Explosive Percolation in Erdős–Rényi-Like Random Graph Processes

Παναγιώτου, Κωνσταντίνος; Spöhel, Reto; Steger, Angelika; Thomas, Henning

doi:10.1017/s0963548312000442

Cited by 12 publications

(14 citation statements)

References 15 publications

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“…The order parameter R behaves as R − R 0 ∼ (K − K c ) β , where R 0 is the jump in the order parameter, and K c is the transition point [20,22,27,28]. The exponent β is approximately β ≈ 0.75, independent of h, which is in contrary to the behavior in the r-ER model for hybrid percolation transitions induced by cluster merging dynamics [18]. However, K c depends on h: K c increases as h is increased.…”

Section: Numerical Resultsmentioning

confidence: 81%

Synchronization in leader-follower switching dynamics

Park,

Kahng

2020

Preprint

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The features of animal population dynamics, for instance, flocking and migration, are often synchronized for survival under large-scale climate change or perceived threats. These coherent phenomena have been explained using synchronization models. However, such models do not take into account asynchronous and adaptive updating of an individual's status at each time. Here, we modify the Kuramoto model slightly by classifying oscillators as leaders or followers, according to their angular velocity at each time, where individuals interact asymmetrically according to their leader/follower status. As the angular velocities of the oscillators are updated, the leader and follower status may also be reassigned. Owing to this adaptive dynamics, oscillators may cooperate by taking turns acting as a leader or follower. This may result in intriguing patterns of synchronization transitions, including hybrid phase transitions, and produce the leader-follower switching pattern observed in bird migration patterns.

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Section: Numerical Resultsmentioning

confidence: 81%

Synchronization in leader-follower switching dynamics

Park,

Kahng

2020

Preprint

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“…In 1960s, two Hungarian mathematicians Erdos and Renyi set up a random graph theory [2], which was regarded as a systematic study of complex networks theory in mathematics. In the next 40 years, people had been using random graph theory as the basic theory of complex networks research.…”

Section: Introductionmentioning

confidence: 99%

A survey of clustering algorithms in community detection of complex networks

Le¹,

Shi

Fang

et al. 2017

Proceedings of the 3rd International Conference on Wireless Communication and Sensor Networks (WCSN 2016)

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Abstract-Complex network analysis begins in the 1930s, and the community structure in complex networks is a major characteristic that has been widely concerned. This paper introduces the basic and core ideas of several typical clustering algorithms in community detecting, and analyzes the advantages and disadvantages of each one. And it also reviews the background, the significance and the performance of these algorithms. Some algorithms may perform well in some specific areas but not in community detecting, while the newest algorithms still need to be tested in the future.

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“…For percolation, hybrid percolation transitions (HPTs) may be classified into two categories: one occurring during the cascade process as in k-core percolation [5][6][7][8][9][10][11][12] , and the other during the cluster merging process [30][31][32] . For the former case, dynamics proceed only in one direction of decreasing occupation probability, and a reverse process may not be well defined, i.e., a cascade cluster aggregation process is hardly imagined.…”

mentioning

confidence: 99%

“…In this paper, we consider a reverse process of the cluster merging dynamics of the so-called restricted Erdős-Rényi (r-ER) model. It is known that the r-ER model [30][31][32] exhibits an HPT. In the reverse fragmentation process, a restriction is given to the breakage of large clusters.…”

mentioning

confidence: 99%

Hysteresis and criticality in hybrid percolation transitions

Park

Kahng

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Phase transitions (PTs) are generally classified into second-order and first-order transitions, each exhibiting different intrinsic properties. For instance, a first-order transition exhibits latent heat and hysteresis when a control parameter is increased and then decreased across a transition point, whereas a second-order transition does not. Recently, hybrid percolation transitions (HPTs) are issued in diverse complex systems, in which the features of first-order and second-order PTs occur at the same transition point. Thus, the question whether hysteresis appears in an HPT arises. Herein, we investigate this fundamental question with a socalled restricted Erdős-Rényi random network model, in which a cluster fragmentation process is additionally proposed. The hysteresis curve of the order parameter was obtained. Depending on when the reverse process is initiated, the shapes of hysteresis curves change, and the critical behavior of the HPT is conserved throughout the forward and reverse processes.

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Explosive Percolation in Erdős–Rényi-Like Random Graph Processes

Cited by 12 publications

References 15 publications

Synchronization in leader-follower switching dynamics

Synchronization in leader-follower switching dynamics

A survey of clustering algorithms in community detection of complex networks

Hysteresis and criticality in hybrid percolation transitions

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