## Graph Theory, Matrices – A Realtime example

Observe the matrix given below

The above Matrix shows all zero at diagonal.

Let me draw a graph for this ,

Assume that A, B and C are entities in database , Say Person entity.

A – Ram , B – Suma, C – Prema

Ram – Posted
Hello ….
Suma – Commented
Idiot 🙂 …
Ram – Replied
You Idiot …
Prema – commented
See every one call you as idiot 🙂

Hold a moment … Does the above graph is correct ?
Observe what is changed in below graph

It is not mandatory that only A has to comment B ! , Even B can comment A .

So the first graph shown  is a directed graph and it is wrong , It should be undirected graph.

Now assume that how a facebook keeps track of connected friends ? Mutual Friends ? how big is the graph of facebook ?

The intention of this article is , to teach you guys how a Matrix concept is used to represent a graph, and how a graph theory is used in realtime to represent a social networking site like facebook.

Now understand why one should learn Graph Theory and Matrices

Let us have a look into facebook DB and Big data
Total Monthly Active users – 1,310,000,000
Total Mobile users  – 680,000,000