An example of a complex network.

The scientific study of networks is an interdisciplinary field that combines ideas from mathematics, physics, biology, computer science, the social sciences, and many other areas. In online databases one can find examples of computer networks, social networks, and biological networks (e.g. the structure of primitive brains).

A project on any level could include studying the properties of one of these networks, comparing two different networks, or generating a new type of network and compare it to existing ones. Is it a small-world network? Is it more clustered that one would expect? Does it contain communities? Here, one can either adopt a very mathematical approach based on linear algebra, or develop computer algorithms to explore the networks.

Suitable for: First year project, Bachelor project, Master’s project

Main disciplines: Complex systems, network science, programming (any language), linear algebra

Related work:

Complex networks on wiki

Newman: Networks – An introduction

Sandpile model

Sandpile models were the first models found to exhibit self-organized criticality. Grains of sand are added on a lattice, one at a time, until the amount of sand on a site exceeds a specific threshold value at which time that site collapses transferring sand into the adjacent sites. If this causes the amount of sand there to exceed the threshold, an avalanche of sand may start.

Sand leaves the model through the boundaries of the lattice. On a network you have no boundary, so you can either add ‘boundary nodes’, let sand dissipate gradually over time, during avalanches, or at the end of avalanches. How does this change the model?

Suitable for: First year project, Bachelor’s project, Master’s project

Main disciplines: Programming (any language), self-organization, complex systems, networks

Related work:

Self-organized criticality: An explanation of the 1/f noise

Sandpile on Scale-Free Networks