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On the computability of graphons [article]

Nathanael L. Ackerman, Jeremy Avigad, Cameron E. Freer, Daniel M. Roy, Jason M. Rute
2018 arXiv   pre-print
We investigate the relative computability of exchangeable binary relational data when presented in terms of the distribution of an invariant measure on graphs, or as a graphon in either L^1 or the cut  ...  We also provide an example of an L^1-computable random-free graphon that is not weakly isomorphic to any graphon with an a.e. continuous version.  ...  Work on this publication was made possible through the support of United States Air Force Office of Scientific Research (AFOSR) Contract No.  ... 
arXiv:1801.10387v1 fatcat:5vg7wxb52rc7jjq476jqa2zt3a

The asymptotics of large constrained graphs

Charles Radin, Kui Ren, Lorenzo Sadun
2014 Journal of Physics A: Mathematical and Theoretical  
We show, through local estimates and simulation, that if one constrains simple graphs by their densities ε of edges and τ of triangles, then asymptotically (in the number of vertices) for over 95% of the  ...  Furthermore the four parameters c, g_11, g_22 and g_12 are smooth functions of (ε,τ) except at two smooth 'phase transition' curves.  ...  The computational codes involved in this research were developed and debugged on the computational cluster of the Mathematics Department of UT Austin.  ... 
doi:10.1088/1751-8113/47/17/175001 fatcat:jx6ym4kzzfb2zezllv3n5zcb4q

Assessment of approaches for dispersive forces employing graphone as a case study [article]

Magdalena Birowska, Maciej Marchwiany, Claudia Draxl, Jacek. A. Majewski
2020 arXiv   pre-print
We have studied two interchange layer systems, (i) free standing partly hydrogenated graphene (graphone), and (ii) graphone on the Nickel (111) surface, to assess various density functional theory based  ...  On the other hand, it turns out that the adsorption of hydrogen layer to graphene is stronger in the presence of the metallic surface.  ...  It is clearly seen that for graphone on Ni(111) the C − C bonds are elongated and C − H bonds shortened, independently on the computational scheme employed.  ... 
arXiv:1707.09795v2 fatcat:rxekdfx7wbdr3kltude5m7hmga

Smoothing Graphons for Modelling Exchangeable Relational Data [article]

Xuhui Fan, Yaqiong Li, Ling Chen, Bin Li, Scott A. Sisson
2020 arXiv   pre-print
We then develop the Latent Feature Smoothing Graphon (LFSG), which improves on the ISG by introducing auxiliary hidden labels to decompose the calculation of the ISG intensity and enable efficient inference  ...  Experimental results on real-world data sets validate the advantages of applying smoothing strategies to the Stochastic Block Model, demonstrating that smoothing graphons can greatly improve AUC and precision  ...  graphons. • We improve on the ISG by devising the LFSG, which achieves the same objective of generating continuous intensity values but without sacrificing computation efficiency.  ... 
arXiv:2002.11159v1 fatcat:4qgsuc7khrbgzmrtdcsempi7aq

Centrality measures for graphons: Accounting for uncertainty in networks [article]

Marco Avella-Medina and Francesca Parise and Michael T. Schaub and Santiago Segarra
2018 arXiv   pre-print
The same concentration inequalities also provide high-probability bounds between the graphon centrality functions and the centrality measures on any sampled graph, thereby establishing a measure of uncertainty  ...  The same concentration inequalities also provide high-probability bounds between the graphon centrality functions and the centrality measures on any sampled graph, thereby establishing a measure of uncertainty  ...  Our main contribution is to show that, based on the inferred graphon, one can compute a latent centrality profile of the nodes that we term graphon centrality function.  ... 
arXiv:1707.09350v4 fatcat:mjs65googrfznhiebsoihj57ry

Classification on Large Networks: A Quantitative Bound via Motifs and Graphons [article]

Andreas Haupt, Mohammad Khatami, Thomas Schultz, Ngoc Mai Tran
2017 arXiv   pre-print
Via graphon theory, we give an explicit quantitative bound for the ability of motif homomorphisms to distinguish large networks under both generative and sampling noise.  ...  This results in an easily computable classifier on graph data with theoretical performance guarantee.  ...  In other words, if one could compute the homomorphism densities of all motifs, then one can distinguish two convergent sequences of large graphs.  ... 
arXiv:1710.08878v1 fatcat:hzipimquy5bglmkbuiq5ptkdqe

The phases of large networks with edge and triangle constraints

Richard Kenyon, Charles Radin, Kui Ren, Lorenzo Sadun
2017 Journal of Physics A: Mathematical and Theoretical  
Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs.  ...  We support simulation evidence with mathematical proof of continuity and discontinuity for many of the phase transitions.  ...  Acknowledgments The main computational results were obtained on the computational facilities in the Texas Super Computing Center (TACC). We gratefully acknowledge this computational support.  ... 
doi:10.1088/1751-8121/aa8ce1 fatcat:r3twymtw2jdwhdxzidvewhmwpu

The Graphon Fourier Transform [article]

Luana Ruiz, Luiz F. O. Chamon, Alejandro Ribeiro
2019 arXiv   pre-print
This result is demonstrated in two numerical experiments where, as expected, the GFT converges, hinting to the possibility of centralizing analysis and design on graphons to leverage transferability.  ...  We define graphon signals and introduce the Graphon Fourier Transform (WFT), to which the Graph Fourier Transform (GFT) is shown to converge.  ...  PROOF OF LEMMA 1 The proof follows by direct computation.  ... 
arXiv:1910.10195v2 fatcat:zpxbvk35fvddnkalhafzci6f3e

Graphon based Clustering and Testing of Networks: Algorithms and Theory [article]

Mahalakshmi Sabanayagam, Leena Chennuru Vankadara, Debarghya Ghoshdastidar
2021 arXiv   pre-print
We prove the statistical consistency of both algorithms under Lipschitz assumptions on the graph degrees.  ...  We propose a novel graph distance based on sorting-and-smoothing graphon estimators.  ...  Figure 8 : 8 Computation time of algorithms on different sets of simulated data for four clusters case demonstrating the scalability of each algorithm. Computation time is plotted in log scale.  ... 
arXiv:2110.02722v2 fatcat:ph7yb2bqe5hqdogpvllyonil6a

Estimation of exchangeable graph models by stochastic blockmodel approximation

Stanley H. Chan, Thiago B. Costa, Edoardo M. Airoldi
2013 2013 IEEE Global Conference on Signal and Information Processing  
We consider a non-parametric perspective of analyzing network data. Our goal is to seek a limiting object of a sequence of exchangeable random arrays called the graphon.  ...  We propose a numerically efficient algorithm for estimating graphons and we show that the proposed algorithm yields a consistent estimate as the size of the graph grows.  ...  Future work will be focused on theoretical aspects of the SBA algorithm and applications of the graphon. Example 2 ( 2 Stochastic Block Models).  ... 
doi:10.1109/globalsip.2013.6736873 dblp:conf/globalsip/ChanCA13 fatcat:e3yc6jj6tvg25h6h5hno75uv64

Increase and Conquer: Training Graph Neural Networks on Growing Graphs [article]

Juan Cervino, Luana Ruiz, Alejandro Ribeiro
2021 arXiv   pre-print
Leveraging the graphon -- the limit object of a graph -- in this paper we consider the problem of learning a graphon neural network (WNN) -- the limit object of a GNN -- by training GNNs on graphs sampled  ...  Bernoulli from the graphon.  ...  In practice, the gradients on the right hand side of ( 13 ) cannot be computed because, being a theoretical limit object, the graphon W is unknown.  ... 
arXiv:2106.03693v2 fatcat:oqar7blbdvfktms5sruxxskjm4

On clustering network-valued data [article]

Soumendu Sundar Mukherjee, Purnamrita Sarkar, Lizhen Lin
2017 arXiv   pre-print
networks by associating a computationally feasible feature vector to each network based on trace of powers of the adjacency matrix.  ...  Community detection, which focuses on clustering nodes or detecting communities in (mostly) a single network, is a problem of considerable practical interest and has received a great deal of attention  ...  This is achieved by first obtaining a graphon estimate of each of the networks, constructing a distance matrix based on the graphon estimates, and then performing spectral clustering on the resulting distance  ... 
arXiv:1606.02401v3 fatcat:o6e7p6idffg7lddfg7xeihvo3q

Peculiar pressure effect on Poisson ratio of graphone as a strain damper

Qing Peng, Albert K. Dearden, Xiao-Jia Chen, Chen Huang, Xiaodong Wen, Suvranu De
2015 Nanoscale  
Abnormal increase in the Poisson ratio of graphone in response to an increase in pressure.  ...  Computational resources were provided by Rensselaer Polytechnic Institute through AMOS, the IBM Blue Gene/Q system at the Center for Computational Innovations.  ...  The authors would like to acknowledge the generous financial support from the Defense Threat Reduction Agency (DTRA) Grant # BRBAA08-C-2-0130 and # HDTRA1-13-1-0025.  ... 
doi:10.1039/c4nr07665f pmid:25853996 fatcat:t5swhj4iw5aa3air4xrnpibmsq

One Side-Graphene Hydrogenation (Graphone): Substrate Effects [article]

Cristiano Francisco Woellner, Pedro Alves da Silva Autreto, and Douglas S. Galvao
2016 arXiv   pre-print
We investigated the structural and dynamical aspects of the hydrogenation of graphene membranes (one-side hydrogenation, the so called graphone structure) on different substrates (graphene, few-layers  ...  Our results also show that a significant number of randomly distributed H clusters are formed during the early stages of the hydrogenation process, regardless of the type of substrate and temperature.  ...  Computational and financial support from the Center for Computational Engineering and Sciences at Unicamp through the FAPESP/CEPID Grant No. 2013/08293-7 is also acknowledged.  ... 
arXiv:1601.04484v1 fatcat:l7wnybavdzcztfez3y5cghxqay

Simulation of hydrogenated graphene field-effect transistors through a multiscale approach

G. Fiori, S. Lebègue, A. Betti, P. Michetti, M. Klintenberg, O. Eriksson, G. Iannaccone
2010 Physical Review B  
to compute ballistic transport in transistors based on functionalized graphene.  ...  graphene (i.e. graphone).  ...  ACKNOWLEDGMENTS The work was supported in part by the EC Seventh  ... 
doi:10.1103/physrevb.82.153404 fatcat:l6arjnsmpndo5hfn4u6bon2qya
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