# Making a faster network starts with mathematics

UU scientist Carla Groenland receives funding from the European Union for her research on aspects of graph theory. Her mathematical research makes algorithms in digital networks simpler and more efficient.

"Basically, a graph is nothing more than a bunch of dots connected by lines," says postdoctoral researcher Carla Groenland. "Think of a schematic roadmap of cities with highways in between. Or social networks, where you want to determine which person has the most 'influence'." Partly because of these applications, Groenland's research direction is, in her own words, "quite up-and-coming". In fact, the work is essential to making computer systems function faster and better. "A year ago, the Abel Prize, which is internationally regarded as the informal Nobel Prize in Mathematics, was awarded to two researchers in my field."

## Determining connectedness from small pieces of network

One of the subfields within network research that Groenland is working on is the ‘reconstruction conjecture’. Groenland: "We want to find out how small pieces of a network determine the global structure of the whole network. How big do the pieces have to be in order to reconstruct a certain property, or the entire network?"

A scientific contribution of Groenland lies in determining connectedness from those small pieces of network. "The road network of the Netherlands, for example, is not connected, because there are also roads on islands that are not connected to the mainland roads. If you give me small parts of a graph, I can tell you whether the whole graph is connected.’’ Groenland discovered this possibility by involving mathematical theory of complex polynomials. "That theory is very old and had been used by other mathematicians in a similar set-up with sequences of numbers. I realised that it could also be used for components of graphs."

## Isomorphism

Another part of Groenland's research focuses on isomorphism in graphs. "Sometimes the structures of two graphs are the same, but this is not recognised because the points have different names. This phenomenon is also common in practice: think of determining whether two chemical structure formulas are the same, or two electronic circuits." Gunther Cornelissen, professor of mathematics at UU, has developed a theory that explains isomorphism for more general mathematical structures. Together, Groenland and Cornelissen will try to make that theory simpler and more efficient for graphs.

A nice aspect of graph theory is that it has connections with all kinds of mathematical theories, but that it also has algorithmic applications.

It has not reached that point yet. Soon, Groenland will first move from the Utrecht University Research Institute of Information and Computing Science to the Mathematical Institute. "One of the nice aspects of graph theory is that it has connections with all kinds of mathematical theories, but that it also has algorithmic applications. At the moment I am still a postdoc at Computer Science, next year I will be an assistant professor at Mathematics. The UU is a logical place for me because the university is strong in both mathematics and algorithms: my research is at the interface of the two."

## Marie Curie Fellowship

With the Marie Sklodowska-Curie Postdoctoral Fellowship, the European Union encourages young researchers to gain experience abroad shortly after obtaining their PhD. In the latest round, apart from Carla Groenland’s grant, two foreign laureates were given the opportunity to work at Utrecht University's Faculty of Science for a period of time.