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Correlation ensembles in complex networks

Eligibility: UK/International (including EU) graduates with the required entry requirements

Duration: Full-Time – between three and three and a half years fixed term. Up to 3.5 full-time.

Application deadline: 27 May 2023

Interview date: Will be confirmed to shortlisted candidates

Start date: September 2023

For further details contact Dr. Charo del Genio 


Coventry University (CU) is inviting applications from suitably-qualified graduates for a fully-funded PhD studentship.

Project details

The project is centred on characterizing a new type of complex network ensemble. In studying complex systems, researchers often use graph-sampling methods to build networks obeying given constraints, such as a degree sequence or a joint-degree matrix (JDM). This project concerns 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 degree sequence can be realized by graphs with different JDMs. Currently, the only way of determining the typical degree correlations of a graph family is sampling their degree sequence or degree distribution and then measure the correlations of the resulting networks. The first goal will be to create an algorithm to build and sample the JDMs corresponding to a given degree sequence without passing through the middle step of explicit graph construction, using a self-consistent approach to identify the bounds on the elements of partially built matrices.

The algorithm will then be used 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.


Tuition fees and stipend.


The successful candidate will receive comprehensive research training including technical, personal and professional skills.

All researchers at Coventry University (from PhD to Professor) are part of the Doctoral College and Centre for Research Capability and Development, which provides support with high-quality training and career development activities. 

Candidate Specification

  • A bachelor’s (honours) degree in a relevant discipline/subject area with a minimum classification of 2:1 and a minimum mark of 60% in the project element (or equivalent), or an equivalent award from an overseas institution.
  • the potential to engage in innovative research and to complete the PhD within 3.5 years
  • An adequate proficiency in English must be demonstrated by applicants whose first language is not English. The general requirement is a minimum overall IELTS Academic score of 7.0 with a minimum of 6.5 in each of the four sections, or the TOEFL iBT test with a minimum overall score of 95 with a minimum of 21 in each of the four sections.

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

Additional requirements

Familiarity and experience with writing C/C++ code in Linux environment.

How to apply

To find out more about the project please contact Dr. Charo del Genio.

Details of all available research opportunities at Coventry University can be found via


All applications require full supporting documentation, and a covering letter and an up-to 2000-word supporting statement  showing how the applicant’s expertise and interests are relevant to the project. 

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