# Using Graph Concepts to Understand the Organization of Complex Systems

@article{Christensen2007UsingGC, title={Using Graph Concepts to Understand the Organization of Complex Systems}, author={Claire Christensen and R{\'e}ka Albert}, journal={Int. J. Bifurc. Chaos}, year={2007}, volume={17}, pages={2201-2214} }

Complex networks are universal, arising in fields as disparate as sociology, physics and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the topologies of different systems. Attempts to explain these similarities have led to the ongoing development and refinement of network models and graph-theoretical analysis techniques with which to characterize and understand complexity. In this tutorial, we…

## 44 Citations

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## References

SHOWING 1-10 OF 162 REFERENCES

Network motifs in computational graphs: a case study in software architecture.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

It is shown the rules of graph evolution seem to be largely responsible for the observed motif distribution, and several highly frequent network motifs appear to be a consequence of network heterogeneity and size, thus suggesting a somewhat less relevant role of functionality.

The Structure and Function of Complex Networks

- Computer ScienceSIAM Rev.
- 2003

Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

The architecture of complex weighted networks.

- Computer ScienceProceedings of the National Academy of Sciences of the United States of America
- 2004

This work studies the scientific collaboration network and the world-wide air-transportation network, which are representative examples of social and large infrastructure systems, respectively, and defines appropriate metrics combining weighted and topological observables that enable it to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices.

Uncovering the overlapping community structure of complex networks in nature and society

- Computer ScienceNature
- 2005

After defining a set of new characteristic quantities for the statistics of communities, this work applies an efficient technique for exploring overlapping communities on a large scale and finds that overlaps are significant, and the distributions introduced reveal universal features of networks.

Hierarchical organization in complex networks.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

It is found that several real networks, such as the Worldwideweb, actor network, the Internet at the domain level, and the semantic web obey this scaling law, indicating that hierarchy is a fundamental characteristic of many complex systems.

Scale-free networks in cell biology

- BiologyJournal of Cell Science
- 2005

The observed topologies of cellular networks give clues about their evolution and how their organization influences their function and dynamic responses, and the opportunity to describe quantitatively a network of hundreds or thousands of interacting components is offered.

The topological relationship between the large-scale attributes and local interaction patterns of complex networks

- Computer ScienceProceedings of the National Academy of Sciences of the United States of America
- 2004

It is shown that a network's large-scale topological organization and its local subgraph structure mutually define and predict each other, as confirmed by direct measurements in five well studied cellular networks.

Evolution of networks

- Computer Science
- 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.

Subnetwork hierarchies of biochemical pathways

- Computer ScienceBioinform.
- 2003

A method to decompose biochemical networks into subnetworks based on the global geometry of the network is presented and is applied to 43 organisms from the WIT database.

Emergence of scaling in random networks

- Computer ScienceScience
- 1999

A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.