Navigability of Complex Networks

@article{Bogu2007NavigabilityOC,
  title={Navigability of Complex Networks},
  author={Mari{\'a}n Bogu{\~n}{\'a} and Dmitri V. Krioukov and Kimberly C. Claffy},
  journal={ArXiv},
  year={2007},
  volume={abs/0709.0303}
}
In many real-world processes that can be mapped onto complex networks—from cell signalling to transporting people—communication between distant nodes is surprisingly efficient, considering that no node has a full view of the entire network. A framework sets out to explain why ‘navigability’ is so efficient in these networks. 

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References

SHOWING 1-10 OF 67 REFERENCES

The Structure and Function of Complex Networks

TLDR
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.

TLDR
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.

Statistical mechanics of complex networks

TLDR
A simple model based on these two principles was able to reproduce the power-law degree distribution of real networks, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network.

Hierarchical structure and the prediction of missing links in networks

TLDR
This work presents a general technique for inferring hierarchical structure from network data and shows that the existence of hierarchy can simultaneously explain and quantitatively reproduce many commonly observed topological properties of networks.

Networks Become Navigable as Nodes Move and Forget

TLDR
The first formal proof that navigability in small worlds can emerge from a dynamic process for network evolution is presented, based on the combination of two dynamics: a random walk (spatial) process, and an harmonic forgetting (temporal) process.

Efficient Navigation in Scale-Free Networks Embedded in Hyperbolic Metric Spaces

In this work we show that: i) the roughly hierarchical structure of complex networks is congruent with negatively curved geometries hidden beneath the observed topologies; ii) the most

Vertex similarity in networks.

TLDR
A measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar is proposed, which leads to a self-consistent matrix formulation of similarity that can be evaluated iteratively using only a knowledge of the adjacency matrix of the network.

Collective dynamics of ‘small-world’ networks

TLDR
Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.

Navigation in a small world

TLDR
The small-world phenomenon was first investigated as a question in sociology and is a feature of a range of networks arising in nature and technology and is investigated by modelling how individuals can find short chains in a large social network.
...