Article
Mechanics
Frank Duque, Daniel Ramirez-Gomez, Alejandro Roldan-Correa, Leon A. Valencia
Summary: This study focuses on a new type of percolation problem called accessibility percolation, inspired by evolutionary biology. Each vertex of a graph is assigned a random number called its fitness, and a path in the graph is accessible if fitnesses strictly increase along it. The paper determines the values of an additional parameter for achieving RMF (Rough Mount Fuji) accessibility percolation on the hypercube, as well as the two-dimensional lattices L-2 and L-alt(2).
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2023)
Article
Mechanics
Pawat Akara-pipattana, Thiparat Chotibut, Oleg Evnin
Summary: In this paper, we study the distribution of resistance distances in an Erdos-Renyi random graph and develop an auxiliary field representation for this quantity. Using a 1/c expansion and a saddle point evaluation, we analyze the distribution and find that it exhibits different characteristics at different values of c, including the presence of subleading peaks. A more refined saddle point scheme allows us to analytically recover some of these subleading peaks.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2022)
Article
Physics, Fluids & Plasmas
Peter Mann, V. Anne Smith, John B. O. Mitchell, Simon Dobson
Summary: In this paper, percolation theory is used to analyze clustered networks with simple cycles and cliques of any order, providing solutions for critical properties and giant component size of Poisson and power-law networks using the generating function formulation. The study finds that networks with larger simple cycles behave more like trees, while clustering with larger cliques deviates from treelike solutions, influenced by degree-assortativity.
Article
Computer Science, Interdisciplinary Applications
Edson A. Soares, Andre A. Moreira
Summary: The structural phase transition in complex network models is important for practical applications such as resilience of artificial networks and dynamics of epidemic spreading. The random graph model is the simplest model of complex networks and falls into the universality class mean field percolation. In this work, the focus is on the structural phase transition in the ensemble of random acyclic graphs, utilizing the exact combinatorial enumeration of the whole ensemble to determine the entropy and critical transition. The results are compared with other models and illustrated with Monte-Carlo simulations.
INTERNATIONAL JOURNAL OF MODERN PHYSICS C
(2023)
Article
Mathematics
Adrian Marius Deaconu, Delia Spridon
Summary: This paper discusses the adaptation of the Erdos-Renyi model to generate random flow networks, with a developed algorithm based on the decomposition of flows into directed paths and cycles, allowing for quick construction of large-scale networks.
Article
Physics, Fluids & Plasmas
Fei Ma, Ping Wang
Summary: The study proposes a simple algorithmic framework for generating power-law graphs with small diameters and examines their structural properties. The results show that these graphs have unique features such as density characteristics and higher trapping efficiency compared to existing scale-free models, confirmed through extensive simulations.
Article
Physics, Fluids & Plasmas
Fabian Coupette, Tanja Schilling
Summary: This study proposes a simple percolation criterion for solving various percolation problems, which can accurately calculate the percolation threshold for many solved problems. The criterion has a wide range of applicability, including random graphs, small-world networks, and percolation problems on various lattices. In addition, the study introduces a method to generate simple planar lattices with a prescribed percolation threshold.
Article
Physics, Mathematical
Clement Cosco, Inbar Seroussi, Ofer Zeitouni
Summary: This study examines the directed polymer model for general graphs and random walks beyond Z(d), providing conditions for the presence or absence of weak disorder phases, L-2 regions, and very strong disorder based on graph and random walk properties. The study delves into (biased) random walks on various trees, including Galton-Watson trees, and offers a range of examples that demonstrate counterexamples to intuitive extensions of the Z(d)/SRW results.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2021)
Article
Physics, Multidisciplinary
Bnaya Gross, Ivan Bonamassa, Shlomo Havlin
Summary: This study investigates percolation in interdependent resistor networks and demonstrates the impact of spatiality on their coupled functioning. It shows that interdependent resistor networks are more vulnerable than traditional percolation-based networks. The results highlight the significance of different node functionality definitions on the collective properties of coupled processes in networks.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2021)
Article
Computer Science, Hardware & Architecture
B. R. Vinay Kumar, Navin Kashyap, D. Yogeshwaran
Summary: This article focuses on the energy-efficient broadcasting problem in large ad-hoc networks. The networks are modeled using random geometric graphs (RGGs), where nodes are uniformly deployed in a square area and can receive each other's broadcast if within a Euclidean distance of 1. The source node encodes k data packets into n (> k) coded packets and transmits to its one-hop neighbors. The goal is to determine the minimum forwarding probability that enables a large fraction of nodes to decode the information from the source, while minimizing the expected total number of transmissions. Compared to probabilistic forwarding with no coding, the study shows that a judicious choice of n can reduce the expected total number of transmissions while ensuring a near-broadcast.
PERFORMANCE EVALUATION
(2023)
Article
Mechanics
Luca Dall'Asta
Summary: This study investigates the statistical properties of Nash equilibria in coordination models on networks, focusing on random graphs. The research sheds light on the mechanisms behind the onset of coordination/miscoordination on large networks through analyzing different processes of dynamical equilibrium selection. The results show that while full coordination remains globally stochastically stable, certain equilibrium selection processes may be trapped in inefficient equilibria, preventing full coordination.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2021)
Article
Physics, Multidisciplinary
Yangyang Liu, Qiangjuan Huang, Gaogao Dong, Meng Yao, Louis M. Shekhtman, H. Eugene Stanley
Summary: This study proposes an immunization strategy that takes into account limited knowledge of the network structure. It generalizes the acquaintance immunization by immunizing the acquaintance with the highest degree among n acquaintances. Both mathematical modeling and experimental verification show that this strategy is more effective than acquaintance immunization and random immunization under limited knowledge conditions.
NEW JOURNAL OF PHYSICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Hao Peng, Yifan Zhao, Dandan Zhao, Ming Zhong, Zhaolong Hu, Jianming Han, Runchao Li, Wei Wang
Summary: In recent years, the research of multilayer interdependent networks with higher-order interactions has become a hotspot in complex networks. This paper introduces the concept of simplicial complexes to better reflect real-world complex networks. A theoretical model of a two-layer network with simplicial complexes is constructed, and percolation theory is applied to study the network's robustness and properties. The density of the triangle and the dependent strength between the two networks are found to affect the network's percolation behaviors.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mechanics
Dor Minzer, Yaron Oz, Muli Safra, Lior Wainstain
Summary: Working within the multi-type Galton-Watson branching-process framework, we analyzed the spread of a pandemic through a general multi-type random contact graph. Our model, consisting of multiple communities, determines outbreak likelihood and calculates the size of the giant-connected-component of the graph to predict population infection rates. The pandemic spread is shown to have a natural evolution direction determined by the Perron-Frobenius eigenvector, with the basic reproduction number as the corresponding eigenvalue. Numerical simulations compare homogeneous and heterogeneous spread graphs, emphasizing the impact of countermeasures on infected population fractions.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2021)
Article
Physics, Multidisciplinary
Junjie Lu, Tobias Hofmann, Ulrich Kuhl, Hans-Juergen Stoeckmann
Summary: Quantum graphs are useful for studying the spectral statistics of chaotic systems. Neumann and Dirichlet graphs have different boundary conditions at the vertices. The Neumann spectral statistics deviate from random matrix predictions due to the interlacing theorem. We provide analytic expressions for level spacing distribution and number variance of ensemble averaged spectra of Dirichlet graphs, and compare them with numerical results. The deviations of numerical results for small Neumann graphs from random matrix predictions are also discussed.
Article
Mechanics
Ginestra Bianconi
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2019)
Article
Mechanics
Nicola Cinardi, Andrea Rapisarda, Ginestra Bianconi
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2019)
Article
Mechanics
Ginestra Bianconi, Sergey N. Dorogovstev
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2020)
Article
Physics, Multidisciplinary
Ginestra Bianconi
Summary: Maximum entropy network ensembles have been effective in modeling and solving inference problems in sparse network topologies. However, existing models have limitations which have been addressed by proposing hierarchical models for exchangeable networks that can handle fixed or arbitrary number of nodes in a grand canonical approach.
Article
Physics, Fluids & Plasmas
Ginestra Bianconi, Ivan Kryven, Robert M. Ziff
Article
Business, Finance
Marco Bardoscia, Ginestra Bianconi, Gerardo Ferrara
INTERNATIONAL JOURNAL OF FINANCE & ECONOMICS
(2019)
Article
Physics, Fluids & Plasmas
Ivan Kryven, Ginestra Bianconi
Article
Physics, Fluids & Plasmas
Ivan Kryven, Robert M. Ziff, Ginestra Bianconi
Article
Physics, Multidisciplinary
Eleonora Kreacic, Ginestra Bianconi
Article
Physics, Fluids & Plasmas
Ana P. Millan, Joaquin J. Torres, Ginestra Bianconi
Article
Physics, Fluids & Plasmas
Francesco Coghi, Filippo Radicchi, Ginestra Bianconi
Article
Physics, Fluids & Plasmas
Ginestra Bianconi, Robert M. Ziff
Article
Mathematics, Interdisciplinary Applications
Christoph Rahmede, Jacopo Iacovacci, Alex Arenas, Ginestra Bianconi
JOURNAL OF COMPLEX NETWORKS
(2018)
Article
Physics, Fluids & Plasmas
Owen T. Courtney, Ginestra Bianconi
Article
Physics, Fluids & Plasmas
Diamantino C. da Silva, Ginestra Bianconi, Rui A. da Costa, Sergey N. Dorogovtsev, Jose F. F. Mendes