| 1. |
- Holme, Petter, et al.
(författare)
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Attack vulnerability of complex networks
- 2002
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1063-651X .- 1095-3787. ; 65:5, s. 056109-
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Tidskriftsartikel (refereegranskat)abstract
- We study the response of complex networks subject to attacks on vertices and edges. Several existing complex network models as well as real-world networks of scientific collaborations and Internet traffic are numerically investigated, and the network performance is quantitatively measured by the average inverse geodesic length and the size of the largest connected subgraph. For each case of attacks on vertices and edges, four different attacking strategies are used: removals by the descending order of the degree and the betweenness centrality, calculated for either the initial network or the current network during the removal procedure. It is found that the removals by the recalculated degrees and betweenness centralities are often more harmful than the attack strategies based on the initial network, suggesting that the network structure changes as important vertices or edges are removed. Furthermore, the correlation between the betweenness centrality and the degree in complex networks is studied.
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| 2. |
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| 3. |
- Holme, Petter, 1973-
(författare)
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Form and function of complex networks
- 2004
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Networks are all around us, all the time. From the biochemistry of our cells to the web of friendships across the planet. From the circuitry of modern electronics to chains of historical events. A network is the result of the forces that shaped it. Thus the principles of network formation can be, to some extent, deciphered from the network itself. All such information comprises the structure of the network. The study of network structure is the core of modern network science. This thesis centres around three aspects of network structure: What kinds of network structures are there and how can they be measured? How can we build models for network formation that give the structure of networks in the real world? How does the network structure affect dynamical systems confined to the networks? These questions are discussed using a variety of statistical, analytical and modelling techniques developed by physicists, mathematicians, biologists, chemists, psychologists, sociologists and anthropologists. My own research touches all three questions. In this thesis I present works trying to answer: What is the best way to protect a network against sinister attacks? How do groups form in friendship networks? Where do traffic jams appear in a communication network? How is cellular metabolism organised? How do Swedes flirt on the Internet? . . . and many other questions.
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| 4. |
- Holme, Petter, et al.
(författare)
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Growing scale-free networks with tunable clustering
- 2002
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1063-651X .- 1095-3787. ; 65:2, s. 026107-
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Tidskriftsartikel (refereegranskat)abstract
- We extend the standard scale-free network model to include a "triad formation step." We analyze the Geometric properties of networks Generated by this algorithm both analytically and by numerical calculations, and find that our model possesses the same characteristics as the standard scale-free networks such as the power-law degree distribution and the small average geodesic length, but with the high clustering at the same time. In our model, the clustering coefficient is also shown to be tunable simply by changing a control parameter-the average number of triad formation trials per time step.
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| 5. |
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| 6. |
- Holme, Petter, et al.
(författare)
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Network bipartivity
- 2003
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1063-651X .- 1095-3787. ; 68:5 Pt 2
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Tidskriftsartikel (refereegranskat)abstract
- Systems with two types of agents with a preference for heterophilous interaction produce networks that are more or less close to bipartite. We propose two measures quantifying the notion of bipartivity. The two measures-one well known and natural, but computationally intractable, and the other computationally less complex, but also less intuitive-are examined on model networks that continuously interpolate between bipartite graphs and graphs with many odd circuits. We find that the bipartivity measures increase as we tune the control parameters of the test networks to intuitively increase the bipartivity, and thus conclude that the measures are quite relevant. We also measure and discuss the values of our bipartivity measures for empirical social networks (constructed from professional collaborations, Internet communities, and field surveys). Here we find, as expected, that networks arising from romantic online interaction have high, and professional collaboration networks have low, bipartivity values. In some other cases, probably due to low average degree of the network, the bipartivity measures cannot distinguish between romantic and friendship oriented interaction.
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| 7. |
- Holme, Petter, et al.
(författare)
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Network Bipartivity
- 2003
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Ingår i: Physical Review E. - 1063-651X. ; 68:5, s. 056107-
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Tidskriftsartikel (refereegranskat)
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| 8. |
- Holme, Petter, et al.
(författare)
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Phase transitions in the two-dimensional random gauge XY model
- 2003
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 67:10
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Tidskriftsartikel (refereegranskat)abstract
- The two-dimensional random gauge XY model, where the quenched random variables are magnetic bond angles uniformly distributed within [(-)rpi,rpi](0less than or equal torless than or equal to1), is studied via Monte Carlo simulations. We investigate the phase diagram in the plane of the temperature T and the disorder strength r and infer, in contrast to a prevailing conclusion in many earlier studies, that the system is superconducting at any disorder strength r for sufficiently low T. It is also argued that the superconducting to normal transition has different nature at weak disorder and strong disorder: termed Kosterlitz-Thouless (KT) type and non-KT type, respectively. The results are compared to earlier works.
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| 9. |
- Holme, Petter, et al.
(författare)
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Prisoners' dilemma in real-world acquaintance networks : Spikes and quasiequilibria induced by the interplay between structure and dynamics
- 2003
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1063-651X .- 1095-3787. ; 68:3, s. 030901-
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Tidskriftsartikel (refereegranskat)abstract
- We study Nowak and May's spatial prisoners' dilemma game driven by mutations (random choices of suboptimal strategies) on empirical social networks. The time evolution of the cooperation level is highly complex containing spikes and steps between quasistable levels. A statistical characterization of the quasistable states and a study of the mechanisms behind the steps are given. We argue that the crucial structural ingredients causing the observed behavior is an inhomogeneous degree distribution and that the connections within vertices of highest degree are rather sparse. Based on these observations we construct model networks with a similar complex time evolution of the cooperation level.
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| 10. |
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