Accelerating networks

Abstract

Evolving out-of-equilibrium networks have been under intense scrutiny recently. In many real-world settings the number of links added per new node is not constant but depends on the time at which the node is introduced in the system. This simple idea gives rise to the concept of accelerating networks, for which we review an existing definition and -- after finding it somewhat constrictive -- offer a new definition. The new definition provided here views network acceleration as a time dependent property of a given system, as opposed to being a property of the specific algorithm applied to grow the network. The defnition also covers both unweighted and weighted networks. As time-stamped network data becomes increasingly available, the proposed measures may be easily carried out on empirical datasets. As a simple case study we apply the concepts to study the evolution of three different instances of Wikipedia, namely, those in English, German, and Japanese, and find that the networks undergo different acceleration regimes in their evolution.

12 pages, 8 figures

References in corpus (9)

• Emergence of scaling in random networks
• The architecture of complex weighted networks
• Mean-field theory for scale-free random networks
• Quantifying social group evolution
• Scaling properties of scale-free evolving networks: Continuous approach
• Effect of the accelerating growth of communications networks on their structure
• Accelerating, hyper-accelerating, and decelerating probabilistic networks
• Accelerated growth in outgoing links in evolving networks: deterministic vs. stochastic picture
• The inhomogeneous evolution of subgraphs and cycles in complex networks

Cited by in corpus (8)

• Zipf's Law Leads to Heaps' Law: Analyzing Their Relation in Finite-Size Systems
• Densification and Structural Transitions in Networks that Grow by Node Copying
• Modeling the average shortest path length in growth of word-adjacency networks
• Assessing the Value of Coooperation in Wikipedia
• Phase Changes in the Evolution of the IPv4 and IPv6 AS-Level Internet Topologies
• Master-equation analysis of accelerating networks
• The Accelerating Growth of Online Tagging Systems
• Link-Space and Network Analysis