# PhD Studentship: Correlation Ensembles in Complex Networks

### Coventry University - Centre for Fluid and Complex Systems

Qualification Type: PhD Coventry UK Students, EU Students, International Students Fully Funded with stipend Full Time
Placed On: 8th August 2023 25th October 2023 FCSR002

You will be registered and conduct your work within the Centre for Fluid and Complex Systems at Coventry University. You will have a strong interest in complexity science, and some experience in one or more areas amongst graph theory, computational physics, statistical physics and network science. You will have the opportunity to work in the Statistical Physics of Complex Systems group of Dr. Charo del Genio, in a stimulating multidisciplinary environment where you will be frequently interacting with other postgraduate researchers and postdoctoral scientists.

The project is centred on determining the characteristics of a new type of complex network ensemble. Networks are a highly successful approach to model complex systems. The key idea of this paradigm is to represent systems as graphs, which are mathematical structures in which pairs of related discrete elements, called nodes, are linked by connections called edges. In studying such systems, researchers often use different graph-sampling methods to build networks obeying a given set of constraints. Typically, the constraint used is the degree sequence of the network, which specifies the number of connections belonging to each node. More recently, the attention has shifted towards higher-order constraints, such as joint-degree matrices (JDMs), which completely specify the pairwise degree correlations of a network. In this project, you will study how to directly determine the JDMs corresponding to a given degree sequence.

JDMs uniquely specify the degree sequences of the graphs that realize them; however, the vice versa is not necessarily true, as, in general, each graphical sequence of integers can be realized by graphs with different JDMs. Currently, the only way of determining the typical degree correlations of a family of graphs is to sample their degree sequence or degree distribution and then measure the correlations of the resulting networks. Your main initial goal will be to find a method to build and sample the JDMs corresponding to a given degree sequence without having to pass through the middle step of explicit graph construction.

You will start from existing results and theorems in graph-sampling algorithms and JDM graphicality, using them to create a self-consistent approach to identify the bounds on the elements of a partially built matrix, and work your way up towards a systematic method to construct JDMs. Upon completion of the algorithm, you will use it to study and compare the correlation ensembles of the main families of complex networks, shedding light on the mesoscopic relations that give rise to the observed preferred correlation structures. Your results will not only reveal the features of this new statistical ensemble, but will also allow for the quick comparison of the degree correlations found in real-world networks with those that would be found on average in an equivalent but random case, enabling the fast detection of the length scale at which evolutionary drivers act in the formation of the systems studied.

Candidate Specification

For further details please visit:  https://www.coventry.ac.uk/research/research-opportunities/research-students/making-an-application/research-entry-criteria/

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