### Taming complexity: controlling networks

10 Feb 2012

Albert-László Barabási

Center for Complex Network Research

Northeastern University

#### Abstract

The ultimate proof of our understanding of biological or technological systems is reflected in our ability to control them. While control theory offers mathematical tools to steer engineered and natural systems towards a desired state, we lack a framework to control complex self-organized systems. Here we develop analytical tools to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes whose time-dependent control can guide the system's entire dynamics. We apply these tools to several real networks, finding that the number of driver nodes is determined mainly by the network's degree distribution. We show that sparse inhomogeneous networks, which emerge in many real complex systems, are the most difficult to control, but dense and homogeneous networks can be controlled via a few driver nodes. Counterintuitively, we find that in both model and real systems the driver nodes tend to avoid the hubs.

In collaboration with Y Liu and JJ Slotine.

#### References

- Y Y Liu, J J Slotine, L Barabási,
*"Controllability of complex networks"*, Nature 473:167-73 2011. PubMed

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