1,813 research outputs found
Percolation and reinforcement on complex networks
Complex networks appear in almost every aspect of our daily life and are widely studied in
the fields of physics, mathematics, finance, biology and computer science. This work utilizes
percolation theory in statistical physics to explore the percolation properties of
complex networks and develops a reinforcement scheme on improving network resilience.
This dissertation covers two major parts of my Ph.D. research on complex networks:
i) probe—in the context of both traditional percolation and k-core percolation—the resilience
of complex networks with tunable degree distributions or directed dependency links under
random, localized or targeted attacks; ii) develop and propose a
reinforcement scheme to eradicate catastrophic collapses that occur very often in interdependent networks.
We first use generating function and probabilistic methods to obtain analytical solutions to
percolation properties of interest, such as the giant component size and the critical occupation probability.
We study uncorrelated random networks with Poisson, bi-Poisson, power-law, and Kronecker-delta degree
distributions and construct those networks which are based on the configuration model.
The computer simulation results show remarkable agreement
with theoretical predictions.
We discover an increase of network robustness as the degree distribution
broadens and a decrease of network robustness as directed dependency links come into play
under random attacks. We also find that targeted attacks exert the biggest damage to
the structure of both single and interdependent networks in k-core percolation.
To strengthen the resilience of interdependent networks, we develop and propose a reinforcement
strategy and obtain the critical amount of reinforced nodes analytically for interdependent
Erdős-Rényi networks and numerically for scale-free and for random regular networks.
Our mechanism leads to improvement of network stability of the West U.S. power grid.
This dissertation provides us with a deeper understanding of the effects of structural features on network
stability and fresher insights into designing resilient interdependent infrastructure networks
Higher-order percolation processes on multiplex hypergraphs
17 pages, 13 figuresHigher-order interactions are increasingly recognised as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraphs as well as simplicial complexes capture the higher-order interactions of complex systems and allow to investigate the relation between their higher-order structure and their function. Here we establish a general framework for assessing hypergraph robustness and we characterize the critical properties of simple and higher-order percolation processes. This general framework builds on the formulation of the random multiplex hypergraph ensemble where each layer is characterized by hyperedges of given cardinality. We observe that in presence of the structural cutoff the ensemble of multiplex hypergraphs can be mapped to an ensemble of multiplex bipartite networks. We reveal the relation between higher-order percolation processes in random multiplex hypergraphs, interdependent percolation of multiplex networks and -core percolation. The structural correlations of the random multiplex hypergraphs are shown to have a significant effect on their percolation properties. The wide range of critical behaviors observed for higher-order percolation processes on multiplex hypergraphs elucidates the mechanisms responsible for the emergence of discontinuous transition and uncovers interesting critical properties which can be applied to the study of epidemic spreading and contagion processes on higher-order networks
Competing contagion processes: Complex contagion triggered by simple contagion
Empirical evidence reveals that contagion processes often occur with
competition of simple and complex contagion, meaning that while some agents
follow simple contagion, others follow complex contagion. Simple contagion
refers to spreading processes induced by a single exposure to a contagious
entity while complex contagion demands multiple exposures for transmission.
Inspired by this observation, we propose a model of contagion dynamics with a
transmission probability that initiates a process of complex contagion. With
this probability nodes subject to simple contagion get adopted and trigger a
process of complex contagion. We obtain a phase diagram in the parameter space
of the transmission probability and the fraction of nodes subject to complex
contagion. Our contagion model exhibits a rich variety of phase transitions
such as continuous, discontinuous, and hybrid phase transitions, criticality,
tricriticality, and double transitions. In particular, we find a double phase
transition showing a continuous transition and a following discontinuous
transition in the density of adopted nodes with respect to the transmission
probability. We show that the double transition occurs with an intermediate
phase in which nodes following simple contagion become adopted but nodes with
complex contagion remain susceptible.Comment: 9 pages, 4 figure
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