نتایج جستجو برای: laplacian spectrum of graph
تعداد نتایج: 21193420 فیلتر نتایج به سال:
Given a graph G with vertex set V (G) = V and edge set E(G) = E, let Gl be the line graph and Gc the complement of G. Let G0 be the graph with V (G0) = V and with no edges, G1 the complete graph with the vertex set V , G+ = G and G− = Gc. Let B(G) (Bc(G)) be the graph with the vertex set V ∪E and such that (v, e) is an edge in B(G) (resp., in Bc(G)) if and only if v ∈ V , e ∈ E and vertex v is ...
To some extent, graph evolutionary mechanisms can be explained by its spectra. Here, we are interested in two graph operations, namely, motif (subgraph) doubling and attachment that are biologically relevant. We investigate how these two processes affect the spectrum of the normalized graph Laplacian. A high (algebraic) multiplicity of the eigenvalues 1, 1±0.5, 1± √ 0.5 and others has been obse...
Let G be a graph with n vertices and m edges. The degree sequence of G is denoted by d1 ≥ d2 ≥ · · · ≥ dn. Let A(G) and D(G) = diag(di : 1 ≤ i ≤ n) be the adjacency matrix and the degree diagonal matrix of G, respectively. The Laplacian matrix of G is L(G) = D(G) − A(G). It is well known that L(G) is a symmetric, semidefinite matrix. We assume the spectrum of L(G), or the Laplacian spectrum of ...
This paper examines the system dynamics of a controlled networked multi-agent system, operating with a consensus-type algorithm, that is under the influence of attached node(s). We introduce an identification scheme, involving excitation and observation of the network by the attached node(s), that identifies the spectrum of the underlying system matrix in this case the influenced network’s modi...
A 2-edge-covering between G and H is an onto homomorphism from the vertices of G to the vertices of H so that each edge is covered twice and edges in H can be lifted back to edges in G. In this note we show how to compute the spectrum of G by computing the spectrum of two smaller graphs, namely a (modified) form of the covered graph H and another graph which we term the anti-cover. This is done...
Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacia...
The smallest eigenvalues and the associated eigenvectors (i.e.,eigenpairs) of a graph Laplacian matrix have been widelyused for spectral clustering and community detection. How-ever, in real-life applications the number of clusters or com-munities (say, K) is generally unknown a-priori. Conse-quently, the majority of the existing methods either chooseK heuristically or t...
In this paper we introduce the k’th isoperimetric constant of a directed graph as the minimum of the mean outgoing normalized flows from a given set of k disjoint subsets of the vertex set of the graph. In this direction we show that the second isoperimetric constant in the general setting coincides with (the mean version of) the classical Cheeger constant of the graph, while for the rest of th...
نمودار تعداد نتایج جستجو در هر سال
با کلیک روی نمودار نتایج را به سال انتشار فیلتر کنید