Dear Ranga Dabarera,

in a sociophysics of opinion formation, the initial idea is that the most connected node will be the most influential one due to the number of connections.

However, has been showed by Kitsak et al. that the most influential node is not related only to the most connected node (high betwenneess centrality), but also to the location of the node, being the best spreaders those located within the core of the network.

For further information, you can see the following paper:

M. Kitsak, L. K. Gallos, S. Havlin, F. Liljeros, L. Muchnik, H. E. Stanley, and H. A.

Makse, Identifying influential spreaders in complex networks, Nature Physics 6, 888

(2010),

that is available in http://www.nature.com/nphys/journal/v6/n11/abs/nphys1746.html

This problem is formally stated as "minimal input or actuator selection problem" in the context of "controlling" networks. The seminal contribution was an idea called structural controllability [1]. The idea has been resurrected after 30 odd years again, and the problem of finding "driver nodes" (most influential for control purposes) for controlling a network is fully solved in linear models case [2,3].

[1] Lin, Ching Tai. "Structural controllability." Automatic Control, IEEE Transactions on 19.3 (1974): 201-208.

[2] Olshevsky, Alex. "Minimum input selection for structural controllability." American Control Conference (ACC), 2015. IEEE, 2015.

[3] Liu, Yang-Yu, Jean-Jacques Slotine, and Albert-László Barabási. "Controllability of complex networks." Nature 473.7346 (2011): 167-173.

Another way to see the problem : the campaign problem http://arxiv.org/pdf/1410.8419.pdf

• Professor Fabricio Luchesi Forgerini: The paper you cited in Nature is a great work and I am in the process of simulating a scenario in showing that effect. Thank you for the publication... 
• To Aravind: It is fascinating how influential nodes have been modeled with "driver nodes". I will read more on that via the publications you have listed. Thanks for the response. 
• Professor Frédéric Amblard: It was a pleasure for me to have your response and paper you have given is spot-on. I have been citing many publications of you and I really value your response in this regard. 

All in all I thank you for your valuable responses and these will really help me in my research in studying the influential agents in a network. 

You need to evaluate authority and hub centrality.  

• Professor Jorge Mejía: I will look into that as well... Thank you for the response.  

You need to compute the pagerank scores, and then derive the underlying hierarchy indicated by ht-index:

https://www.researchgate.net/publication/2177752_Ranking_Space_for_Predicting_Human_Movement_in_an_Urban_Environment

https://www.researchgate.net/publication/236627484_Ht-Index_for_Quantifying_the_Fractal_or_Scaling_Structure_of_Geographic_Features

Article Ranking Space for Predicting Human Movement in an Urban Environment

Article Ht-Index for Quantifying the Fractal or Scaling Structure of...

Professor Bin Jiang: Thank you very much for the publications. Yes I need to study on the use of PageRank too. Professor D.L.Shepelyansky's group also has looked into that. Your publications made me even more compelling to follow up on PageRank based methods. Thanks again. 

http://www.sciencedirect.com/science/article/pii/S0378437112005511

This paper, in particular, the measuring part might be of your interest:

https://www.researchgate.net/publication/272159333_Wholeness_as_a_Hierarchical_Graph_to_Capture_the_Nature_of_Space?ev=prf_pub

Article Wholeness as a Hierarchical Graph to Capture the Nature of Space

Professor Bin Jiang: Thank you very much for the publication professor. Really appreciate your insight in this. 

For viral marketing in Social Net, these are some prominent papers of pioneer researchers:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.407.4750&rep=rep1&type=pdf

http://snap.stanford.edu/class/cs224w-readings/chen09influence.pdf

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.722.4522&rep=rep1&type=pdf

https://www.microsoft.com/en-us/research/wp-content/uploads/2010/01/kdd10_influence_revised.pdf

http://dl.acm.org/citation.cfm?id=1963217

beast of luck Mr Ranga.

~Ashis

I suggest to identify the structure of the network in terms of hubs and authorities nodes. I attached an example taken from patents citation networks. The patent in the middle is an authority, others are hubs (connected to many nodes). This kind of structure allows diffusion.

A good starting point would be the work of prof. Peter Grindrod.

Especially, take a look at his book, Mathematical Underpinnings of Analytics, (2014) OUP, Oxford. ISBN: 9780198725091.

Take a look at chapter 3.3: Validating the identification of influencers.