Journal articles: 'Statistical graphs'

1

Haigh, William E. "Statistical Graphs and Logo." School Science and Mathematics 89, no. 3 (March 1989): 228–38. http://dx.doi.org/10.1111/j.1949-8594.1989.tb11914.x.

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Nowicki, Krzysztof. "Asymptotic Poisson distributions with applications to statistical analysis of graphs." Advances in Applied Probability 20, no. 02 (June 1988): 315–30. http://dx.doi.org/10.1017/s0001867800016992.

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Various types of graph statistics for graphs and digraphs are presented as numerators of incompleteU-statistics, with symmetric and asymmetric kernels, respectively. Thus, asymptotic Poisson limits of these statistics are provided by using limit theorems for the sums of dissociated random variables. Several applications to statistical analysis of graphs are given.

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Nowicki, Krzysztof. "Asymptotic Poisson distributions with applications to statistical analysis of graphs." Advances in Applied Probability 20, no. 2 (June 1988): 315–30. http://dx.doi.org/10.2307/1427392.

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Various types of graph statistics for graphs and digraphs are presented as numerators of incomplete U-statistics, with symmetric and asymmetric kernels, respectively. Thus, asymptotic Poisson limits of these statistics are provided by using limit theorems for the sums of dissociated random variables. Several applications to statistical analysis of graphs are given.

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Ghafouri, Saeid, and Seyed Hossein Khasteh. "A survey on exponential random graph models: an application perspective." PeerJ Computer Science 6 (April 6, 2020): e269. http://dx.doi.org/10.7717/peerj-cs.269.

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The uncertainty underlying real-world phenomena has attracted attention toward statistical analysis approaches. In this regard, many problems can be modeled as networks. Thus, the statistical analysis of networked problems has received special attention from many researchers in recent years. Exponential Random Graph Models, known as ERGMs, are one of the popular statistical methods for analyzing the graphs of networked data. ERGM is a generative statistical network model whose ultimate goal is to present a subset of networks with particular characteristics as a statistical distribution. In the context of ERGMs, these graph’s characteristics are called statistics or configurations. Most of the time they are the number of repeated subgraphs across the graphs. Some examples include the number of triangles or the number of cycle of an arbitrary length. Also, any other census of the graph, as with the edge density, can be considered as one of the graph’s statistics. In this review paper, after explaining the building blocks and classic methods of ERGMs, we have reviewed their newly presented approaches and research papers. Further, we have conducted a comprehensive study on the applications of ERGMs in many research areas which to the best of our knowledge has not been done before. This review paper can be used as an introduction for scientists from various disciplines whose aim is to use ERGMs in some networked data in their field of expertise.

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Burda, Zdzisław, Jerzy Jurkiewicz, and André Krzywicki. "Statistical mechanics of random graphs." Physica A: Statistical Mechanics and its Applications 344, no. 1-2 (December 2004): 56–61. http://dx.doi.org/10.1016/j.physa.2004.06.087.

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LEWANDOWSKY, STEPHAN, and IAN SPENCE. "The Perception of Statistical Graphs." Sociological Methods & Research 18, no. 2-3 (November 1989): 200–242. http://dx.doi.org/10.1177/0049124189018002002.

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Hosamani, S. M., V. B. Awati, and R. M. Honmore. "On graphs with equal dominating and c-dominating energy." Applied Mathematics and Nonlinear Sciences 4, no. 2 (December 24, 2019): 503–12. http://dx.doi.org/10.2478/amns.2019.2.00047.

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AbstractGraph energy and domination in graphs are most studied areas of graph theory. In this paper we try to connect these two areas of graph theory by introducing c-dominating energy of a graph G. First, we show the chemical applications of c-dominating energy with the help of well known statistical tools. Next, we obtain mathematical properties of c-dominating energy. Finally, we characterize trees, unicyclic graphs, cubic and block graphs with equal dominating and c-dominating energy.

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Livingston, Mark A., Laura Matzen, Derek Brock, Andre Harrison, and Jonathan W. Decker. "Testing the Value of Salience in Statistical Graphs." Electronic Imaging 2021, no. 1 (January 18, 2021): 329–1. http://dx.doi.org/10.2352/issn.2470-1173.2021.1.vda-329.

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Expert advice and conventional wisdom say that important information within a statistical graph should be more salient than the other components. If readers are able to find relevant information quickly, in theory, they should perform better on corresponding response tasks. To our knowledge, this premise has not been thoroughly tested. We designed two types of salient cues to draw attention to task-relevant information within statistical graphs. One type primarily relied on text labels and the other on color highlights. The utility of these manipulations was assessed with groups of questions that varied from easy to hard. We found main effects from the use of our salient cues. Error and response time were reduced, and the portion of eye fixations near the key information increased. An interaction between the cues and the difficulty of the questions was also observed. In addition, participants were given a baseline skills test, and we report the corresponding effects. We discuss our experimental design, our results, and implications for future work with salience in statistical graphs.

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Salti, Dror, and Yakir Berchenko. "Random Intersection Graphs and Missing Data." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 5579–85. http://dx.doi.org/10.1609/aaai.v34i04.6010.

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Random-graphs and statistical inference with missing data are two separate topics that have been widely explored each in its field. In this paper we demonstrate the relationship between these two different topics and take a novel view of the data matrix as a random intersection graph. We use graph properties and theoretical results from random-graph theory, such as connectivity and the emergence of the giant component, to identify two threshold phenomena in statistical inference with missing data: loss of identifiability and slower convergence of algorithms that are pertinent to statistical inference such as expectation-maximization (EM). We provide two examples corresponding to these threshold phenomena and illustrate the theoretical predictions with simulations that are consistent with our reduction.

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Sudev, N. K., K. P. Chithra, K. A. Germina, S. Satheesh, and Johan Kok. "On certain coloring parameters of Mycielski graphs of some graphs." Discrete Mathematics, Algorithms and Applications 10, no. 03 (June 2018): 1850030. http://dx.doi.org/10.1142/s1793830918500301.

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Coloring the vertices of a graph [Formula: see text] according to certain conditions can be considered as a random experiment and a discrete random variable [Formula: see text] can be defined as the number of vertices having a particular color in the proper coloring of [Formula: see text]. The concepts of mean and variance, two important statistical measures, have also been introduced to the theory of graph coloring and determined the values of these parameters for a number of standard graphs. In this paper, we discuss the coloring parameters of the Mycielskian of certain standard graphs.

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Ruelle, David. "Graph-Counting Polynomials for Oriented Graphs." Journal of Statistical Physics 173, no. 2 (August 21, 2018): 243–48. http://dx.doi.org/10.1007/s10955-018-2137-3.

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Wilks, Allan R. "Constraint-Based Representations of Statistical Graphs." Journal of Computational and Graphical Statistics 5, no. 4 (December 1996): 400. http://dx.doi.org/10.2307/1390892.

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Chindelevitch, Leonid, Po-Ru Loh, Ahmed Enayetallah, Bonnie Berger, and Daniel Ziemek. "Assessing statistical significance in causal graphs." BMC Bioinformatics 13, no. 1 (2012): 35. http://dx.doi.org/10.1186/1471-2105-13-35.

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Karr, Alan F. "Random Graphs for Statistical Pattern Recognition." Journal of the American Statistical Association 101, no. 475 (September 2006): 1317. http://dx.doi.org/10.1198/jasa.2006.s134.

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Seaver, William L. "Random Graphs for Statistical Pattern Recognition." Technometrics 47, no. 1 (February 2005): 96. http://dx.doi.org/10.1198/tech.2005.s826.

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Priebe, Carey E., Daniel L. Sussman, Minh Tang, and Joshua T. Vogelstein. "Statistical Inference on Errorfully Observed Graphs." Journal of Computational and Graphical Statistics 24, no. 4 (October 2, 2015): 930–53. http://dx.doi.org/10.1080/10618600.2014.951049.

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Wilks, Allan R. "Constraint-Based Representations of Statistical Graphs." Journal of Computational and Graphical Statistics 5, no. 4 (December 1996): 400–414. http://dx.doi.org/10.1080/10618600.1996.10474720.

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GIBERT, JAUME, ERNEST VALVENY, and HORST BUNKE. "EMBEDDING OF GRAPHS WITH DISCRETE ATTRIBUTES VIA LABEL FREQUENCIES." International Journal of Pattern Recognition and Artificial Intelligence 27, no. 03 (May 2013): 1360002. http://dx.doi.org/10.1142/s0218001413600021.

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Graph-based representations of patterns are very flexible and powerful, but they are not easily processed due to the lack of learning algorithms in the domain of graphs. Embedding a graph into a vector space solves this problem since graphs are turned into feature vectors and thus all the statistical learning machinery becomes available for graph input patterns. In this work we present a new way of embedding discrete attributed graphs into vector spaces using node and edge label frequencies. The methodology is experimentally tested on graph classification problems, using patterns of different nature, and it is shown to be competitive to state-of-the-art classification algorithms for graphs, while being computationally much more efficient.

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Ivakin, Y., and S. Potapichev. "ALGORITHM OF BIOGRAPHICAL HYPOTHESES TESTING BASED ON GEOCHRONOLOGICAL TRACKING." Telecom IT 7, no. 1 (2019): 60–74. http://dx.doi.org/10.31854/2307-1303-2019-7-1-60-74.

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Research subject. Information technology of the geochronological tracking is an assembly of processes that accumulate and integrate data about geographic relocation of historical figures for a given time interval and represent the results as a generalizing graph in GIS. Method. Hypotheses on the stable tendencies in migration could be represented as the above graph’s sub-graphs. Such tendencies testing would be reduced to the search and evaluation of the statistical significance for the matching graphs’ isomorphism. Full-featured development of computer interpretation of the graph theory methods based on geochronological tracking provides new quality of historical research using modern GIS-tools. Practical relevance. Namely, researcher can use the quantitative methods of the corresponding logical-analytical apparatus. The proposed paper deals with a consideration of qualitatively new possibilities of such an approach and the corresponding algorithmic apparatus.

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Höfler, Michael, Tanja Brückl, Antje Bittner, and Roselind Lieb. "Visualizing Multivariate Dependencies with Association Chain Graphs." Methodology 3, no. 1 (January 2007): 24–34. http://dx.doi.org/10.1027/1614-2241.3.1.24.

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In a recent paper, a new type of graph to visualize the results from graphical models was proposed. Association chain graphs (ACGs) provide a richer visualization than conventional graphs (directed acyclic and recursive regression graphs) if the data can be described with only a small number of parameters. ACGs display not only which associations reach statistical significance, but also the magnitude of associations (confidence intervals for statistical main effects) as the contrast color to the background color of the graph. In this paper, the ACG visualization is extended especially for the case where all variables are binary by illustrating their relative frequencies. This shows the degrees of associations not only on the individual (as expressed by odds ratios or other indexes of association) but also on the community level. We applied the approach to an extensive example of birth and childhood factors for the onset of affective mental disorders using data from the EDSP (Early Developmental Stages of Psychopathology) Study.

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Ghoniem, Mohammad, Jean-Daniel Fekete, and Philippe Castagliola. "On the Readability of Graphs Using Node-Link and Matrix-Based Representations: A Controlled Experiment and Statistical Analysis." Information Visualization 4, no. 2 (May 12, 2005): 114–35. http://dx.doi.org/10.1057/palgrave.ivs.9500092.

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In this article, we describe a taxonomy of generic graph related tasks along with a computer-based evaluation designed to assess the readability of two representations of graphs: matrix-based representations and node-link diagrams. This evaluation encompasses seven generic tasks and leads to insightful recommendations for the representation of graphs according to their size and density. Typically, we show that when graphs are bigger than twenty vertices, the matrix-based visualization outperforms node-link diagrams on most tasks. Only path finding is consistently in favor of node-link diagrams throughout the evaluation.

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Hilton, N. Zoe, Elke Ham, Kevin L. Nunes, Nicole C. Rodrigues, Cairina Frank, and Michael C. Seto. "Using Graphs to Improve Violence Risk Communication." Criminal Justice and Behavior 44, no. 5 (September 22, 2016): 678–94. http://dx.doi.org/10.1177/0093854816668916.

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We examined the use of graphs as an aid to communicating statistical risk among forensic clinicians. We first tested four graphs previously used or recommended for forensic risk assessment among 442 undergraduate students who made security recommendations about two offenders whose risk differed by one actuarial category of risk for violent recidivism (Study 1). Effective decision making was defined as actuarially higher risk offenders being assigned to greater security than lower risk offenders. The graph resulting in the largest distinction among less numerate students was a probability bar graph. We then tested this graph among 54 forensic clinicians (Study 2). The graph had no overall effect. Among more experienced staff, however, decisions were insensitive to actuarial risk in the absence of the graph and in the desirable direction with the addition of the graph. Further research into the benefit of graphs in violence risk communication appears viable.

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An, Byung Hee, and Tomasz Maciazek. "Geometric Presentations of Braid Groups for Particles on a Graph." Communications in Mathematical Physics 384, no. 2 (April 28, 2021): 1109–40. http://dx.doi.org/10.1007/s00220-021-04095-x.

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AbstractWe study geometric presentations of braid groups for particles that are constrained to move on a graph, i.e. a network consisting of nodes and edges. Our proposed set of generators consists of exchanges of pairs of particles on junctions of the graph and of certain circular moves where one particle travels around a simple cycle of the graph. We point out that so defined generators often do not satisfy the braiding relation known from 2D physics. We accomplish a full description of relations between the generators for star graphs where we derive certain quasi-braiding relations. We also describe how graph braid groups depend on the (graph-theoretic) connectivity of the graph. This is done in terms of quotients of graph braid groups where one-particle moves are put to identity. In particular, we show that for 3-connected planar graphs such a quotient reconstructs the well-known planar braid group. For 2-connected graphs this approach leads to generalisations of the Yang–Baxter equation. Our results are of particular relevance for the study of non-abelian anyons on networks showing new possibilities for non-abelian quantum statistics on graphs.

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Agarwal, Shubhangi, Sourav Dutta, and Arnab Bhattacharya. "ChiSeL." Proceedings of the VLDB Endowment 13, no. 10 (June 2020): 1654–68. http://dx.doi.org/10.14778/3401960.3401964.

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Subgraph querying is one of the most important primitives in many applications. Although the field is well studied for deterministic graphs, in many situations, the graphs are probabilistic in nature. In this paper, we address the problem of subgraph querying in large probabilistic labeled graphs. We employ a novel algorithmic framework, called ChiSeL, that uses the idea of statistical significance for approximate subgraph matching on uncertain graphs that have uncertainty in edges. For each candidate matching vertex in the target graph that matches a query vertex, we compute its statistical significance using the chi-squared statistic. The search algorithm then proceeds in a greedy manner by exploring the vertex neighbors having the largest chi-square score. In addition to edge uncertainty, we also show how ChiSeL can handle uncertainty in labels and/or vertices. Experiments on large real-life graphs show the efficiency and effectiveness of our algorithm.

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Khoroshkin, Anton, Thomas Willwacher, and Marko Živković. "Differentials on graph complexes II: hairy graphs." Letters in Mathematical Physics 107, no. 10 (May 8, 2017): 1781–97. http://dx.doi.org/10.1007/s11005-017-0964-9.

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Grothendieck, John, Carey E. Priebe, and Allen L. Gorin. "Statistical inference on attributed random graphs: Fusion of graph features and content." Computational Statistics & Data Analysis 54, no. 7 (July 2010): 1777–90. http://dx.doi.org/10.1016/j.csda.2010.01.017.

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Lauritzen, Steffen, Alessandro Rinaldo, and Kayvan Sadeghi. "On Exchangeability in Network Models." Journal of Algebraic Statistics 10, no. 1 (April 10, 2019): 85–114. http://dx.doi.org/10.18409/jas.v10i1.73.

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We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their implications, between statistical network models that are finitely exchangeable and models that define a consistent sequence of probability distributions on graphs of increasing size.

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Isaacs, Andrew C., and Catherine Randall Kelso. "Pictures, Tables, Graphs, and Questions: Statistical Processes." Teaching Children Mathematics 2, no. 6 (February 1996): 340–45. http://dx.doi.org/10.5951/tcm.2.6.0340.

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In an address to the American Association for the Advancement of Science, John Dewey (1910) contrasted the facts of science with the method of science and argued that the method, rather than the facts, should he preeminent in the school curriculum.

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Majka, Arkadiusz, and Wojciech Wiślicki. "Statistical thermodynamics for choice models on graphs." Physica A: Statistical Mechanics and its Applications 337, no. 3-4 (June 2004): 645–63. http://dx.doi.org/10.1016/j.physa.2004.01.063.

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Switsur, Roy. "Statistical Quality Control Graphs in Radiocarbon Dating." Radiocarbon 32, no. 3 (1990): 347–54. http://dx.doi.org/10.1017/s0033822200012996.

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d'Auriac, J. C. Anglès, M. Preissmann, and A. Sebö. "Optimal cuts in graphs and statistical mechanics." Mathematical and Computer Modelling 26, no. 8-10 (October 1997): 1–11. http://dx.doi.org/10.1016/s0895-7177(97)00195-7.

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Garren, Steven. "Fast Graphs of Statistical Distributions Using R." Archives of Current Research International 5, no. 4 (January 10, 2016): 1–9. http://dx.doi.org/10.9734/acri/2016/29429.

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Barra, Adriano, and Elena Agliari. "Equilibrium statistical mechanics on correlated random graphs." Journal of Statistical Mechanics: Theory and Experiment 2011, no. 02 (February 18, 2011): P02027. http://dx.doi.org/10.1088/1742-5468/2011/02/p02027.

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Joardar, Soumalya, and Arnab Mandal. "Quantum symmetry of graph C∗-algebras associated with connected graphs." Infinite Dimensional Analysis, Quantum Probability and Related Topics 21, no. 03 (September 2018): 1850019. http://dx.doi.org/10.1142/s0219025718500194.

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We define a notion of quantum automorphism groups of graph [Formula: see text]-algebras for finite, connected graphs. Under the assumption that the underlying graph does not have any multiple edge or loop, the quantum automorphism group of the underlying directed graph in the sense of Banica [Quantum automorphism groups of homogeneous graphs, J. Funct. Anal. 224 (2005) 243–280] (which is also the symmetry object in the sense of [S. Schmidt and M. Weber, Quantum symmetry of graph [Formula: see text]-algebras, arXiv:1706.08833 ] is shown to be a quantum subgroup of quantum automorphism group in our sense. Quantum symmetries for some concrete graph [Formula: see text]-algebras have been computed.

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Hora, Akihito. "Central Limit Theorems and Asymptotic Spectral Analysis on Large Graphs." Infinite Dimensional Analysis, Quantum Probability and Related Topics 01, no. 02 (April 1998): 221–46. http://dx.doi.org/10.1142/s0219025798000144.

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Regarding the adjacency matrix of a graph as a random variable in the framework of algebraic or noncommutative probability, we discuss a central limit theorem in which the size of a graph grows in several patterns. Various limit distributions are observed for some Cayley graphs and some distance-regular graphs. To obtain the central limit theorem of this type, we make combinatorial analysis of mixed moments of noncommutative random variables on one hand, and asymptotic analysis of spectral structure of the graph on the other hand.

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Hurts, Karel. "The Effect of Configural Graphs on Concurrent and Retrospective Performance." Proceedings of the Human Factors and Ergonomics Society Annual Meeting 40, no. 23 (October 1996): 1160–64. http://dx.doi.org/10.1177/154193129604002303.

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Following up on a previous study showing the performance on integrated tasks for non-configural graphs to be superior to that for configural graphs if the memory for the graph is tested (retrospective or memory-based conditions), this paper further contrasts retrospective and concurrent (display-based) task performance. This was done by experimentally investigating the effect of various configural and non-configural static graphs on integrated task performance (requiring the consideration of lower-level graph information as well as higher-level graph information), using both retrospective and concurrent conditions. Subjects were asked to answer a question about each graph, which was phrased in terms of the domain of the data and which could not be easily anticipated. Graphs also differed in the amount of fit between graph structure and data structure (data-graph compatibility). The results confirmed the expectation that the reversal effect (inferior performance for configural graphs) is only found under memory-based conditions. Both display-based and memory-based performance were better for the configural graphs with high data-graph compatibility, although only significantly so for display-based search time. The two separable types of graphs could only be compared with respect to the amount of time needed to memorize the graphs: longer times were found for the graph type with low data-graph compatibility. However, the latter effect may also be due to a difference in data structure complexity, as this factor was confounded with data-graph compatibility in the two separable graph types. Although more research is needed to disambiguate some of the present results and to make other and better comparisons, the results of this study still show the importance of structural and semantic factors in determining the effectiveness of configurality in statistical graphs.

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Chen, Hanlin, Renfang Wu, Guihua Huang, and Hanyuan Deng. "Dimer–monomer model on the Towers of Hanoi graphs." International Journal of Modern Physics B 29, no. 23 (September 17, 2015): 1550173. http://dx.doi.org/10.1142/s0217979215501738.

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The number of dimer–monomers (matchings) of a graph [Formula: see text] is an important graph parameter in statistical physics. Following recent research, we study the asymptotic behavior of the number of dimer–monomers [Formula: see text] on the Towers of Hanoi graphs and another variation of the Sierpiński graphs which is similar to the Towers of Hanoi graphs, and derive the recursion relations for the numbers of dimer–monomers. Upper and lower bounds for the entropy per site, defined as [Formula: see text], where [Formula: see text] is the number of vertices in a graph [Formula: see text], on these Sierpiński graphs are derived in terms of the numbers at a certain stage. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of the entropy can be evaluated with more than a hundred significant figures accuracy.

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Sharma, Sudhansh. "Graphs for Research." Global Journal of Enterprise Information System 7, no. 1 (March 1, 2015): 59. http://dx.doi.org/10.18311/gjeis/2015/3037.

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Graph transforms raw data into information, nowadays the electronic environment leads to exponential data growth rate. To analyze such voluminous data, Big Data Analytics is the upcoming field, where Graphs plays dominant role. Further, in any research, this graphical representation of the data strengthens the data analysis to a great extent. Business Data Analytics uses statistical techniques to a great extent; the outcomes of such techniques are generally represented in the form of graphs for better interpretation and analysis. In this paper after studying lots of research work from various disciplines, a brief report of the various types of graphs is prepared along with their area of application and possible alternative techniques. The work performed in this paper is domain independent, and the outcome of the performed work will help to strengthen the research in all disciplines and domain.

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Arizmendi, Octavio, and Tulio Gaxiola. "On the spectral distribution of distance-k graph of free product graphs." Infinite Dimensional Analysis, Quantum Probability and Related Topics 19, no. 03 (August 31, 2016): 1650017. http://dx.doi.org/10.1142/s021902571650017x.

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We calculate the distribution with respect to the vacuum state of the distance-[Formula: see text] graph of a [Formula: see text]-regular tree. From this result we show that the distance-[Formula: see text] graph of a [Formula: see text]-regular graphs converges to the distribution of the distance-[Formula: see text] graph of a regular tree. Finally, we prove that, properly normalized, the asymptotic distributions of distance-[Formula: see text] graphs of the [Formula: see text]-fold free product graph, as [Formula: see text] tends to infinity, is given by the distribution of [Formula: see text], where [Formula: see text] is a semicirlce random variable and [Formula: see text] is the [Formula: see text]th Chebychev polynomial.

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Mitic, Vojislav V., Branislav Randjelovic, Ivana Ilic, Srdjan Ribar, An-Lu Chun, Aleksandar Stajcic, and Branislav Vlahovic. "The 3D graph approach for breakdown voltage calculation in BaTiO3 ceramics." International Journal of Modern Physics B 35, no. 07 (March 6, 2021): 2150103. http://dx.doi.org/10.1142/s0217979221501034.

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After pioneering attempts for the introduction of graph theory in the field of ceramics and microstructures, where 1D and 2D graphs were used, in this paper we applied 3D graphs for the breakdown voltage calculation in BaTiO3 sample with some predefined constraints. We have described the relations between grains in the sample and established a mathematical approach for the calculation of breakdown voltage using experimental results. As a result, we introduced mapping between the property of sample and grain structure, then between the grain structure and mathematical graph, using various crystal structures. The main idea was to apply 3D graph theory for the distribution of electronic parameters between the neighboring grains. With this study, we successfully confirmed the possibilities for applications of graphs as a tool for the determination of properties even at the intergranular level.

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Wartan, Hasmeek. "Use of graphs in the statistical modeling process." JOURNAL OF EDUCATION AND SCIENCE 27, no. 1 (March 1, 2014): 142–57. http://dx.doi.org/10.33899/edusj.2014.162138.

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Martinez, Wendy L. "Book Review: Random graphs for statistical pattern recognition." Statistical Methods in Medical Research 14, no. 5 (October 2005): 532–33. http://dx.doi.org/10.1177/096228020501400514.

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Schmidt, Christian, Nils-Eric Guenther, and Lenka Zdeborová. "Circular coloring of random graphs: statistical physics investigation." Journal of Statistical Mechanics: Theory and Experiment 2016, no. 8 (August 24, 2016): 083303. http://dx.doi.org/10.1088/1742-5468/2016/08/083303.

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Arteaga, Pedro, Danilo Díaz-Levicoy, and Carmen Batanero. "Chilean Primary School Children’s Understanding of Statistical Graphs." Acta Scientiae 22, no. 5 (September 17, 2020): 2–24. http://dx.doi.org/10.17648/acta.scientiae.5884.

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Korepanov, I. G., D. V. Talalaev, and G. I. Sharygin. "Integrable 3D Statistical Models on Six-Valent Graphs." Proceedings of the Steklov Institute of Mathematics 302, no. 1 (August 2018): 198–216. http://dx.doi.org/10.1134/s008154381806010x.

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Chertkov, Michael, and Vladimir Y. Chernyak. "Loop series for discrete statistical models on graphs." Journal of Statistical Mechanics: Theory and Experiment 2006, no. 06 (June 14, 2006): P06009. http://dx.doi.org/10.1088/1742-5468/2006/06/p06009.

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NETTLETON, DAVID F., and VICENÇ TORRA. "DATA PRIVACY FOR SIMPLY ANONYMIZED SOCIAL NETWORK LOGS REPRESENTED AS GRAPHS – CONSIDERATIONS FOR GRAPH ALTERATION OPERATIONS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 19, supp01 (December 2011): 107–25. http://dx.doi.org/10.1142/s0218488511007374.

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In this paper we review the state of the art on graph privacy with special emphasis on applications to online social networks, and we consider some novel aspects which have not been greatly covered in the specialized literature on graph privacy. The following key considerations are covered: (i) choice of different operators to modify the graph; (ii) information loss based on the cost of graph operations in terms of statistical characteristics (degree, clustering coefficient and path length) in the original graph; (iii) computational cost of the operations; (iv) in the case of the aggregation of two nodes, the choice of similar adjacent nodes rather than isomorphic topologies, in order to maintain the overall structure of the graph; (v) a statistically knowledgeable attacker who is able to search for regions of a simply anonymized graph based on statistical characteristics and map those onto a given node and its immediate neighborhood.

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Priebe, Carey E., Youngser Park, David J. Marchette, John M. Conroy, John Grothendieck, and Allen L. Gorin. "Statistical inference on attributed random graphs: Fusion of graph features and content: An experiment on time series of Enron graphs." Computational Statistics & Data Analysis 54, no. 7 (July 2010): 1766–76. http://dx.doi.org/10.1016/j.csda.2010.01.008.

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LEE, HUN HEE, and NOBUAKI OBATA. "DISTANCE-k GRAPHS OF HYPERCUBE AND q-HERMITE POLYNOMIALS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 16, no. 02 (June 2013): 1350011. http://dx.doi.org/10.1142/s0219025713500112.

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Maciążek, Tomasz, and Adam Sawicki. "Non-abelian Quantum Statistics on Graphs." Communications in Mathematical Physics 371, no. 3 (October 9, 2019): 921–73. http://dx.doi.org/10.1007/s00220-019-03583-5.

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Abstract We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of particles constrained to move in a topological space X. The framework involves a study of isomorphism classes of flat complex vector bundles over the configuration space of X which can be achieved by determining its homology groups. We apply this methodology for configuration spaces of graphs. As a conclusion, we provide families of graphs which are good candidates for studying simple effective models of anyon dynamics as well as models of non-abelian anyons on networks that are used in quantum computing. These conclusions are based on our solution of the so-called universal presentation problem for homology groups of graph configuration spaces for certain families of graphs.

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Journal articles on the topic 'Statistical graphs'

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