellites.

In this chapter, you learned that the function of the physical layer is to transmit data. In addition you learned that the following types of networking media may be used to connect computers:

• Coaxial cable consists of a hollow outer cylindrical conductor that surrounds a single inner wire conductor.
• UTP cable is a four-pair wire medium used in a variety of networks.
• STP cable combines the techniques of shielding, cancellation, and twisting of wires.
• Fiber-optic cable is a networking medium capable of conducting modulated light transmissions.

This chapter discussed various criteria, such as rate of data transfer and expense, that help determine which types of networking media should be used. You learned that TIA/EIA-568-A and TIA/EIA-569 are the most widely used standards for technical performance of networking media.

Additionally, this chapter described how bits propagating at the same time on the same network result in a collision.  Lastly, you learned that a network may have one type of physical topology, and a completely different type of logical topology.  In the next chapter, you will learn about LAN media and the IEEE model and how the data link layer provides reliable transit of data across a physical link by using Media Access Control (MAC) addresses.