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Journal articles on the topic 'Triangle counting in graphs'

Author: Grafiati

Published: 24 April 2022

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1

Burkhardt, Paul. "Graphing trillions of triangles." Information Visualization 16, no. 3 (September 12, 2016): 157–66. http://dx.doi.org/10.1177/1473871616666393.

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The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.

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2

Sridevi, P. "A Note on Detection of Communities in Social Networks." International Journal of Engineering and Computer Science 9, no. 03 (March 19, 2020): 24978–83. http://dx.doi.org/10.18535/ijecs/v9i03.4452.

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The modern Science of Social Networks has brought significant advances to our understanding of the Structure, dynamics and evolution of the Network. One of the important features of graphs representing the Social Networks is community structure. The communities can be considered as fairly independent components of the social graph that helps identify groups of users with similar interests, locations, friends, or occupations. The community structure is closely tied to triangles and their count forms the basis of community detection algorithms. The present work takes into consideration, a triangle instead of the edge as the basic indicator of a strong relation in the social graph. A simple triangle counting algorithm is then used to evaluate different metrics that are employed to detect strong communities. The methodology is applied to Zachary Social network and discussed. The results bring out the usefulness of counting triangles in a network to detect strong communities in a Social Network.

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3

Cooper, Jeff, and Dhruv Mubayi. "Counting independent sets in triangle-free graphs." Proceedings of the American Mathematical Society 142, no. 10 (June 6, 2014): 3325–34. http://dx.doi.org/10.1090/s0002-9939-2014-12068-5.

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4

Shin, Kijung, Euiwoong Lee, Jinoh Oh, Mohammad Hammoud, and Christos Faloutsos. "CoCoS: Fast and Accurate Distributed Triangle Counting in Graph Streams." ACM Transactions on Knowledge Discovery from Data 15, no. 3 (April 12, 2021): 1–30. http://dx.doi.org/10.1145/3441487.

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Given a graph stream, how can we estimate the number of triangles in it using multiple machines with limited storage? Specifically, how should edges be processed and sampled across the machines for rapid and accurate estimation? The count of triangles (i.e., cliques of size three) has proven useful in numerous applications, including anomaly detection, community detection, and link recommendation. For triangle counting in large and dynamic graphs, recent work has focused largely on streaming algorithms and distributed algorithms but little on their combinations for “the best of both worlds.” In this work, we propose CoCoS , a fast and accurate distributed streaming algorithm for estimating the counts of global triangles (i.e., all triangles) and local triangles incident to each node. Making one pass over the input stream, CoCoS carefully processes and stores the edges across multiple machines so that the redundant use of computational and storage resources is minimized. Compared to baselines, CoCoS is: (a) accurate: giving up to smaller estimation error; (b) fast : up to faster, scaling linearly with the size of the input stream; and (c) theoretically sound : yielding unbiased estimates.

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Xuan, Wei, Huawei Cao, Mingyu Yan, Zhimin Tang, Xiaochun Ye, and Dongrui Fan. "BSR-TC: Adaptively Sampling for Accurate Triangle Counting over Evolving Graph Streams." International Journal of Software Engineering and Knowledge Engineering 31, no. 11n12 (December 2021): 1561–81. http://dx.doi.org/10.1142/s021819402140012x.

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Triangle counting is a fundamental graph mining problem, widely employed in various real-world application scenarios. Given the large scale of graph streams and limited memory space, it is feasible to achieve the estimation of global and local triangles by sampling. Existing streaming algorithms for triangle counting can be generalized into two categories: Reservoir-based methods and Bernoulli-based methods. The former use a fixed memory budget, whose size is difficult to set for accurate estimation without any prior knowledge about graph streams. The latter sample edges by a specified probability, but memory budget is uncontrollable for following a binomial distribution. In this work, we propose a novel and bounded-sampling-ratio algorithm for both global and local triangle counting, called BSR-TC, by adaptively resizing memory budget upwards over evolving graph streams. Specifically, our proposed single-pass BSR-TC can gain more advantage than the state-of-the-art algorithms over the continuous growth of graph streams. Experimental results show that BSR-TC achieves accuracy of at least 99.8% for global triangles, when the ratio of initial memory budget against whole graph streams [Formula: see text] and given [Formula: see text], respectively.

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6

Che, Yulin, Zhuohang Lai, Shixuan Sun, Yue Wang, and Qiong Luo. "Accelerating truss decomposition on heterogeneous processors." Proceedings of the VLDB Endowment 13, no. 10 (June 2020): 1751–64. http://dx.doi.org/10.14778/3401960.3401971.

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Truss decomposition is to divide a graph into a hierarchy of subgraphs, or trusses. A subgraph is a k -truss ( k ≥ 2) if each edge is in at least k --- 2 triangles in the subgraph. Existing algorithms work by first counting the number of triangles each edge is in and then iteratively incrementing k to peel off the edges that will not appear in ( k + 1)-truss. Due to the data and computation intensity, truss decomposition on billion-edge graphs takes hours to complete on a commodity computer. We propose to accelerate in-memory truss decomposition by (1) compacting intermediate results to optimize memory access, (2) dynamically adjusting the computation based on data characteristics, and (3) parallelizing the algorithm on both the multicore CPU and the GPU. In particular, we optimize the triangle enumeration with data skew handling, and determine at runtime whether to pursue peeling or direct triangle counting to obtain a certain k -truss. We further develop a CPU-GPU co-processing strategy in which the CPU first computes intermediate results and sends the compacted results to the GPU for further computation. Our experiments on real-world datasets show that our implementations outperform the state of the art by up to an order of magnitude. Our source code is publicly available at https://github.com/RapidsAtHKUST/AccTrussDecomposition.

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7

Yang, Xu, Chao Song, Mengdi Yu, Jiqing Gu, and Ming Liu. "Distributed Triangle Approximately Counting Algorithms in Simple Graph Stream." ACM Transactions on Knowledge Discovery from Data 16, no. 4 (August 31, 2022): 1–43. http://dx.doi.org/10.1145/3494562.

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Recently, the counting algorithm of local topology structures, such as triangles, has been widely used in social network analysis, recommendation systems, user portraits and other fields. At present, the problem of counting global and local triangles in a graph stream has been widely studied, and numerous triangle counting steaming algorithms have emerged. To improve the throughput and scalability of streaming algorithms, many researches of distributed streaming algorithms on multiple machines are studied. In this article, we first propose a framework of distributed streaming algorithm based on the Master-Worker-Aggregator architecture. The two core parts of this framework are an edge distribution strategy, which plays a key role to affect the performance, including the communication overhead and workload balance, and aggregation method, which is critical to obtain the unbiased estimations of the global and local triangle counts in a graph stream. Then, we extend the state-of-the-art centralized algorithm TRIÈST into four distributed algorithms under our framework. Compared to their competitors, experimental results show that DVHT-i is excellent in accuracy and speed, performing better than the best existing distributed streaming algorithm. DEHT-b is the fastest algorithm and has the least communication overhead. What’s more, it almost achieves absolute workload balance.

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8

Bulteau, Laurent, Vincent Froese, Konstantin Kutzkov, and Rasmus Pagh. "Triangle Counting in Dynamic Graph Streams." Algorithmica 76, no. 1 (July 23, 2015): 259–78. http://dx.doi.org/10.1007/s00453-015-0036-4.

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9

Kolountzakis, Mihail N., Gary L. Miller, Richard Peng, and Charalampos E. Tsourakakis. "Efficient Triangle Counting in Large Graphs via Degree-Based Vertex Partitioning." Internet Mathematics 8, no. 1-2 (March 2012): 161–85. http://dx.doi.org/10.1080/15427951.2012.625260.

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10

Sheshbolouki, Aida, and M. Tamer Özsu. "sGrapp: Butterfly Approximation in Streaming Graphs." ACM Transactions on Knowledge Discovery from Data 16, no. 4 (August 31, 2022): 1–43. http://dx.doi.org/10.1145/3495011.

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We study the fundamental problem of butterfly (i.e., (2,2)-bicliques) counting in bipartite streaming graphs. Similar to triangles in unipartite graphs, enumerating butterflies is crucial in understanding the structure of bipartite graphs. This benefits many applications where studying the cohesion in a graph shaped data is of particular interest. Examples include investigating the structure of computational graphs or input graphs to the algorithms, as well as dynamic phenomena and analytic tasks over complex real graphs. Butterfly counting is computationally expensive, and known techniques do not scale to large graphs; the problem is even harder in streaming graphs. In this article, following a data-driven methodology, we first conduct an empirical analysis to uncover temporal organizing principles of butterflies in real streaming graphs and then we introduce an approximate adaptive window-based algorithm, sGrapp, for counting butterflies as well as its optimized version sGrapp-x. sGrapp is designed to operate efficiently and effectively over any graph stream with any temporal behavior. Experimental studies of sGrapp and sGrapp-x show superior performance in terms of both accuracy and efficiency.

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11

Lv, Tianzi, Huanzhou Li, Zhangguo Tang, Fangzhou Fu, Jian Cao, and Jian Zhang. "Publishing Triangle Counting Histogram in Social Networks Based on Differential Privacy." Security and Communication Networks 2021 (December 15, 2021): 1–16. http://dx.doi.org/10.1155/2021/7206179.

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The continuous expansion of the number and scale of social networking sites has led to an explosive growth of social network data. Mining and analyzing social network data can bring huge economic value and social benefits, but it will result in privacy leakage and other issues. The research focus of social network data publishing is to publish available data while ensuring privacy. Aiming at the problem of low data availability of social network node triangle counting publishing under differential privacy, this paper proposes a privacy protection method of edge triangle counting. First, an edge-removal projection algorithm TSER based on edge triangle count sorting is proposed to obtain the upper bound of sensitivity. Then, two edge triangle count histogram publishing methods satisfying edge difference privacy are given based on the TSER algorithm. Finally, experimental results show that compared with the existing algorithms, the TSER algorithm can retain more triangles in the original graph, reduce the error between the published data and the original data, and improve the published data availability.

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12

Alolaiyan, Hanan, Muhammad Aamir, Awais Yousaf, and Abdul Razaq. "Counting of Distinct Equivalence Classes of Circuits in PSL 2 , Z -Space." Journal of Mathematics 2022 (April 9, 2022): 1–9. http://dx.doi.org/10.1155/2022/4863429.

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Graham Higman was the first who studied the transitive actions of the extended modular group PGL 2 , Z over PL F q = F q ∪ ∞ graphically and named it as coset diagram. In these sorts of graphs, a closed path of edges and triangles is known as a circuit. Coset diagrams evolve through the joining of these circuits. In a coset diagram, a circuit is termed as a length- l circuit if its one vertex is fixed by x 1 x 2 π 1 x 1 x 2 − 1 π 2 x 1 x 2 π 3 , … , x 1 x 2 − 1 π l ∈ PSL 2 , Z , and it is denoted by π 1 , π 2 , π 3 , … , π l . In this study, we shall formulate combinatorial sequences and find the number of distinct equivalence classes of a length-6 circuit π 1 , π 2 , π 3 , π 4 , π 5 , π 6 for a fixed number of triangle Δ of class Π .

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13

COOPER, JEFF, KUNAL DUTTA, and DHRUV MUBAYI. "Counting Independent Sets in Hypergraphs." Combinatorics, Probability and Computing 23, no. 4 (April 8, 2014): 539–50. http://dx.doi.org/10.1017/s0963548314000182.

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Let G be a triangle-free graph with n vertices and average degree t. We show that G contains at least ${\exp\biggl({1-n^{-1/12})\frac{1}{2}\frac{n}{t}\ln t} \biggl(\frac{1}{2}\ln t-1\biggr)\biggr)}$ independent sets. This improves a recent result of the first and third authors [8]. In particular, it implies that as n → ∞, every triangle-free graph on n vertices has at least ${e^{(c_1-o(1)) \sqrt{n} \ln n}}$ independent sets, where $c_1 = \sqrt{\ln 2}/4 = 0.208138 \ldots$. Further, we show that for all n, there exists a triangle-free graph with n vertices which has at most ${e^{(c_2+o(1))\sqrt{n}\ln n}}$ independent sets, where $c_2 = 2\sqrt{\ln 2} = 1.665109 \ldots$. This disproves a conjecture from [8].Let H be a (k+1)-uniform linear hypergraph with n vertices and average degree t. We also show that there exists a constant ck such that the number of independent sets in H is at least ${\exp\biggl({c_{k} \frac{n}{t^{1/k}}\ln^{1+1/k}{t}\biggr})}.$ This is tight apart from the constant ck and generalizes a result of Duke, Lefmann and Rödl [9], which guarantees the existence of an independent set of size $\Omega\biggl(\frac{n}{t^{1/k}} \ln^{1/k}t\biggr).$ Both of our lower bounds follow from a more general statement, which applies to hereditary properties of hypergraphs.

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14

Kolda, Tamara G., Ali Pinar, Todd Plantenga, C. Seshadhri, and Christine Task. "Counting Triangles in Massive Graphs with MapReduce." SIAM Journal on Scientific Computing 36, no. 5 (January 2014): S48—S77. http://dx.doi.org/10.1137/13090729x.

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15

Nagy, Benedek, and Bashar Khassawneh. "On the Number of Shortest Weighted Paths in a Triangular Grid." Mathematics 8, no. 1 (January 13, 2020): 118. http://dx.doi.org/10.3390/math8010118.

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Counting the number of shortest paths in various graphs is an important and interesting combinatorial problem, especially in weighted graphs with various applications. We consider a specific infinite graph here, namely the honeycomb grid. Changing to its dual, the triangular grid, paths between triangle pixels (we abbreviate this term to trixels) are counted. The number of shortest weighted paths between any two trixels of the triangular grid is discussed. For each trixel, there are three different types of neighbor trixels, 1-, 2- and 3-neighbours, depending the Euclidean distance of their midpoints. When considering weighted distances, the positive values α, β and γ are assigned to the ‘steps’ to various neighbors. We gave formulae for the number of shortest weighted paths between any two trixels in various cases by the respective weight values. The results are nicely connected to various numbers well-known in combinatorics, e.g., to binomial coefficients and Fibonacci numbers.

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16

Wu, Bin, Ke Yi, and Zhenguo Li. "Counting Triangles in Large Graphs by Random Sampling." IEEE Transactions on Knowledge and Data Engineering 28, no. 8 (August 1, 2016): 2013–26. http://dx.doi.org/10.1109/tkde.2016.2556663.

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17

Du, Zhihui, Oliver Alvarado Rodriguez, Joseph Patchett, and David A. Bader. "Interactive Graph Stream Analytics in Arkouda." Algorithms 14, no. 8 (July 21, 2021): 221. http://dx.doi.org/10.3390/a14080221.

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Data from emerging applications, such as cybersecurity and social networking, can be abstracted as graphs whose edges are updated sequentially in the form of a stream. The challenging problem of interactive graph stream analytics is the quick response of the queries on terabyte and beyond graph stream data from end users. In this paper, a succinct and efficient double index data structure is designed to build the sketch of a graph stream to meet general queries. A single pass stream model, which includes general sketch building, distributed sketch based analysis algorithms and regression based approximation solution generation, is developed, and a typical graph algorithm—triangle counting—is implemented to evaluate the proposed method. Experimental results on power law and normal distribution graph streams show that our method can generate accurate results (mean relative error less than 4%) with a high performance. All our methods and code have been implemented in an open source framework, Arkouda, and are available from our GitHub repository, Bader-Research. This work provides the large and rapidly growing Python community with a powerful way to handle terabyte and beyond graph stream data using their laptops.

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18

Shin, Kijung, Sejoon Oh, Jisu Kim, Bryan Hooi, and Christos Faloutsos. "Fast, Accurate and Provable Triangle Counting in Fully Dynamic Graph Streams." ACM Transactions on Knowledge Discovery from Data 14, no. 2 (March 7, 2020): 1–39. http://dx.doi.org/10.1145/3375392.

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Arifuzzaman, Shaikh, Maleq Khan, and Madhav Marathe. "Fast Parallel Algorithms for Counting and Listing Triangles in Big Graphs." ACM Transactions on Knowledge Discovery from Data 14, no. 1 (February 4, 2020): 1–34. http://dx.doi.org/10.1145/3365676.

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20

Lee, Dongjin, Kijung Shin, and Christos Faloutsos. "Temporal locality-aware sampling for accurate triangle counting in real graph streams." VLDB Journal 29, no. 6 (August 12, 2020): 1501–25. http://dx.doi.org/10.1007/s00778-020-00624-7.

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21

Chang, Yi-Jun, Seth Pettie, Thatchaphol Saranurak, and Hengjie Zhang. "Near-optimal Distributed Triangle Enumeration via Expander Decompositions." Journal of the ACM 68, no. 3 (May 13, 2021): 1–36. http://dx.doi.org/10.1145/3446330.

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We present improved distributed algorithms for variants of the triangle finding problem in the model. We show that triangle detection, counting, and enumeration can be solved in rounds using expander decompositions . This matches the triangle enumeration lower bound of by Izumi and Le Gall [PODC’17] and Pandurangan, Robinson, and Scquizzato [SPAA’18], which holds even in the model. The previous upper bounds for triangle detection and enumeration in were and , respectively, due to Izumi and Le Gall [PODC’17]. An -expander decomposition of a graph is a clustering of the vertices such that (i) each cluster induces a subgraph with conductance at least and (ii) the number of inter-cluster edges is at most . We show that an -expander decomposition with can be constructed in rounds for any and positive integer . For example, a -expander decomposition only requires rounds to compute, which is optimal up to subpolynomial factors, and a -expander decomposition can be computed in rounds, for any arbitrarily small constant . Our triangle finding algorithms are based on the following generic framework using expander decompositions, which is of independent interest. We first construct an expander decomposition. For each cluster, we simulate algorithms with small overhead by applying the expander routing algorithm due to Ghaffari, Kuhn, and Su [PODC’17] Finally, we deal with inter-cluster edges using recursive calls.

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22

Meleshko, Ye. "МЕТОДИ КЛАСТЕРИЗАЦІЇ ГРАФІВ СОЦІАЛЬНИХ МЕРЕЖ ДЛЯ ПОБУДОВИ РЕКОМЕНДАЦІЙНИХ СИСТЕМ." Системи управління, навігації та зв’язку. Збірник наукових праць 2, no. 54 (April 11, 2019): 129–34. http://dx.doi.org/10.26906/sunz.2019.2.129.

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Предметом вивчення у статті є процес кластеризації графів соціальних мереж. Метою є виявлення методів кластеризації графів соціальних мереж, які можна використати для побудови рекомендаційних систем для соціальних медіа. Завдання: провести дослідження існуючих методів кластеризації графів соціальних мереж та дослідити можливість і доцільність їх використання у рекомендаційних системах. Отримані такі результати: Проведено дослідження існуючих методів кластеризації графів соціальних мереж двох типів, для одержання кластерів, що не перетинаються, та для одержання кластерів, які можуть перетинатися. Досліджено можливість використання розглянутих методів для побудови рекомендаційних систем соціальних медіа. Досліджено можливості графової СУБД Neo4j по реалізації алгоритмів кластеризації графів. Висновки. Було проведено дослідження різних методів клаcтеризації графів соціальних мереж. Розглянуто методи засновані на оптимізації модулярності графу, на розмітці графу та на методах випадкових блукань, також розглянута окрема група методів, що розбиває граф на кластери, які можуть перетинатися. Досліджено можливість та доцільність використання методів кластеризації графів для побудови рекомендаційних систем. Досліджено можливості графової системи управління базами даних Neo4j для реалізації методів кластеризації графів. Встановлено, що Neo4j надає широкі можливості реалізації розглянутих методів. Для виділення кластерів СУБД Neo4j пропонує декілька реалізованих у її бібліотеці Graph algorithms алгоритмів, а саме Louvain, Label Propagation та Triangle Counting. Проведено тестування функцій бібліотеки Graph algorithms, що реалізують алгоритми Louvain, Label Propagation та Triangle Counting у Neo4j. Інші алгоритми кластеризації графів треба, при необхідності, реалізовувати самостійно, але СУБД Neo4j надає багато зручних інструментів для роботи з даними, які можна використати для реалізації різних алгоритмів кластеризації графів меншими зусиллями, ніж без використання Neo4j.

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23

STARK, DUDLEY, and NICK WORMALD. "The Probability of Non-Existence of a Subgraph in a Moderately Sparse Random Graph." Combinatorics, Probability and Computing 27, no. 4 (May 9, 2018): 672–715. http://dx.doi.org/10.1017/s0963548318000202.

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We develop a general procedure that finds recursions for statistics counting isomorphic copies of a graph G0 in the common random graph models ${\cal G}$(n,m) and ${\cal G}$(n,p). Our results apply when the average degrees of the random graphs are below the threshold at which each edge is included in a copy of G0. This extends an argument given earlier by the second author for G0=K3 with a more restricted range of average degree. For all strictly balanced subgraphs G0, our results give much information on the distribution of the number of copies of G0 that are not in large ‘clusters’ of copies. The probability that a random graph in ${\cal G}$(n,p) has no copies of G0 is shown to be given asymptotically by the exponential of a power series in n and p, over a fairly wide range of p. A corresponding result is also given for ${\cal G}$(n,m), which gives an asymptotic formula for the number of graphs with n vertices, m edges and no copies of G0, for the applicable range of m. An example is given, computing the asymptotic probability that a random graph has no triangles for p=o(n−7/11) in ${\cal G}$(n,p) and for m=o(n15/11) in ${\cal G}$(n,m), extending results of the second author.

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24

Pavan, A., Kanat Tangwongsan, Srikanta Tirthapura, and Kun-Lung Wu. "Counting and sampling triangles from a graph stream." Proceedings of the VLDB Endowment 6, no. 14 (September 2013): 1870–81. http://dx.doi.org/10.14778/2556549.2556569.

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25

Benantar, Messaoud, Uḡur Doḡrusöz, Joseph E. Flaherty, and Mukkai S. Krishnamoorthy. "Triangle graphs." Applied Numerical Mathematics 17, no. 2 (May 1995): 85–96. http://dx.doi.org/10.1016/0168-9274(95)00011-i.

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26

Cormode, Graham, and Hossein Jowhari. "A second look at counting triangles in graph streams." Theoretical Computer Science 552 (October 2014): 44–51. http://dx.doi.org/10.1016/j.tcs.2014.07.025.

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27

Cai, Yue, and Catherine Yan. "Counting with Borel’s triangle." Discrete Mathematics 342, no. 2 (February 2019): 529–39. http://dx.doi.org/10.1016/j.disc.2018.10.031.

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Cormode, Graham, and Hossein Jowhari. "A second look at counting triangles in graph streams (corrected)." Theoretical Computer Science 683 (June 2017): 22–30. http://dx.doi.org/10.1016/j.tcs.2016.06.020.

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29

Imrich, Wilfried, Sandi Klavzar, and Henry Martyn Mulder. "Median Graphs and Triangle-Free Graphs." SIAM Journal on Discrete Mathematics 12, no. 1 (January 1999): 111–18. http://dx.doi.org/10.1137/s0895480197323494.

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30

Gnanam, A., and C. Dinesh. "Farey Triangle Graphs and Farey Triangle Matrices." Advances in Pure Mathematics 05, no. 12 (2015): 738–44. http://dx.doi.org/10.4236/apm.2015.512067.

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Khuller, Samir, and Joseph S. B. Mitchell. "On a triangle counting problem." Information Processing Letters 33, no. 6 (February 1990): 319–21. http://dx.doi.org/10.1016/0020-0190(90)90217-l.

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32

de Fraysseix, Hubert, Patrice Ossona de Mendez, and Pierre Rosenstiehl. "On Triangle Contact Graphs." Combinatorics, Probability and Computing 3, no. 2 (June 1994): 233–46. http://dx.doi.org/10.1017/s0963548300001139.

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It is proved that any plane graph may be represented by a triangle contact system, that is a collection of triangular disks which are disjoint except at contact points, each contact point being a node of exactly one triangle. Representations using contacts of T-or Y-shaped objects follow. Moreover, there is a one-to-one mapping between all the triangular contact representations of a maximal plane graph and all its partitions into three Schnyder trees.

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Sidorenko, A. F. "Triangle-free regular graphs." Discrete Mathematics 91, no. 2 (August 1991): 215–17. http://dx.doi.org/10.1016/0012-365x(91)90114-h.

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Büyükçolak, Yasemin, Sibel Özkan, and Didem Gözüpek. "Triangle‐free equimatchable graphs." Journal of Graph Theory 99, no. 3 (September 29, 2021): 461–84. http://dx.doi.org/10.1002/jgt.22750.

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35

McDiarmid, Colin, and Tobias Müller. "Counting disk graphs." Electronic Notes in Discrete Mathematics 38 (December 2011): 627–32. http://dx.doi.org/10.1016/j.endm.2011.10.005.

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36

Urabe, T. "Dynkin graphs, Gabrielov graphs, and triangle singularities." Journal of Mathematical Sciences 82, no. 5 (December 1996): 3721–29. http://dx.doi.org/10.1007/bf02362581.

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Lim, Yongsub, Minsoo Jung, and U. Kang. "Memory-Efficient and Accurate Sampling for Counting Local Triangles in Graph Streams." ACM Transactions on Knowledge Discovery from Data 12, no. 1 (February 23, 2018): 1–28. http://dx.doi.org/10.1145/3022186.

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Miklavič, Štefko, and Martin Milanič. "Equistable graphs, general partition graphs, triangle graphs, and graph products." Discrete Applied Mathematics 159, no. 11 (July 2011): 1148–59. http://dx.doi.org/10.1016/j.dam.2011.03.011.

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Hladký, Jan, Daniel Král', and Sergey Norin. "Counting flags in triangle-free digraphs." Electronic Notes in Discrete Mathematics 34 (August 2009): 621–25. http://dx.doi.org/10.1016/j.endm.2009.07.105.

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Smiley, Leonard M. "A Quick Solution of Triangle Counting." Mathematics Magazine 66, no. 1 (February 1, 1993): 40. http://dx.doi.org/10.2307/2690473.

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Smiley, Leonard M. "A Quick Solution of Triangle Counting." Mathematics Magazine 66, no. 1 (February 1993): 40. http://dx.doi.org/10.1080/0025570x.1993.11996073.

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Hladký, Jan, Daniel Král’, and Sergey Norin. "Counting flags in triangle-free digraphs." Combinatorica 37, no. 1 (June 17, 2016): 49–76. http://dx.doi.org/10.1007/s00493-015-2662-5.

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Dey, T. K., and H. Edelsbrunner. "Counting triangle crossings and halving planes." Discrete & Computational Geometry 12, no. 3 (September 1994): 281–89. http://dx.doi.org/10.1007/bf02574381.

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Pandey, Santosh, Zhibin Wang, Sheng Zhong, Chen Tian, Bolong Zheng, Xiaoye Li, Lingda Li, et al. "Trust: Triangle Counting Reloaded on GPUs." IEEE Transactions on Parallel and Distributed Systems 32, no. 11 (November 1, 2021): 2646–60. http://dx.doi.org/10.1109/tpds.2021.3064892.

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de Castro, Natalia, Francisco Javier Cobos, Juan Carlos Dana, Alberto Marquez, and Marc Noy. "Triangle-Free Planar Graphs and Segment Intersection Graphs." Journal of Graph Algorithms and Applications 6, no. 1 (2002): 7–26. http://dx.doi.org/10.7155/jgaa.00043.

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Sultana, Shaheena, and Md Saidur Rahman. "Realizability of graphs as triangle cover contact graphs." Theoretical Computer Science 720 (April 2018): 24–35. http://dx.doi.org/10.1016/j.tcs.2018.02.027.

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Munaro, Andrea. "On line graphs of subcubic triangle-free graphs." Discrete Mathematics 340, no. 6 (June 2017): 1210–26. http://dx.doi.org/10.1016/j.disc.2017.01.006.

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Mynhardt, Christina M., and Christopher M. van Bommel. "Triangle decompositions of planar graphs." Discussiones Mathematicae Graph Theory 36, no. 3 (2016): 643. http://dx.doi.org/10.7151/dmgt.1882.

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49

Urabe, Tohsuke. "Dynkin graphs and triangle singularities." Kodai Mathematical Journal 17, no. 3 (1994): 395–401. http://dx.doi.org/10.2996/kmj/1138040031.

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50

Chen, Ya-Chen. "Triangle-free Hamiltonian Kneser graphs." Journal of Combinatorial Theory, Series B 89, no. 1 (September 2003): 1–16. http://dx.doi.org/10.1016/s0095-8956(03)00040-6.

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