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Networks and Databases - What?!

I break my silence with a technical discussion about the rudiments of networks and databases - WHAT THE HECK ARE YOU TALKING ABOUT ARNIE?! I might just as well ask you the same question, because honestly, I did not realize that I have been using concepts related to those two broad categories from way, way back.

Recall the discrete math structure called "graph". Without loss of generality (WLOG) w.r.t. networking concepts, let us assume that the graphs that we would be dealing with are all undirected graphs. Then the familiar classificatory concepts of basic graph types in discrete mathematics readily translate to an important topic under physical and logical networking -- a topic usually referred to as network topologies.

Briefly, a network may possess a particular topology in one of two ways -- either physically (network setup) or logically (protocol specifications). There are essentially 5 basic types of network topologies, to wit:

1. Bus topology - This seems to be equivalent to a path (a "linearly-oriented" graph), although I've initially mistaken it for a tree. In this network setup, a single cable is used to connect all the devices. Thus, a break in any part of the cable leads to adverse effects on the whole network. Additionally, because of the "linear orientation" of this network setup, a terminator needs to be placed at both ends of the (backbone) network cable to prevent interference.

2. Ring topology - Definitely isomorphic to a cycle. In this topology, every two neighbouring devices are connected to each other, thus forming a "circular orientation" for the network setup. Similar to the limitations/disadvantages of the bus topology, this network setup does not lend itself well to good network fault tolerance.

3. Star topology - Boasts a high network fault tolerance for all the topologies, at a significantly lower cost than the mesh topology - the only downside being that the entire network's success depends on a single device (which could be a hub or switch at the middle of the network). This gives the physical network the appearance of a "starfish". The graph-theoretic equivalent of a star network is also called a star.

4. Mesh topology - Best in terms of network fault tolerance, worst in terms of network maintenance and upgrade costs. Also, given the complexity of the physical network setup (with the number of cables used increasing quadratically with the number of network nodes, as in the case of the Full Mesh Topology), troubleshooting this type of network topology can be extremely cumbersome and difficult. Thus, an alternative is to relax the fault tolerance requirement by using a Partial Mesh Topology instead.

5. Tree topology - Again, the graph-theoretic equivalent of the concept in discrete mathematical structures is also called a tree. Sometimes also called the hierarchical network topology, as a certain "hierarchy" is implicit when the tree topology's physical orientation is viewed from the top.

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