Vertex overload breakdown in evolving networks.

  title={Vertex overload breakdown in evolving networks.},
  author={Petter Holme and Beom Jun Kim},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={65 6 Pt 2},
  • Petter Holme, Beom Jun Kim
  • Published 5 April 2002
  • Computer Science
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We study evolving networks based on the Barabási-Albert scale-free network model with vertices sensitive to overload breakdown. The load of a vertex is defined as the betweenness centrality of the vertex. Two cases of load limitation are considered, corresponding to the fact that the average number of connections per vertex is increasing with the network's size ("extrinsic communication activity"), or that it is constant ("intrinsic communication activity"). Avalanchelike breakdowns for both… 
Emergence and disappearance of traffic congestion in weight-evolving networks
A New Cascading Model on Scale-Free Network with Tunable Parameter
The cascading failure on BA networks with scale-free property based on a load redistribution rule is examined, and it is drawn that Tc has a negative correlation with the average degree, i.e., the bigger the value of <k>, the smaller the critical threshold Tc.
Topology and congestion invariant in global internet-scale networks
This thesis studies how to build catastrophic networks, particularly on packet-oriented networks, which are vulnerable to catastrophic failure in infrastructure like telecommunication systems, power transmission grids and the Internet.
Building catastrophes: networks designed to fail by avalanche-like breakdown
The method simulates an avalanche in reverse, building a network designed to fail by avalanche-like breakdown, and it is seen that networks that are almost homogeneous in node degree may still fail catastrophically.
Overload-based cascades on multiplex networks and effects of inter-similarity
This paper proposes a new model for load-based cascading failures in multiplex networks, and is the first to report the competition between the positive and the negative impacts of overlapping links on the robustness of coupled networks.
Resilience of Small Social Networks
The ability of a network to retain one or more specified properties under perturbation of its structure is referred to as resilience. In this thesis, we focus on the resilience of small social
The positive-feedback preference model of the AS-level Internet topology
  • Shi Zhou, R. Mondragón
  • Computer Science
    IEEE International Conference on Communications, 2005. ICC 2005. 2005
  • 2005
The positive-feedback preference (PFP) model is introduced, which is the most precise and complete Internet topology generator to date and accurately reproduces many topological properties of the AS-level Internet, including degree distribution, the maximum degree, rich-club connectivity, disassortative mixing, shortest-path length, short cycles and betweenness centrality.
Growth, collapse, and self-organized criticality in complex networks
This work addresses the question of whether a complex network of nonlinear oscillators can maintain its synchronization stability as it expands and demonstrates the generality of the phenomenon of synchronization collapse using a variety of complex network models, and uncover the underlying dynamical mechanism through an eigenvector analysis.


Emergence of scaling in random networks
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.
Incipient spanning cluster on small-world networks
We analyze the scaling properties of the largest cluster size for the site percolation problem on small-world graphs. It is shown how the presence of the extra length-scale, the small-world crossover
A simple model of global cascades on random networks
  • D. Watts
  • Computer Science
    Proceedings of the National Academy of Sciences of the United States of America
  • 2002
It is shown that heterogeneity plays an ambiguous role in determining a system's stability: increasingly heterogeneous thresholds make the system more vulnerable to global cascades; but anincreasingly heterogeneous degree distribution makes it less vulnerable.
Classes of small-world networks.
Evidence of the occurrence of three classes of small-world networks, characterized by a vertex connectivity distribution that decays as a power law law, and the nature of such constraints may be the controlling factor for the emergence of different classes of networks are presented.
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.
Internet: Diameter of the World-Wide Web
The World-Wide Web becomes a large directed graph whose vertices are documents and whose edges are links that point from one document to another, which determines the web's connectivity and consequently how effectively the authors can locate information on it.
The small world inside large metabolic networks
  • Andreas Wagner, D. Fell
  • Biology
    Proceedings 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.
Exploring complex networks
This work aims to understand how an enormous network of interacting dynamical systems — be they neurons, power stations or lasers — will behave collectively, given their individual dynamics and coupling architecture.
A set of measures of centrality based upon betweenness
A family of new measures of point and graph centrality based on early intuitions of Bavelas (1948) is introduced, used to index centrality in any large or small network of symmetrical relations, whether connected or unconnected.
On power-law relationships of the Internet topology
Despite the apparent randomness of the Internet, some surprisingly simple power-laws of theInternet topology are discovered, which hold for three snapshots of the internet.