Epidemics have so far been mostly studied in undirected networks. However, many real-world networks, such as the online social network Twitter and the world wide web, on which information, emotion, or malware spreads, are directed networks, composed of both unidirectional links and bidirectional links. We define the directionality ξ as the percentage of unidirectional links. The epidemic thresh...

Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to {+, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefficients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.

The ε-pseudospectral abscissa and radius of an n × n matrix are respectively the maximal real part and the maximal modulus of points in its ε-pseudospectrum, defined using the spectral norm. Existing techniques compute these quantities accurately but the cost is multiple singular value decompositions and eigenvalue decompositions of order n, making them impractical when n is large. We present n...

For any 1-dimensional simplicial complex G defined by a finite simple graph, the hydrogen identity |H| = L−L−1 holds, where |H| = (|d| + |d|∗)2 is the sign-less Hodge Laplacian defined by the sign-less incidence matrix |d| and where L is the connection Laplacian. Having linked the Laplacian spectral radius ρ of G with the spectral radius of the adjacency matrix its connection graph G′ allows fo...

In this paper we propose a new method of parameter space design for robust control synthesis, in particular in terms of real stability radius, using quantifier elimination (QE). We also aim at practicality by employing the scheme to combine the sign definition condition (SDC) and a special QE algorithm using Sturm-Habicht sequence. The validity of our approach is confirmed by some concrete exam...

Let G be a simple connected graph with pendant vertex set ∂V and nonpendant vertex set V0. The signless Laplacian matrix of G is denoted by Q(G). The signless Dirichlet eigenvalue is a real number λ such that there exists a function f ̸= 0 on V (G) such that Q(G)f(u) = λf(u) for u ∈ V0 and f(u) = 0 for u ∈ ∂V . The signless Dirichlet spectral radius λ(G) is the largest signless Dirichlet eigenva...