## All things are connected

There are networks everywhere. Not just the Internet or the LAN at work, but everywhere. A network could loosely be defined as being comprised of a number of nodes and a number of connections between them. A node is a point or thing which is connected through a connection to another node. A connection is what joins nodes together. This rather circular definition will do for now.

A family can be described by a network. Let’s consider a typical average nuclear family with parents and 2.4 kids. Errm, on second thoughts, lets make that 3 kids. If each person in the family is a node, we can’t really have 0.4 of a kid.

So there are multiple connections between any one family member and another. The father has a connection with his wife, his daughter and his sons. The daughter has connections with her father, her mother and her brothers. One way that this could be shown in a diagram is to draw a pentagon, each vertex of which is a member of the family and lines between the family member showing the relationships.

That’s a total of 15 interrelationships in a small family. Actually depending on the way you look at it, there may be more, as the father is the father of his daughter but the daughter is not the father of the father (obviously). This can be looked at at two relationships, one from father to daughter (A is B’s father) and another from the daughter to the father (B is A’s daughter), or one relationship between father and daughter.

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If you consider that there are two relationships between any two family members, then each relationship can be considered to have a direction and a value. “A is B’s brother” and “B is A’s brother”, for example. Alternatively the relationship could be simple viewed as “brothers”, in which case the relationship has a value, but is non-directional.

I’ve described the familiar relationships in detail to hopefully bring out the facts that relationships between nodes and connections can be complex or describe complex situations. It’s entirely a matter of what you want the network to show.

The Internet is what people tend to think of when someone says “network” and it is indeed a complex network with myriads of interconnections across the globe, but in another way it is quite simple. Basically you have a computer, say your desktop or laptop, connected to the Internet. When you request a webpage, your request is sent to another node on the network, which then sends it to another node, and that forwards it on to yet another node and eventually the request arrives at the destination.

The clever part is that you might think that every “node” on the Internet needs to know where all the other nodes are, but in fact all it needs to know is where to send the request next.

It seems almost magical. Your computer doesn’t know where wordpress.com is, though it does look up its unique address (known as an IP address). It still doesn’t know where wordpress.com is, so it sends the request and the IP address to your ISP. Your ISP looks at the IP address and sees that it isn’t one local to the ISP, so it passes it on.

As noted above the message is passed on and on until it reaches its destination and then more magic happens as the remote machine responds to the request and sends the response all the way back. It may even travel back by a different route.

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The magic is that some of the nodes know around 200,000 addresses on the Internet and where the next step should go. These addresses are in the most part partial in that the address will be like the street address, without the building number.

So although the Internet is a complex network with many many connections between nodes, the basic principle by which it works is simple, based on an address lookup system (DNS) and a simple unique address for each device on the Internet.

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(OK there’s more to it than that, but the complexities are mainly at the “edges” of the Internet and mainly spring from the need for security and for organisations to have a “gateway” or single address on the Internet).

When we plan a journey over the road network, we generally have some idea of where we are going or we get out a map. We then scan it for the start and end of our journey and work out what direction we need to travel and the intermediate towns.

But if we travelled like a message travels on the Internet we would first travel to the nearest town and ask someone where we need to go to get to our destination. He or she would point us to the next town to which he or she believes we should go. We would then travel to the next destination and ask again.

It would seem that such a process could result in us going round and round in circles, but eventually we will reach a place where the traffic director knows a large part of the roading network and is able to redirect us to another city which is known to be closer to our destination. Once we are on the right road, the process will eventually result in us reaching our destination.

Another network is the network formed by people we know and the people that they know, and the people that they know and so on. There is a theory that to from you, to someone you know to someone they know and so on, it takes six or less steps to reach any person on the planet. This is referred to as “six degrees of separation“.

Similar numbers can be calculated for smaller sets of people. The Kevin Bacon Number relates movie stars through films that they have starred in with other people. Number higher than 4 are rare. The Erdős Number relates people by the number of scientific papers that they have co-authored.

These somewhat whimsical numbers do demonstrate how closely linked the human race is. So far as I know no study has been done of the importance of bridging individuals is. I’m talking about those who perhaps emigrate to a country, thereby directly linking together two populations that may be less loosely connected, increasing the connectivity and reducing the number of degrees of separation.