Transition matrixGraph spectraEigenvaluesStrongly regular graphsQuasi-symmetric designsWe give a combinatorial characterization of graphs whose normalized Laplacian has three distinct eigenvalues. Strongly regular graphs and complete bipartite graphs are examples of such graphs, but we also construct more exotic...
normalized Laplacian matrixLet G be a finite group and Γ be a (di)graph. Then Γ is called an n-Cayley (di)graph over G if Aut(Γ) admits a semiregular subgroup isomorphic to G with n orbits on V(Γ). In this paper, we determine the normalized Laplacian polynomial of n-Cayley (...
Normalized LaplacianContractionReplicationDuplicationWe consider the normalized Laplacian matrix for signed graphs and derive interlacing results for its spectrum. In particular, we investigate the effects of several basic graph operations, such as edge removal and addition and vertex contraction, on the ...
Many interesting graphs have rich structure which can help in determining the eigenvalues associated with a particular graph matrix. This survey looks at some common techniques in working with and determining the eigenvalues associated with the normalized Laplacian matrix, in addition to some algebraic ...
For complete clarity, this is how igraph (and most authors) define the Laplacian L of an undirected graph with adjacency matrix A: L=D−A, where D is a diagonal matrix containing the degrees. More precisely, Dii=∑jAij, keeping in mind that A is symmetric. The normalized version is ...
We solve the graph-cut problem using spectral clustering with generalized eigen-decomposition and show that the second smallest eigenvector provides a cutting so- lution since its absolute value indicates the likelihood that a token belongs to a foreground object....
Disease semantic similarity matrix The Disease Ontology (DO) provides open-source ontology for the integration of biomedical data that is associated with human disease [46]. The terms in DO are diseases or ideas of disease-related that are organized in a directed acyclic graph (DAG). Applying ...
基于图论的方法是将基因表达数据的样本视为高维空间中的点其低样本特性决定了构造的矩阵规模较小从而具有较低的运算复针对基因表达数据的小样本特性作者提出一种基于normalizedcut的基因表达数据聚类方法首先以点与点之间的亲近程度构造赋权图通过所得的亲近矩阵和度矩阵构造正规laplacian矩阵进而对laplacian矩阵进行svd分解...
•Wecareabouttwoterms:graphandcuts ? GraphCutBackground GraphCutBackground •Whataregraphs? Nodes •usuallypixels •sometimessamples Edges •weightsassociated(W(i,j)) •E.g.RGBvaluedifference GraphCutBackground •Whatarecuts? •Each“cut”->points,W(I,j) ...
3) Laplacian matrix 拉普拉斯矩阵 1. Then the matrix L(G)=D(G)-A(G) is called the Laplacian matrix of a graph G. 设G=(V,E)是n阶简单连通图,D(G)和A(G)分别表示图G的度对角矩阵和邻接矩阵,则L(G)=D(G)-A(G)称为G的拉普拉斯矩阵。 2. L (G )= D - A is called as the ...