MCMC vs Network Theory for Big Data and Data Science applications [Apologies if this post sounds naive, I'm fairly new to the world of data science/big data and very unsure where I'm heading career-wise]

I'm currently an undergraduate MMath [integrated master's] Mathematics student in the UK who has finished the third year of the course [out of four years].

As I have been considering the possibility of doing further research in Mathematics/Statistics/Operational Research/Data Science, I have decided to stay on and complete the Master's component of the course [as it is the only Master's course I can get funding for at this stage]. After the Master's I may continue on and do a PhD.

There are currently two projects that appeal to me that seem to have relevant applications. The first one is on improved MCMC [Markov Chain Monte Carlo] methods, in particular MCMC using Hamiltonian Dynamics. There is scope for some big data applications here.

The other project that I could take part in is one on the centrality/communities detection of networks within network science. This could possibly be useful with applications in Operational Research.

Does anyone have an idea as to which project will be more relevant to data science/analytics?
Both MCMC methods and network analysis play an important role in data science. I think you should go for the project you like more. However, in my experience, community detection in networks is a niche (applied math/graph theory) of network analysis, while MCMC methods involve lots of statistical and computational concepts. Personally, being a statistician, I would go for the MCMC methods.