A photo by Nicolai Berntsen. unsplash.com/photos/2Qm47LI0W1c

Networks: the study of complex systems

I am interested in the relationship between network structure and dynamics, and in particular unravelling the relationship between the topological, spectral and dynamical properties of a graph. Applications in this area include distributed computing or sensing, social or opinion networks, and swarming, flocking or synchronization of coupled oscillators.

In particular, I have focused on the link between a particular graph partition, the external equitable partition (EEP), and Laplacian consensus dynamics [1]. In a sense, the EEP characterises a fundamental symmetry in the graph, also observable in the spectral properties of the Laplacian matrix, and enables a direct correspondence between dynamics of the full graph and dynamics of a collapsed ‘quotient’ graph (where each node represents a cell in the full graph). Since the quotient graph inherits certain spectral properties of the full graph, it is possible to exploit this relationship to reveal, for example, nodes in the full graph with increased rate of asymptotic convergence to the consensus value.

Building on this work, a second study [2] showed that the existence of an EEP describes partial synchronisation dynamics on a network of coupled oscillators.

Forthcoming work [3], also exploiting the link between dynamics and structure, the proposes a novel and highly efficient approach for the local computation of the global dynamical properties of networks. 

  1. Schaub M, O’Clery N, Billeh Y, Delvenne J-C, Lambiotte R & Barahona M (2016) Graph partitions and cluster synchronization in networks of oscillators. Chaos 2016;26 (9).
  2. O’Clery N, Yuan Y, Stan G-B & Barahona M (2013) Observability and coarse graining of consensus dynamics through the external equitable partition. Physical Review E. 2013;88 (4).
  3. O’Clery N, Yuan Y, Stan G-B, Barahona M (2017) Fast Decentralised Sensing and Node Ranking for Complex Systems. Forthcoming.