Dynamic community detection and embedding in evolving networks

In many real-world networks, a mesoscale organization of nodes, called community structure, exists.
Community structure implies that a network is composed of groups of nodes such that the nodes are
densely connected within the same group and relatively sparsely connected across different groups.
For instance, social networks exhibit groups of friends, families, organizations. How to partition a
complex network into communities is a widely studied problem [1, 2]: several works, from a broad set
of disciplines, proposed different approaches to retrieve such structures automatically. [3, 4] can be
cited, among many others.

The objective of this project is to build a DCD algorithm (i) fitting real-world network structures and
that (ii) can be applied on-the-fly as new data (nodes, edges) enter the system. In particular, in realworld networks, communities are often overlapping and do not change too drastically within small
time periods, while the numbers of nodes and edges can vary over time.
The aim of our work is therefore to exploit the promises of combining community detection and
embeddings on static networks with the promises of node embedding methods on dynamic
networks, to perform efficient on-the-fly community detection on dynamic networks. The hope is
to incorporate dynamic community properties into network embeddings to leverage community
discovery. To our knowledge's extent, no work has been carried out in this direction. Because the
interpretability of models has becoming an important issue in applied science, we aim at using
probabilistic and/or optimization classical and transparent approaches.

This project falls within the EPSRC Mathematical Analysis research area. It intends to create a new
tool to exploit the amount of data brought by 21st century products and industrial systems. It is
supervised by Professor Renaud Lambiotte (Mathematical Institute, University of Oxford) and
Professor Doyne Farmer (Institute for New Economic Thinking, University of Oxford).