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Stochastic consensus problems for linear time-invariant multi-agent systems over Markovian switching networks with time-varying delays and topology uncertainties are dealt with. By using the linear matrix inequality method and the stability theory of Markovian jump linear system, we show that consensus can be achieved for appropriate time delays and topology uncertainties which are not caused by the Markov process, provided the union of topologies associated with the positive recurrent states of the Markov process admits a spanning tree and the agent dynamics is stabilizable. Feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time-varying delays. Numerical examples are given to show the feasibility of theoretical results. [ABSTRACT FROM AUTHOR]

The average consensus in continuous-time multi-agent systems with dynamically changing topologies and multiple time-varying delays is studied in this paper. The network topology is captured by weighted digraphs which are weakly connected and balanced. Some feasible linear matrix inequalities are established to determine the allowable upper bounds of multiple delays that guarantee the average consensus of the system. Numerical examples are provided to show the usefulness of the theoretical results. [ABSTRACT FROM AUTHOR]

• A growing simplicial network model is proposed to study higher-order interactions. • Degree and clique distributions are analytically derived. • Sombor index and its computation are compared with known bounds. • Power-law and small-word effect of the network are observed. • The scaling constant for Sombor index is determined for the model. Many dynamical effects in biology, social and technological complex systems have recently revealed their relevance to group interactions beyond traditional dyadic relationships between individual units. In this paper, we propose a growing simplicial network to model the higher-order interactions represented by clique structures. We analytically study the degree distribution and clique distribution of the network model. As an important degree-based topological index, Sombor index of the model has been derived in an iterative manner and an approximation method with closed expression is proposed. Moreover, we observe power-law and small-word effect for the simplicial networks and examine the effectiveness of the approximation method for Sombor index through computational experiments. We discover the scaling constant for Sombor index with the evolution of the network when the initial seed network is modeled as an Erdős-Rényi random graph. Our findings suggest the relevance and potential applicability of simplicial networks in modelling higher-order interactions in complex networked systems. [ABSTRACT FROM AUTHOR]

Abstract: Analytical description of disease propagation on random networks has become one of the most productive fields in recent years, yet more complex contact patterns and dynamics have been resorted to numerical study. In this paper, an epidemic model is defined in which each individual, once infected, has chances to recover from infection at certain rate. The chance is represented by a parameter . This model can be viewed as an interpolation between classical SI model () and SIR model (). We develop a low-dimensional system of non-linear ordinary differential equations to model the mixed susceptible-infected (-recovered) SI (R) epidemics on random network with general degree distributions. Both the final size of epidemics and the time-dependent behaviors are derived within this simple framework. In addition, we present the exact transmissibility and the epidemic threshold for this model. [Copyright &y& Elsevier]

• This paper studies the distance Laplacian spectral ordering of sun type graphs. • The distance Laplacian eigenvalues and energies of sun and partial sun graphs are obtained. • The partial sun graphs can be ordered based on their second-largest distance Laplacian eigenvalue. • Sun type graphs can be ordered based on their distance Laplacian energies. Let G be a simple, connected graph of order n. Its distance Laplacian energy D L E (G) is given by D L E (G) = ∑ i = 1 n | ρ i L − 2 W (G) n | , where ρ 1 L ≥ ρ 2 L ≥ ⋯ ≥ ρ n L are the distance Laplacian eigenvalues and W (G) is the Wiener index of G. Distance Laplacian eigenvalues of sun and partial sun graphs have been characterized. We order the partial sun graphs by using their second largest distance Laplacian eigenvalue. Moreover, the distance Laplacian energy of sun and partial sun graphs have been derived in this paper. These graphs are also ordered by using their distance Laplacian energies. [ABSTRACT FROM AUTHOR]