Normalized Laplacian matrixGraph energyGeneral Randić indexIn this paper, we consider the energy of a simple graph with respect to its normalized Laplacian eigenvalues, which we call the L-energy. Over graphs of order n that contain no isolated vertices, we characterize the graphs with minimal ...
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 ...
We 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 Laplacian eigenvalues. We also study vertex ...
In these expressions, the matrix L is the normalized Laplacian whose elements are given by Lij = D − A/s, where si = ∑jAij is a node’s degree or weighted degree and D is the degree diagonal matrix (a square matrix the elements of s along its diagonal). The ...
. . , vn the corresponding (normalized) eigenvectors. In this paper we propose to...E. Bozzo and M. Franceschet, "Approximations of the general- ized inverse of the graph Laplacian matrix," Internet Mathemat- ics, vol. 8, no. 4, pp. 456-481, 2012....
图中,a)是150个输入点,b)是150个Normalized Laplacian矩阵的特征向量,其中1-50是聚成堆状的50个点对应的特征向量。c)显示了采用高斯加权的欧氏距离计算相似度时,参数的不同取值对应两个cluster之间的距离。d)e)f)比较了两种算法的性能度量。 我的想法: ...
定义二(拉普拉斯矩阵,Laplacian Matrix): 给定一个图 ,其邻接矩阵为 ,其拉普拉斯矩阵定义为 ,其中度矩阵 。 定义三(对称归一化的拉普拉斯矩阵,Symmetric normalized Laplacian): 给定一个图 ,其邻接矩阵为 ,其规范化的拉普拉斯矩阵定义为 二、复现代码 举个小栗子,给出如下的矩阵: ...
The spirit of the approach is similar to the one adopted in spectral methods for dimensionality reduction, where a lossy representation of a network is obtained by suppressing an arbitrary number of eigencomponents of a graph operator (e.g., combinatorial and normalized Laplacians, adjacency matrix...
In this paper, we investigate the Laplacian, i.e., the normalized Laplacian tensor of a k-uniform hypergraph. We show that the real parts of all the eigenvalues of the Laplacian are in the interval [0,2], and the real part is zero (respectively two) if and only if the eigenvalue is...
where the functions r are the normalized response of a predator to the abundance of a certain prey population. The factors in front of the normalized functions are expressed in terms of scale parameters, the interpretation of which are listed in Table 2. Apart from the α, which are the bio...