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Simultaneous Dimensionality and Complexity Model Selection for Spectral Graph Clustering
[article]

2020
*
arXiv
*
pre-print

The first contribution is a probabilistic model which approximates the distribution of the extended

arXiv:1904.02926v4
fatcat:fru3b7fcivf35l6lxbhcox4ffy
*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. ...##
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Spectral properties of complex unit gain graphs

2012
*
Linear Algebra and its Applications
*

We extend some fundamental concepts from

doi:10.1016/j.laa.2011.10.021
fatcat:5uzim2j4lfbg3efs2d2tl7vxpy
*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 ...##
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Graph spectral characterization of the XY model on complex networks

2017
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Physical review. E
*

This work opens new avenues to analyse and characterise dynamics on

doi:10.1103/physreve.96.012312
pmid:29347091
fatcat:bizxpowtcrg3zmvhfoq2totviy
*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 ...##
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CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters
[article]

2018
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arXiv
*
pre-print

The core ingredient of our model is a new class of parametric rational

arXiv:1705.07664v2
fatcat:kgu74rfizzcurkg5ovq45vqi6i
*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. ...##
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Spectral Complexity of Directed Graphs and Application to Structural Decomposition
[article]

2018
*
arXiv
*
pre-print

We introduce a new measure of

arXiv:1808.06004v2
fatcat:xa2vyhsa6ba4vjj66xzufydwfy
*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. ...##
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Graph product multilayer networks: spectral properties and applications

2017
*
Journal of Complex Networks
*

This paper aims to establish theoretical foundations of

doi:10.1093/comnet/cnx042
fatcat:kruvevvcafhhpehdy6svqhcrhu
*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 ...##
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First-principles multiway spectral partitioning of graphs

2014
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Journal of Complex Networks
*

We consider the minimum-cut partitioning of a

doi:10.1093/comnet/cnt021
fatcat:mdbiql3ry5d45mttkbtsbcpqiu
*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. ...##
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Higher rank graphs from cube complexes and their spectral theory
[article]

2021
*
arXiv
*
pre-print

We introduce Ramanujan k-

arXiv:2111.09120v1
fatcat:ea3ygubh4fdbnhdcbbc3tj4s4m
*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*. ...##
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Spectral Lower Bounds on the I/O Complexity of Computation Graphs
[article]

2020
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arXiv
*
pre-print

Executions of

arXiv:1909.09791v2
fatcat:if7i3g3norbhrlupbujmzzakbu
*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. ...##
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Spectral Complexity of Directed Graphs and Application to Structural Decomposition

2019
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Complexity
*

We introduce a new measure of

doi:10.1155/2019/9610826
fatcat:hn32fl37dnd2dlzklqofolm35a
*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. ...##
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Spectral Sufficient Conditions on Pancyclic Graphs

2021
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Complexity
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in terms of the

doi:10.1155/2021/3630245
fatcat:reiksb2q3rfk5lrbk3uhrdne2a
*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. ...##
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A Manifold-Based Dimension Reduction Algorithm Framework for Noisy Data Using Graph Sampling and Spectral Graph

2020
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Complexity
*

Subsequently, the specific range of localities is determined using

doi:10.1155/2020/8954341
fatcat:27hfyl6qrze7hotdssmqnalxre
*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. ...##
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A graph complexity measure based on the spectral analysis of the Laplace operator
[article]

2021
*
arXiv
*
pre-print

In this work we introduce a concept of

arXiv:2109.06706v1
fatcat:mh53alg7v5b4vipcjbl3kpp36a
*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 ...##
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The Limit Spectral Graph in the Semi-Classical Approximation for the Sturm-Liouville Problem With a Complex Polynomial Potential
[article]

2016
*
arXiv
*
pre-print

It is shown that at large parameter values, the eigenvalues are concentrated along the so-called limit

arXiv:1603.08905v2
fatcat:i4yzgx23pbhblcyypnqzi2i2ee
*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). ...##
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Low-Complexity Factor Graph Receivers for Spectrally Efficient MIMO-IDMA

2008
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2008 IEEE International Conference on Communications
*

Gaussian approximations for certain messages propagated through the factor

doi:10.1109/icc.2008.151
dblp:conf/icc/NovakHM08
fatcat:rlnoxorkevexxf6zxuw6tslqrq
*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. ...
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