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Most of us have a profile on a social networking website such as LinkedIn or Facebook and are familiar with the concept of “degrees away from you”.  So, if X is 2 degrees away from you on LinkedIn then you and X (although not connected to each other) share a common connection say S.

The figure below illustrates this:

This can be viewed in terms of a graph where you and X are nodes on a Graph connected to each other through the node S.  In case you and X have more common connections besides S then there are multiple paths between the node “you” and node “X” as shown below:

In case there is no connection between you and a person z, then you and z are points on two separate graphs (out of your network in terms of Linked In).

Now the question that follows is this:

Just like in Graph Theory where one can find best path(s) among a given set of paths based on some criteria (example, shortest distance between two cities connected by multiple routes). Can we choose the best path in case of Social Networking Graphs as well?

In other words, which is the best path connecting you and X in the example above?

To answer this, we need to come up with some criterion based on which we can run a Standard Algorithm to find the best path. In case of LinkedIn, this criterion can be the number of connections that you have.

For starters, we can say that the more connections a person has the higher his/her quality is. This may be modified further to give weightage related to quality of each individual connection as well.  Based on this, each node may be assigned a weight and then the best path can be determined.

Some of the obvious real life problems this criterion will face are that of Quantity Vs Quality.  Some people might have only 30 connections but all of them might be big shots, compared to someone else who has 100 connections but each of them have just 10-15 connections each.

The above example shows how the concepts of Graph theory can be related to Professional Networking media like LinkedIn, etc.  The same concepts can be used in some areas of SEM as well.

There are many other interesting examples about application of Graph Theory concepts. In fact, among the scientific community there is something known as an Erdos number which measures the “collaborative distance” between a person and prolific mathematician Paul Erd?s, which is measured by authorship of mathematical papers. You can read about it here.

Contributed by Ravi Shukla

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Tags: degrees away, Erdős number, Professional Networking, social networking