Approximating the largest eigenvalue of network adjacency matrices

Abstract

The largest eigenvalue of the adjacency matrix of a network plays an important role in several network processes (e.g., synchronization of oscillators, percolation on directed networks, linear stability of equilibria of network coupled systems, etc.). In this paper we develop approximations to the largest eigenvalue of adjacency matrices and discuss the relationships between these approximations. Numerical experiments on simulated networks are used to test our results.

7 pages, 4 figures

References in corpus (20)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• Finding and evaluating community structure in networks
• Assortative mixing in networks
• Mixing patterns in networks
• Resilience of the Internet to random breakdowns
• Epidemic spreading in correlated complex networks
• Spectra of "Real-World" Graphs: Beyond the Semi-Circle Law
• The onset of synchronization in large networks of coupled oscillators
• Spectra of complex networks
• Resilience to damage of graphs with degree correlations
• Spectra and eigenvectors of scale-free networks
• Frequency synchronization in random oscillator network
• Synchronization transition in scale-free networks: Clusters of synchrony
• Synchronization in large directed networks of coupled phase oscillators
• Spectral Analysis and the Dynamic Response of Complex Networks
• The emergence of coherence in complex networks of heterogeneous dynamical systems
• Synchronizabilities of Networks: A New index
• Vibrational modes and spectrum of oscillators on a scale-free network

Cited by in corpus (43)

• Thresholds for epidemic spreading in networks
• Discrete-time Markov chain approach to contact-based disease spreading in complex networks
• Predicting criticality and dynamic range in complex networks: effects of topology
• Maximal-entropy random walks in complex networks with limited information
• The effect of network topology on the stability of discrete state models of genetic control
• Inhibition causes ceaseless dynamics in networks of excitable nodes
• Relating Topological Determinants of Complex Networks to Their Spectral Properties: Structural and Dynamical Effects
• Statistical Properties of Avalanches in Networks
• Spectral properties of complex networks
• Mean field theory of assortative networks of phase oscillators
• Hub Synchronization in Scale-Free Networks
• Effects of network topology, transmission delays, and refractoriness on the response of coupled excitable systems to a stochastic stimulus
• Effects of degree-frequency correlations on network synchronization: universality and full phase-locking
• Multiplex visibility graphs to investigate recurrent neural networks dynamics
• Modeling the Network Dynamics of Pulse-Coupled Neurons
• Correlations Induced by Depressing Synapses in Critically Self-Organized Networks with Quenched Dynamics
• Linear stability analysis for large dynamical systems on directed random graphs
• Hypergraph assortativity: a dynamical systems perspective
• Scaling behaviour in probabilistic neuronal cellular automata
• Stability of Boolean networks: The joint effects of topology and update rules
• Approximating the Largest Eigenvalue of the Modified Adjacency Matrix of Networks with Heterogeneous Node Biases
• On the spectral unfolding of chaotic and mixed systems
• Social Climber attachment in forming networks produces phase transition in a measure of connectivity
• Sample-to-sample fluctuations in real-network ensembles
• A network approach for power grid robustness against cascading failures
• Persistent individual bias in a voter model with quenched disorder
• The Hamiltonian Mean Field model: effect of network structure on synchronization dynamics
• Failure of the simultaneous block diagonalization technique applied to complete and cluster synchronization of random networks
• Random subshifts of finite type
• On the role of anaxonic local neurons in the crossover to continuously varying exponents for avalanche activity
• Spectral properties of the hierarchical product of graphs
• Impacts of suppressing guide on information spreading
• The effect of retardation in the random networks of excitable nodes embeddable in the Euclidean space
• The K Shortest Paths Problem with Application to Routing
• Network Extreme Eigenvalue - from Multimodal to Scale-free Network
• Spectral bounds for percolation on directed and undirected graphs
• Testing Simultaneous Diagonalizability
• Neural network spectral robustness under perturbations of the underlying graph
• Switching Checkerboards
• Incremental formation of scale-free fitness networks
• Asymptotics of the spectral radius for directed Chung-Lu random graphs with community structure
• Spectral signatures of structural change in financial networks
• Statistics of the non-zero eigenvalues and singular values of low-rank random matrices with non-negative entries