The aim is to create a simulation environment for social network such as Twitter. The simulation is based on tweets distribution over the network. You'll create the network with Matlab, then test it.

Please consider the social network as a graph. Each node has some neighbours, etc. Let say that one node shared a product. Then, its neighbours will observe and going to choose whether or not to share that product. Once it chooses to share the product, its neighbours will be aware of the product. So on and so forth, each node tries to affect its neighbours and eventually the product will be popular within the majority of the network.

Now, Hopfield's job is to create a network based on each node's neighbour. Secondly, it helps nodes to choose whether or not share the information by its activation threshold. If a node activates itself, then its neighbours can have the chance to activate themselves. Hopfield network provides us the right properties to construct and simulate. However, the key is that once a node is activated, it cannot be deactivated and there is almost no guarantee for it in Hopfield network.

1. I need you to create a text file for a social network, Twitter as an example. The data, in the text file, should represent relationship information for each user. That contains at least 1000 users and also capable of having more users. However, please put friendship among them very very sparse. There could be some isolated users and generally it should be more likely a chain of friendship. I'm going to use my own dataset so please make it understandable.

2. Then, you'll create the Hopfield Neural Network for the friendship data. (http://www.mathworks.com/help/toolbox/nnet/ug/bss4hat-43.html). Please use Hopfield network tool provided by Matlab to create the network.

3. Test the network with few influential users by using (the one you created above) network for the task. Let's say user A is the most retweeted person. Then, you'll just put user A in the test matrix for Matlab and then run matlab to observe the distribution of A's tweet (retweets) in the network. Of course, I'll need more than one user in the test matrix.

4. As I said, the important thing is that once a user retweets, his state is fixed; he cannot go back to his previous stage(unretweet) or cannot retweet again. I want you to guarantee and explain it in the document with reasons. In other words, once a node is activated, it cannot be deactivated during the test runs. I want you to prove & guarantee it for network.