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Simultaneous Dimensionality and Complexity Model Selection for Spectral Graph Clustering
[article]
2020
arXiv
pre-print
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The first contribution is a probabilistic model which approximates the distribution of the extended spectral embedding of a graph. ...
We illustrate our method via application to a collection of brain graphs. ...
In this paper, we propose a novel simultaneous dimensionality and complexity model selection framework for spectral graph clustering. ...
arXiv:1904.02926v4
fatcat:fru3b7fcivf35l6lxbhcox4ffy
Spectral properties of complex unit gain graphs
2012
Linear Algebra and its Applications
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We extend some fundamental concepts from spectral graph theory to complex unit gain graphs. We define the adjacency, incidence and Laplacian matrices, and study each of them. ...
A complex unit gain graph is a graph where each orientation of an edge is given a complex unit, which is the inverse of the complex unit assigned to the opposite orientation. ...
A T-gain graph (or complex unit gain graph) is a graph with the additional structure that each orientation of an edge is given a complex unit, called a gain, which is the inverse of the complex E-mail ...
doi:10.1016/j.laa.2011.10.021
fatcat:5uzim2j4lfbg3efs2d2tl7vxpy
Graph spectral characterization of the XY model on complex networks
2017
Physical review. E
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This work opens new avenues to analyse and characterise dynamics on complex networks using temporal Graph Signal Analysis. ...
We then use the temporal Graph Signal Transform technique to decompose the time series of the spins on the eigenbasis of the Laplacian. ...
detection error probability behavior § Relations to the phase and phase transition phenomenon § In empty graph and chain graph, : ; (<) never reduces to 0. § In complete graph and lattice graph, there ...
doi:10.1103/physreve.96.012312
pmid:29347091
fatcat:bizxpowtcrg3zmvhfoq2totviy
CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters
[article]
2018
arXiv
pre-print
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The core ingredient of our model is a new class of parametric rational complex functions (Cayley polynomials) allowing to efficiently compute spectral filters on graphs that specialize on frequency bands ...
In this paper, we introduce a new spectral domain convolutional architecture for deep learning on graphs. ...
In this paper we focus on spectral graph CNNs. ...
arXiv:1705.07664v2
fatcat:kgu74rfizzcurkg5ovq45vqi6i
Spectral Complexity of Directed Graphs and Application to Structural Decomposition
[article]
2018
arXiv
pre-print
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We introduce a new measure of complexity (called spectral complexity) for directed graphs. We start with splitting of the directed graph into its recurrent and non-recurrent parts. ...
We show that the total complexity of the graph can then be defined in terms of the spectral complexity, complexities of individual components and edge weights. ...
The following fact on the graph with least spectral complexity is obvious: Fact: The graph with K disconnected nodes has complexity 0. ...
arXiv:1808.06004v2
fatcat:xa2vyhsa6ba4vjj66xzufydwfy
Graph product multilayer networks: spectral properties and applications
2017
Journal of Complex Networks
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This paper aims to establish theoretical foundations of graph product multilayer networks (GPMNs), a family of multilayer networks that can be obtained as a graph product of two or more factor networks ...
SPECTRAL PROPERTIES OF NONSIMPLE GPMNS In this paper, we aim to extend the definitions of GPMNs to make them capable of capturing a greater variety of complex networks. ...
SIMPLE GRAPH PRODUCT MULTILAYER NETWORKS AND THEIR SPECTRAL PROPERTIES We define graph product multilayer networks (GPMNs) as a particular family of multilayer networks that can be obtained by applying ...
doi:10.1093/comnet/cnx042
fatcat:kruvevvcafhhpehdy6svqhcrhu
First-principles multiway spectral partitioning of graphs
2014
Journal of Complex Networks
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We consider the minimum-cut partitioning of a graph into more than two parts using spectral methods. ...
defined by the leading eigenvectors of the graph Laplacian. ...
SPECTRAL BISECTION The term spectral bisection refers to the special case in which we partition a graph into exactly k = 2 parts. ...
doi:10.1093/comnet/cnt021
fatcat:mdbiql3ry5d45mttkbtsbcpqiu
Higher rank graphs from cube complexes and their spectral theory
[article]
2021
arXiv
pre-print
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We introduce Ramanujan k-graphs satisfying optimal spectral gap property, and show explicitly how to construct such k-graphs. ...
Guided by geometric insight, we obtain several new series of k-graphs using cube complexes covered by Cartesian products of trees, for k ≥ 3. ...
Spectral theory of k-graphs. ...
arXiv:2111.09120v1
fatcat:ea3ygubh4fdbnhdcbbc3tj4s4m
Spectral Lower Bounds on the I/O Complexity of Computation Graphs
[article]
2020
arXiv
pre-print
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Executions of complex computations can be formalized as an evaluation order over the underlying computation graph. ...
This spectral bound is not only efficiently computable by power iteration, but can also be computed in closed form for graphs with known spectra. ...
This spectral bound is efficiently computable and can be applied to arbitrarily large and complex graphs. For graphs with known spectra, this bound can also be computed in closed form. ...
arXiv:1909.09791v2
fatcat:if7i3g3norbhrlupbujmzzakbu
Spectral Complexity of Directed Graphs and Application to Structural Decomposition
2019
Complexity
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We introduce a new measure of complexity (called spectral complexity) for directed graphs. We start with splitting of the directed graph into its recurrent and nonrecurrent parts. ...
We show that the total complexity of the graph can then be defined in terms of the spectral complexity, complexities of individual components, and edge weights. ...
The following fact on the graph with least spectral complexity is obvious: Fact. The graph with disconnected nodes has spectral complexity 0. ...
doi:10.1155/2019/9610826
fatcat:hn32fl37dnd2dlzklqofolm35a
Spectral Sufficient Conditions on Pancyclic Graphs
2021
Complexity
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in terms of the spectral radius and the signless Laplacian spectral radius of the graph. ...
Because the spectrum of graphs is convenient to be calculated, in this study, we try to use the spectral theory of graphs to study this problem and give some sufficient conditions for a graph to be pancyclic ...
Laplacian spectral radius conditions for a graph to be pancyclic. ...
doi:10.1155/2021/3630245
fatcat:reiksb2q3rfk5lrbk3uhrdne2a
A Manifold-Based Dimension Reduction Algorithm Framework for Noisy Data Using Graph Sampling and Spectral Graph
2020
Complexity
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Subsequently, the specific range of localities is determined using graph spectral analysis, and the density within each local range is estimated to obtain the distribution parameters. ...
The proposed framework follows the idea of the localization of manifolds and uses graph sampling to determine some local anchor points from the given data. ...
A spectral graph is a special type of spectral analysis. e spectral analysis itself is based on the frequency domain where a signal is characterized by its spectral coefficient or spectral energy. ...
doi:10.1155/2020/8954341
fatcat:27hfyl6qrze7hotdssmqnalxre
A graph complexity measure based on the spectral analysis of the Laplace operator
[article]
2021
arXiv
pre-print
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In this work we introduce a concept of complexity for undirected graphs in terms of the spectral analysis of the Laplacian operator defined by the incidence matrix of the graph. ...
Second, complexity of complementary graphs coincide. ...
In order to introduce our definition of spectral complexity of a graph, let us set Z to denote the null graph, i.e w ij = 0 for every i, j = 1, ..., n and F the complete graph i.e w ij = 1 for every i ...
arXiv:2109.06706v1
fatcat:mh53alg7v5b4vipcjbl3kpp36a
The Limit Spectral Graph in the Semi-Classical Approximation for the Sturm-Liouville Problem With a Complex Polynomial Potential
[article]
2016
arXiv
pre-print
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It is shown that at large parameter values, the eigenvalues are concentrated along the so-called limit spectral graph; the curves forming this graph are classified. ...
The limit distribution of the discrete spectrum of the Sturm-Liouville problem with complex-valued polynomial potential on an interval, on a half-axis, and on the entire axis is studied. ...
On the right: Limit spectral graph (red). Example 2. Limit spectral set (red); examples of singular and critical curves which are not essential singular and not essential critical (black). ...
arXiv:1603.08905v2
fatcat:i4yzgx23pbhblcyypnqzi2i2ee
Low-Complexity Factor Graph Receivers for Spectrally Efficient MIMO-IDMA
2008
2008 IEEE International Conference on Communications
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Gaussian approximations for certain messages propagated through the factor graph lead to a complexity that scales only linearly with the number of users. ...
In this paper, we consider a MIMO-IDMA system with increased spectral efficiency due to the use of higher-order symbol constellations. ...
The complex transmit symbol x [n] ∈ S with the one-to-one symbol mapping χ. We will refer to c
III. FACTOR GRAPH AND MESSAGES We next derive a factor graph for an iterative MIMO-IDMA receiver. ...
doi:10.1109/icc.2008.151
dblp:conf/icc/NovakHM08
fatcat:rlnoxorkevexxf6zxuw6tslqrq
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