نتایج جستجو برای: spectral graph theory
تعداد نتایج: 1061952 فیلتر نتایج به سال:
The basic inverse problem in spectral graph theory consists in determining the graph given its eigenvalue spectrum. In this paper, we are interested in a network of technological agents whose graph is unknown, communicating by means of a consensus protocol. Recently, the use of artificial noise added to consensus signals has been proposed to reconstruct the unknown graph, although errors are po...
The bottleneck concept in reinforcement learning has played a prominent role in automatically finding temporal abstractions from experience. Lacking significant theory, it has however been regarded by some as being merely a trick. This thesis attempts to gain better intuition about this approach using spectral graph theory. A connection to the theory of Nearly Decomposable Markov Chains is also...
So far, we have been adopting the usual approach to spectral graph theory: understand graphs via the eigenvectors and eigenvalues of associated matrices. For example, given a graph G = (V,E), we defined an adjacency matrix A and considered the eigensystem Av = λv, and we also defined the Laplacian matrix L = D−A and considered the Laplacian quadratic form xTLx− ∑ (ij)∈E(xi−xj). There are other ...
A characteristic of the normalized Laplacian matrix is the possibility for cospectral graphs which do not have the same number of edges. We give a construction of an infinite family of weighted graphs that are pairwise cospectral and which can be transformed into simple graphs. In particular, some of these graphs are cospectral with subgraphs of themselves. In the proof we deconstruct these gra...
We present a framework for categorical shape recognition. The coarse shape of an object is captured by a multiscale blob decomposition, representing the compact and elongated parts of an object at appropriate scales. These parts, in turn, map to nodes in a directed acyclic graph, in which edges encode both semantic relations (parent/child or sibling) as well as geometric relations. Given two im...
Using the technique of semantic mirroring a graph is obtained that represents words and their translations from a parallel corpus or a bilingual lexicon. The connectedness of the graph holds information about the semantic relations of words that occur in the translations. Spectral graph theory is used to partition the graph, which leads to a grouping of the words in different clusters. We illus...
Let H(n; q, n1, n2) be a graph with n vertices containing a cycle Cq and two hanging paths Pn1 and Pn2 attached at the same vertex of the cycle. In this paper, we prove that except for the A-cospectral graphs H(12; 6, 1, 5) and H(12; 8, 2, 2), no two non-isomorphic graphs of the form H(n; q, n1, n2) are A-cospectral. It is proved that all graphs H(n; q, n1, n2) are determined by their L-spectra...
We characterize the distance-regular Ivanov–Ivanov–Faradjev graph from the spectrum, and construct cospectral graphs of the Johnson graphs, Doubled Odd graphs, Grassmann graphs, Doubled Grassmann graphs, antipodal covers of complete bipartite graphs, and many of the Taylor graphs. We survey the known results on cospectral graphs of the Hamming graphs, and of all distance-regular graphs on at mo...
A graph is said to be determined by the adjacency and Laplacian spectrum (or to be a DS graph, for short) if there is no other non-isomorphic graph with the same adjacency and Laplacian spectrum, respectively. It is known that connected graphs of index less than 2 are determined by their adjacency spectrum. In this paper, we focus on the problem of characterization of DS graphs of index less th...
The spectrum of the normalized Laplacian matrix cannot determine the number of edges in a graph, however finding constructions of cospectral graphs with differing number of edges has been elusive. In this paper we use basic properties of twins and scaling to show how to construct such graphs. We also give examples of families of graphs which are cospectral with a subgraph for the normalized Lap...
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