Navigability of Complex Networks

  title={Navigability of Complex Networks},
  author={Mari{\'a}n Bogu{\~n}{\'a} and Dmitri V. Krioukov and Kimberly C. Claffy},
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. 

Informational cost and networks navigability

This approach reveals that environmental pressure has shaped the ways in which information is transferred in bacterial metabolic net-works and allowed us to determine the levels of noise at which a protein-protein interaction network seems to work in normal conditions in a cell.

Complex spatial networks in application

The last five years has seen a considerable growth in the application of graph and network theory to “real-world” networks, and some of the advances in the analysis of such real-world networks are reviewed, highlighting the continuing difficulties involved.

Exploring the Morphospace of Communication Efficiency in Complex Networks

This work defines analytic measures directed at characterizing network communication when signals flow in a random walk process and identifies specific aspects of network topology that differentially favor efficient communication for routing and diffusion processes.

Bridging the gap between graphs and networks

The need for further cross-pollination between fields – bridging the gap between graphs and networks – is discussed and promises and challenges accompanying the convergence of formal graph theory and data-inspired network science are discussed.


This paper constructs a deterministic network by a mapping method based on a recursive graph, and analyzes its topological characteristics, including degree distribution, clustering coefficient, network diameter, average path length and degree correlations.

Routes Obey Hierarchy in Complex Networks

A striking result is presented that the paths in various networks are significantly stretched compared to their shortest counterparts.

The geometric nature of weights in real complex networks

This work introduces a very general and versatile model and uses it to quantify the level of coupling between their topology, their weights and an underlying metric space, and suggests that the formation of connections and the assignment of their magnitude are ruled by different processes.

Sizing the length of complex networks

A new synoptic representation is established that allows for a complete and accurate interpretation of the pathlength (and efficiency) of complex networks and frees network comparison from the need to rely on the choice of reference graph models (e.g., random graphs and ring lattices).

The Organization of Strong Links in Complex Networks

A general organization is identified for complex systems that strikes a balance between efficient local and global communication in their strong interactions, while allowing for robust, exploratory development of weak interactions.

Evaluating Structure of Complex Networks by Navigation Entropy

  • Xiaoping Sun
  • Computer Science
    2012 Eighth International Conference on Semantics, Knowledge and Grids
  • 2012
This paper uses the navigability to model the basic structural complexity of a network and applies the navigation entropy model on a set of structural and random network topologies to show how the model can show the different complexity of networks.



The Structure and Function of Complex Networks

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.

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

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

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

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.

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

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

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.