# Small Cycles in Small Worlds

@article{Gleiss2000SmallCI, title={Small Cycles in Small Worlds}, author={Petra M. Gleiss and Peter F. Stadler and Andreas Wagner and David A. Fell}, journal={arXiv: Condensed Matter}, year={2000} }

We characterize the distributions of short cycles in a large metabolic network previously shown to have small world characteristics and a power law degree distribution. Compared with three networks of the same connectivity, the metabolic network has a particularly large number of triangles and a deficit in large cycles. Short cycles reduce the length of detours when a connection is clipped, so we propose that long cycles in metabolism may have been selected against in order to shorten…

## 22 Citations

The Connectivity of Large Genetic Networks

- Biology
- 2006

Data is presented suggesting that highly connected proteins are not distinguishably older than other proteins, and this finding is explained with a simple model of how a proteins degree changes in evolutionary time.

The small world inside large metabolic networks

- Biology, MedicineProceedings of the Royal Society of London. Series B: Biological Sciences
- 2001

A graph theoretical analysis of the E. coli metabolic network is found that this network is a small–world graph, a type of graph distinct from both regular and random networks and observed in a variety of seemingly unrelated areas, such as friendship networks in sociology, the structure of electrical power grids, and the nervous system of Caenorhabditis elegans.

The Connectivity of Large Genetic Networks: Design, History, or Mere Chemistry?

- Biology
- 2007

Data is presented suggesting that highly connected proteins are not distinguishably older than other proteins, and this finding is explained with a simple model of how a protein’s degree changes in evolutionary time.

Evolution of networks

- Physics, Biology
- 2002

The recent rapid progress in the statistical physics of evolving networks is reviewed, and how growing networks self-organize into scale-free structures is discussed, and the role of the mechanism of preferential linking is investigated.

The large-scale structure of metabolic networks: a glimpse at life's origin?

- Biology
- 2002

The structure of large pieces of an organism’s metabolic network, originally scattered through thousands of articles of original literature, has increasingly found its way into larger collections including encyclopedias and online databases.

J un 2 00 1 Evolution of random networks

- 2002

We review a recent fast progress in statistical physics of evolving networks. Interest focuses mainly on the structure properties of random hierarchically organized networks in communications,…

The Large-scale Structure of Metabolic Networks : A Glimpse at Life ’ s Origin ? Mapping an Organism ’ s Network Structure

- Biology
- 2002

The structure of large pieces of an organism’s metabolic network, originally scattered through thousands of articles of original literature, has increasingly found its way into larger collections including encyclopedias and online databases.

On the spectra of large sparse graphs with cycles

- Physics, Mathematics
- 2012

We present a general method for obtaining the spectra of large graphs with short cycles using ideas from statistical mechanics of disordered systems. This approach leads to an algorithm that…

Optimal Signal Processing in Small Stochastic Biochemical Networks

- Physics, MedicinePloS one
- 2007

A generic network, constrained to low molecule numbers and reasonable response times, can transduce more information than a simple binary switch and, in fact, manages to achieve close to the optimal information transmission fidelity.

Spectra of "real-world" graphs: beyond the semicircle law.

- Mathematics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

Methods to determine the eigenvalues of networks comparable in size to real systems are developed, obtaining several surprising results on the spectra of adjacency matrices corresponding to models of real-world graphs.

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