The many facets of the Estrada indices of graphs and networks

DOI10.1007/s40324-021-00275-wzbMath1484.05046OpenAlexW3208594009MaRDI QIDQ2128861

Ernesto Estrada

Publication date: 22 April 2022

Published in: S\(\vec{\text{e}}\)MA Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40324-021-00275-w

zbMATH Keywords

matrix functionsalgebraic graph theorycomplex networkseigenvalues of graphsEstrada indices

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Small world graphs, complex networks (graph-theoretic aspects) (05C82) Random graphs (graph-theoretic aspects) (05C80) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Inequalities involving eigenvalues and eigenvectors (15A42) Distance in graphs (05C12) Signed and weighted graphs (05C22) Matrix exponential and similar functions of matrices (15A16) Graphical indices (Wiener index, Zagreb index, Randi? index, etc.) (05C09) Chemical graph theory (05C92)

Related Items

The trace and Estrada index of uniform hypergraphs with cut vertices ⋮ Estrada index of dynamic random graphs ⋮ XT<scp>race</scp>: Making the Most of Every Sample in Stochastic Trace Estimation ⋮ Communicability cosine distance: similarity and symmetry in graphs/networks ⋮ Every nonsingular spherical Euclidean distance matrix is a resistance distance matrix

Uses Software

• mftoolbox

Cites Work

• Lower bounds for Estrada Index
• On the laplacian estrada index of a graph
• More on the Laplacian Estrada index
• Spectral criterion for cycle balance in networks
• Algebraic Graph Theory
• The Physics of Solids
• Exploring the “Middle Earth” of network spectra via a Gaussian matrix function
• Novel Bounds for the Normalized Laplacian Estrada and Normalized Energy Index of Graphs
• Mittag--Leffler Functions and their Applications in Network Science
• Estimating the distance Estrada index
• On the energy and Estrada index of Cayley graphs
• An Introduction to Mathematical Epidemiology
• Inequalities for Graph Eigenvalues
• Collective dynamics of ‘small-world’ networks
• Tetracyclic graphs with maximal Estrada index
• THE NORMALIZED LAPLACIAN ESTRADA INDEX OF GRAPHS
• Functions of Matrices
• On the maximum Laplacian Estrada index of graphs
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Estrada index of cactus graphs
• New lower bounds for Estrada index
• A fractional order recovery SIR model from a stochastic process
• The Laplacian energy and Laplacian Estrada index of random multipartite graphs
• On the number of spanning trees, the Laplacian eigenvalues, and the Laplacian Estrada index of subdivided-line graphs
• On the calculation of functions of matrices
• The Estrada index of unicyclic graphs
• Path Laplacian matrices: introduction and application to the analysis of consensus in networks
• Characterizing graphs with maximal Laplacian Estrada index
• Maximum Estrada index of bicyclic graphs
• A generic model for a single strain mosquito-transmitted disease with memory on the host and the vector
• Mathematics of epidemics on networks. From exact to approximate models
• Accounting for the role of long walks on networks via a new matrix function
• The Estrada index of trees
• New upper bounds for estrada index of bipartite graphs
• On the Estrada and Laplacian Estrada indices of graphs
• Bounds of the Estrada index of graphs
• Use of the Szeged index and the revised Szeged index for measuring network bipartivity
• On Estrada index of trees
• Bounds on the estrada index of ISR (4,6)-fullerenes
• Finding and counting given length cycles
• Tricyclic graph with maximal Estrada index
• Spektren endlicher Grafen
• Instability of Hagen-Poiseuille flow for non-axisymmetric mode
• Double Gaussianization of graph spectra
• On the Estrada index conjecture
• The Estrada index of chemical trees
• Mathematical epidemiology.
• A little statistical mechanics for the graph theorist
• Lower bounds for Estrada index and Laplacian Estrada index
• Quadrature rule-based bounds for functions of adjacency matrices
• Feasibility conditions for the existence of walk-regular graphs
• Relaxing the uniformity and independence assumptions using the concept of fractal dimension
• A mathematical bibliography of signed and gain graphs and allied areas
• Diffusion processes on fractal fields: Heat kernel estimates and large deviations
• Dynamical analysis of a fractional SIR model with birth and death on heterogeneous complex networks
• Gaussianization of the spectra of graphs and networks. Theory and applications
• Computing the matrix Mittag-Leffler function with applications to fractional calculus
• Dynamical systems associated with adjacency matrices
• Laplacian spectral moment and Laplacian Estrada index of random graphs
• Generalized walks-based centrality measures for complex biological networks
• On the signless Laplacian Estrada index of cacti
• Some properties on Estrada index of folded hypercubes networks
• Walk entropy and walk-regularity
• Further results on distance estrada index of random graphs
• Parallel empirical pseudopotential electronic structure calculations for million atom systems
• The role of fractional calculus in modeling biological phenomena: a review
• Extremal graphs for Estrada indices
• Fractional-order susceptible-infected model: definition and applications to the study of COVID-19 main protease
• Vertex distinction with subgraph centrality: a proof of Estrada's conjecture and some generalizations
• Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order
• A note on some bounds of the \(\alpha\)-Estrada index of graphs
• On the energy and Estrada index of strongly quotient graphs
• Graph characteristics from the heat kernel trace
• A note on new bounds for the Estrada index
• An increasing sequence of lower bounds for the Estrada index of graphs and matrices
• Rethinking structural balance in signed social networks
• Lower bounds for Gaussian Estrada index of graphs
• Network bipartivity and the transportation efficiency of European passenger airlines
• Estimating the Estrada index
• Estrada index of random bipartite graphs
• Reaction, diffusion and non-local interaction
• Walk entropies in graphs
• Lower bounds for the Estrada index using mixing time and Laplacian spectrum
• A note on walk entropies in graphs
• Graph theory and statistical physics
• Functions of matrices
• Graphs with maximum Laplacian and signless Laplacian Estrada index
• A new status index derived from sociometric analysis
• A note lower bounds for the Estrada index
• Wavefronts in traffic flows and crowds dynamics
• Random Graphs and Complex Networks
• ESTRADA INDEX OF GENERAL WEIGHTED GRAPHS
• More on Laplacian Estrada indices of trees
• Distance Estrada index of random graphs
• Random Walks and Heat Kernels on Graphs
• More on the normalized Laplacian Estrada index
• The normalized Laplacian Estrada index of a graph
• Network Properties Revealed through Matrix Functions
• Perturbation results for the Estrada index in weighted networks
• On the Estrada index of graphs with given number of cut edges
• Emergence of Scaling in Random Networks
• Laplacian Estrada index of trees
• Lower bounds for the Estrada index