Evolution of Scale Free Networks

Literature: Network of tRNA Gene Sequences

2005-01-09T13:43:00.000-08:00

What is more, the tRNA similarity network behaves scale-free properties when s0 is large. As we know the scale-free nature is rooted in two generic mechanisms[9]. Firstly scale-free networks describe open systems that grow by the continuous addition of new nodes. Secondly scale-free networks exhibit preferential attachment that means the likelihood of connecting to a node depends on the node’s degree. With these mechanisms, the ”very connected” nodes in scale-free networks usually are added in the network at early time during the growth of the network. It has been found that most recent tRNA genes are evolved from a few common precursors[12, 15], and these oldest evolutionary sequences, comparing to the recent tRNA genes. Therefore, in tRNA similarity netwok, the ”very connected” tRNA genes may have diverged less from their ancestors than weakly connected ones.

Literature: Scale Free Networks from Self-Organisation

2005-01-09T11:50:00.000-08:00

We show how scale-free degree distributions can emerge naturally from growing networks by using random walks on the network. The algorithm uses only local graph information so this is a process of self-organisation. We demonstrate that this result holds for a wide range of parameters of the walk algorithm. We show that the standard mean field equations are an excellent approximation to the real networks we grow, but that fall short of a true scale-free network when the number of vertices is one million or smaller. We also generalise the random walk algorithm to produce weighted networks with power law distributions of both weight and degree. We suggest that a random walk self-organisation mechanism lies behind the many scale-free networks found in the real world.

Scale Free Networks: (persons) Albert-László Barabási

2005-01-09T08:52:00.000-08:00

Albert-László Barabási is one of the foremost experts on scale free networks and author of:

"LINKED: The New Science of Networks"

Description

This book has a simple message: think networks. It is about how networks emerge, what they look like, and how they evolve. It aims to develop a web-based view of nature, society, and technology, providing a unified framework to better understand issues ranging from the vulnerability of the Internet to the spread of diseases. Networks are present everywhere. All we need is an eye for them...We will see the challenges doctors face when they attempt to cure a disease by focusing on a single molecule or gene, disregarding the complex interconnected nature of the living matter. We will see that hackers are not alone in attacking networks: we all play Goliath, firing shots at a fragile ecological network that, without further support, could soon replicate our worst nightmares by turning us into an isolated group of species...Linked is meant to be an eye-opening trip that challenges you to walk across disciplines by stepping out of the box of reductionism. It is an invitation to explore link by link the next scientific revolution: the new science of networks.

Relevant Links

The protein-protein interaction network of yeast also has a scale-free topology: a few proteins interact with a large number of other proteins, while most proteins have only one or two links.