Journal articles: 'Directed graphs'

1

Zelinka, Bohdan. "Small directed graphs as neighbourhood graphs." Czechoslovak Mathematical Journal 38, no. 2 (1988): 269–73. http://dx.doi.org/10.21136/cmj.1988.102221.

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Zelinka, Bohdan. "Distances between directed graphs." Časopis pro pěstování matematiky 112, no. 4 (1987): 359–67. http://dx.doi.org/10.21136/cpm.1987.108565.

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3

Bauer, Frank. "Normalized graph Laplacians for directed graphs." Linear Algebra and its Applications 436, no. 11 (June 2012): 4193–222. http://dx.doi.org/10.1016/j.laa.2012.01.020.

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4

de Graaf, M., A. Schrijver, and P. D. Seymour. "Directed triangles in directed graphs." Discrete Mathematics 110, no. 1-3 (December 1992): 279–82. http://dx.doi.org/10.1016/0012-365x(92)90719-v.

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5

de Graaf, Maurits. "Directed triangles in directed graphs." Discrete Mathematics 280, no. 1-3 (April 2004): 219–23. http://dx.doi.org/10.1016/j.disc.2003.11.002.

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6

Schwarz, Štefan. "Common consequents in directed graphs." Czechoslovak Mathematical Journal 35, no. 2 (1985): 212–47. http://dx.doi.org/10.21136/cmj.1985.102012.

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7

Zelinka, Bohdan. "Circular distance in directed graphs." Mathematica Bohemica 122, no. 2 (1997): 113–19. http://dx.doi.org/10.21136/mb.1997.125917.

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8

Alsardary, Salar Y. "A note on small directed graphs as neighborhood graphs." Czechoslovak Mathematical Journal 44, no. 4 (1994): 577–78. http://dx.doi.org/10.21136/cmj.1994.128492.

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Quinn, Christopher J., Negar Kiyavash, and Todd P. Coleman. "Directed Information Graphs." IEEE Transactions on Information Theory 61, no. 12 (December 2015): 6887–909. http://dx.doi.org/10.1109/tit.2015.2478440.

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10

Manoussakis, Yannis. "Directed hamiltonian graphs." Journal of Graph Theory 16, no. 1 (March 1992): 51–59. http://dx.doi.org/10.1002/jgt.3190160106.

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11

Wang, Hong. "Disjoint directed cycles in directed graphs." Discrete Mathematics 343, no. 8 (August 2020): 111927. http://dx.doi.org/10.1016/j.disc.2020.111927.

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12

Pardo-Guerra, Sebastian, Vivek Kurien George, Vikash Morar, Joshua Roldan, and Gabriel Alex Silva. "Extending Undirected Graph Techniques to Directed Graphs via Category Theory." Mathematics 12, no. 9 (April 29, 2024): 1357. http://dx.doi.org/10.3390/math12091357.

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We use Category Theory to construct a ‘bridge’ relating directed graphs with undirected graphs, such that the notion of direction is preserved. Specifically, we provide an isomorphism between the category of simple directed graphs and a category we call ‘prime graphs category’; this has as objects labeled undirected bipartite graphs (which we call prime graphs), and as morphisms undirected graph morphisms that preserve the labeling (which we call prime graph morphisms). This theoretical bridge allows us to extend undirected graph techniques to directed graphs by converting the directed graphs into prime graphs. To give a proof of concept, we show that our construction preserves topological features when applied to the problems of network alignment and spectral graph clustering.

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13

Zelinka, Bohdan. "Edge-domatic numbers of directed graphs." Czechoslovak Mathematical Journal 45, no. 3 (1995): 449–55. http://dx.doi.org/10.21136/cmj.1995.128531.

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14

Gutierrez, Marisa, and Silvia B. Tondato. "On Models of Directed Path Graphs Non Rooted Directed Path Graphs." Graphs and Combinatorics 32, no. 2 (August 9, 2015): 663–84. http://dx.doi.org/10.1007/s00373-015-1600-z.

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15

Kalampakas, Antonios, and Stefanos Spartalis. "Hyperoperations on directed graphs." Journal of Discrete Mathematical Sciences and Cryptography 27, no. 3 (2024): 1011–25. http://dx.doi.org/10.47974/jdmsc-1714.

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We analyze three hyper-operations derived from directed graphs, demonstrate the influence of the underlying graph structure on these hyper-operations and study the algebraic properties of the related classes of graphs. The paper also illustrates the relationship between directed graphs and hyper-structures using graph hyper-operations. In addition, we investigate the property of commutativity for an appropriate type of hyper-groupoids and its relationship to properties of directed graphs. Therefore, the paper consists of three sections, section one introduces and investigates three distinct hyper-groupoids derived from hyperoperations on directed graphs, section two discusses the fundamental ideas of directed graphs, and section three elaborates on path, simple path, and ancestry hyper-operations.

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16

Duval, Art M. "A directed graph version of strongly regular graphs." Journal of Combinatorial Theory, Series A 47, no. 1 (January 1988): 71–100. http://dx.doi.org/10.1016/0097-3165(88)90043-x.

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17

Sardellitti, Stefania, Sergio Barbarossa, and Paolo Di Lorenzo. "On the Graph Fourier Transform for Directed Graphs." IEEE Journal of Selected Topics in Signal Processing 11, no. 6 (September 2017): 796–811. http://dx.doi.org/10.1109/jstsp.2017.2726979.

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18

Fan, Shaohua, Shuyang Zhang, Xiao Wang, and Chuan Shi. "Directed Acyclic Graph Structure Learning from Dynamic Graphs." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 6 (June 26, 2023): 7512–21. http://dx.doi.org/10.1609/aaai.v37i6.25913.

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Estimating the structure of directed acyclic graphs (DAGs) of features (variables) plays a vital role in revealing the latent data generation process and providing causal insights in various applications. Although there have been many studies on structure learning with various types of data, the structure learning on the dynamic graph has not been explored yet, and thus we study the learning problem of node feature generation mechanism on such ubiquitous dynamic graph data. In a dynamic graph, we propose to simultaneously estimate contemporaneous relationships and time-lagged interaction relationships between the node features. These two kinds of relationships form a DAG, which could effectively characterize the feature generation process in a concise way. To learn such a DAG, we cast the learning problem as a continuous score-based optimization problem, which consists of a differentiable score function to measure the validity of the learned DAGs and a smooth acyclicity constraint to ensure the acyclicity of the learned DAGs. These two components are translated into an unconstraint augmented Lagrangian objective which could be minimized by mature continuous optimization techniques. The resulting algorithm, named GraphNOTEARS, outperforms baselines on simulated data across a wide range of settings that may encounter in real-world applications. We also apply the proposed approach on two dynamic graphs constructed from the real-world Yelp dataset, demonstrating our method could learn the connections between node features, which conforms with the domain knowledge.

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19

Othman, Hakeem, Ahmed Ayache, and Amin Saif. "On L2−directed topological spaces in directed graphs theory." Filomat 37, no. 29 (2023): 10005–13. http://dx.doi.org/10.2298/fil2329005o.

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Here we give the notion of L2?directed topological spaces of directed graphs, and some results about this notion such as Alexandroff property. Next, we study the form of L2?directed topological space on E-generated subdirected graphs and their relation with the relative topologies. The relations between some fundamental properties in topological spaces with their corresponding properties in graphs such as the isomorphically and connectedness are introduced.

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20

Rizzi, Romeo, and Marco Rospocher. "Covering partially directed graphs with directed paths." Discrete Mathematics 306, no. 13 (July 2006): 1390–404. http://dx.doi.org/10.1016/j.disc.2006.01.024.

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21

Lipsky, Ari M., and Sander Greenland. "Causal Directed Acyclic Graphs." JAMA 327, no. 11 (March 15, 2022): 1083. http://dx.doi.org/10.1001/jama.2022.1816.

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22

Kumudakshi, S. M. Hegde, and Anusha. "On sequential directed graphs." Materials Today: Proceedings 54 (2022): 738–42. http://dx.doi.org/10.1016/j.matpr.2021.11.028.

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23

Bapat, R. B., D. Kalita, and S. Pati. "On weighted directed graphs." Linear Algebra and its Applications 436, no. 1 (January 2012): 99–111. http://dx.doi.org/10.1016/j.laa.2011.06.035.

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24

Melo, Bruno, Igor Brandão, Carlos Tomei, and Thiago Guerreiro. "Directed graphs and interferometry." Journal of the Optical Society of America B 37, no. 7 (July 1, 2020): 2199. http://dx.doi.org/10.1364/josab.394110.

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25

Pircalabelu, Eugen, Gerda Claeskens, and Irène Gijbels. "Copula directed acyclic graphs." Statistics and Computing 27, no. 1 (August 12, 2015): 55–78. http://dx.doi.org/10.1007/s11222-015-9599-9.

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26

Brinkmann, Gunnar. "Generating regular directed graphs." Discrete Mathematics 313, no. 1 (January 2013): 1–7. http://dx.doi.org/10.1016/j.disc.2012.09.014.

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27

Michel, Jesse, Sushruth Reddy, Rikhav Shah, Sandeep Silwal, and Ramis Movassagh. "Directed random geometric graphs." Journal of Complex Networks 7, no. 5 (April 8, 2019): 792–816. http://dx.doi.org/10.1093/comnet/cnz006.

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Abstract Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet and the network of followers on Twitter among many others. The challenge, however, is to create a network model that has many of the properties of real-world networks such as power-law degree distributions and the small-world property. To meet these challenges, we introduce the Directed Random Geometric Graph (DRGG) model, which is an extension of the random geometric graph model. We prove that it is scale-free with respect to the indegree distribution, has binomial outdegree distribution, has a high clustering coefficient, has few edges and is likely small-world. These are some of the main features of aforementioned real-world networks. We also empirically observed that word association networks have many of the theoretical properties of the DRGG model.

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28

Kratochvíl, Jan, and Zsolt Tuza. "Rankings of Directed Graphs." SIAM Journal on Discrete Mathematics 12, no. 3 (January 1999): 374–84. http://dx.doi.org/10.1137/s0895480197330242.

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29

Björner, Anders, and Volkmar Welker. "Complexes of Directed Graphs." SIAM Journal on Discrete Mathematics 12, no. 4 (January 1999): 413–24. http://dx.doi.org/10.1137/s0895480198338724.

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30

Bloom, G. S., and D. F. Hsu. "On Graceful Directed Graphs." SIAM Journal on Algebraic Discrete Methods 6, no. 3 (July 1985): 519–36. http://dx.doi.org/10.1137/0606051.

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31

Holton, C., and L. Q. Zamboni. "Directed Graphs and Substitutions." Theory of Computing Systems 34, no. 6 (January 1, 2001): 545–64. http://dx.doi.org/10.1007/s00224-001-1038-y.

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32

Gray, Robert, Dugald Macpherson, Cheryl E. Praeger, and Gordon F. Royle. "Set-homogeneous directed graphs." Journal of Combinatorial Theory, Series B 102, no. 2 (March 2012): 474–520. http://dx.doi.org/10.1016/j.jctb.2011.08.002.

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33

Smith, Simon M. "Infinite primitive directed graphs." Journal of Algebraic Combinatorics 31, no. 1 (July 28, 2009): 131–41. http://dx.doi.org/10.1007/s10801-009-0190-3.

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34

Bang-Jensen, Jorgen, and Tibor Jordán. "On persistent directed graphs." Networks 52, no. 4 (April 9, 2008): 271–76. http://dx.doi.org/10.1002/net.20248.

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35

CHENG, EDDIE, and MARC J. LIPMAN. "UNIDIRECTIONAL (n, k)-STAR GRAPHS." Journal of Interconnection Networks 03, no. 01n02 (March 2002): 19–34. http://dx.doi.org/10.1142/s0219265902000525.

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Arrangement graphs14 and (n, k)-star graphs11 were introduced as generalizations of star graphs1. They were introduced to provide a wider set of choices for the order of topologically attractive interconnection networks. Unidirectional interconnection networks are more appropriate in many applications. Cheng and Lipman5, and Day and Tripathi17 studied the unidirectional star graphs, and Cheng and Lipman7 studied orientation of arrangement graphs. In this paper, we show that every (n, k)-star graph can be oriented to a maximally arc-connected graph when the regularity of the graph is even. If the regularity is odd, then the resulting directed graph can be augmented to a maximally arc-connected directed graph by adding a directed matching. In either case, the diameter of the resulting directed graph is small. Moreover, there exists a simple and near-optimal routing algorithm.

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36

Chartrand, Gary, Michael Raines, and Ping Zhang. "The directed distance dimension of oriented graphs." Mathematica Bohemica 125, no. 2 (2000): 155–68. http://dx.doi.org/10.21136/mb.2000.125961.

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37

Carlsen, Toke Meier, and Marius Lie Winger. "Orbit equivalence of graphs and isomorphism of graph groupoids." MATHEMATICA SCANDINAVICA 123, no. 2 (August 13, 2018): 239–48. http://dx.doi.org/10.7146/math.scand.a-105087.

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We show that the groupoids of two directed graphs are isomorphic if and only if the two graphs are orbit equivalent by an orbit equivalence that preserves isolated eventually periodic points. We also give a complete description of the (topological) isolated points of the boundary path space of a graph. As a result, we are able to show that the groupoids of two directed graphs with finitely many vertices and no sinks are isomorphic if and only if the two graphs are orbit equivalent, and that the groupoids of the stabilisations of two such graphs are isomorphic if and only if the stabilisations of the graphs are orbit equivalent.

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38

Babel, L., I. N. Ponomarenko, and G. Tinhofer. "The Isomorphism Problem For Directed Path Graphs and For Rooted Directed Path Graphs." Journal of Algorithms 21, no. 3 (November 1996): 542–64. http://dx.doi.org/10.1006/jagm.1996.0058.

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39

Gutierrez, Marisa, and João Meidanis. "Recognizing clique graphs of directed edge path graphs." Discrete Applied Mathematics 126, no. 2-3 (March 2003): 297–304. http://dx.doi.org/10.1016/s0166-218x(02)00203-2.

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40

Cooper, Colin, and Alan Frieze. "Hamilton cycles in random graphs and directed graphs." Random Structures and Algorithms 16, no. 4 (2000): 369–401. http://dx.doi.org/10.1002/1098-2418(200007)16:4<369::aid-rsa6>3.0.co;2-j.

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41

Alon, N. "Monochromatic directed walks in arc-colored directed graphs." Acta Mathematica Hungarica 49, no. 1-2 (March 1987): 163–67. http://dx.doi.org/10.1007/bf01956320.

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42

Montanaro, A. "Quantum walks on directed graphs." Quantum Information and Computation 7, no. 1&2 (January 2007): 93–102. http://dx.doi.org/10.26421/qic7.1-2-5.

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We consider the definition of quantum walks on directed graphs. Call a directed graph reversible if, for each pair of vertices $(v_i, v_j)$, if $v_i$ is connected to $v_j$ then there is a path from $v_j$ to $v_i$. We show that reversibility is a necessary and sufficient condition for a directed graph to allow the notion of a discrete-time quantum walk, and discuss some implications of this condition. We present a method for defining a "partially quantum'' walk on directed graphs that are not reversible.

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43

Abuthawabeh, Ala, and Dirk Zeckzer. "Topological Decomposition of Directed Graphs." Journal of Graph Algorithms and Applications 21, no. 4 (2017): 589–630. http://dx.doi.org/10.7155/jgaa.00431.

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44

Sun, Jiankai, and Srinivasan Parthasarathy. "Symmetrization for Embedding Directed Graphs." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 10043–44. http://dx.doi.org/10.1609/aaai.v33i01.330110043.

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In this paper, we propose to solve the directed graph embedding problem via a two stage approach: in the first stage, the graph is symmetrized in one of several possible ways, and in the second stage, the so-obtained symmetrized graph is embeded using any state-of-the-art (undirected) graph embedding algorithm. Note that it is not the objective of this paper to propose a new (undirected) graph embedding algorithm or discuss the strengths and weaknesses of existing ones; all we are saying is that whichever be the suitable graph embedding algorithm, it will fit in the above proposed symmetrization framework.

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45

Cosco, Clément, Inbar Seroussi, and Ofer Zeitouni. "Directed Polymers on Infinite Graphs." Communications in Mathematical Physics 386, no. 1 (March 1, 2021): 395–432. http://dx.doi.org/10.1007/s00220-021-04034-w.

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46

Enriquez, Enrico, Grace Estrada, Carmelita Loquias, Reuella J. Bacalso, and Lanndon Ocampo. "Domination in Fuzzy Directed Graphs." Mathematics 9, no. 17 (September 2, 2021): 2143. http://dx.doi.org/10.3390/math9172143.

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A new domination parameter in a fuzzy digraph is proposed to espouse a contribution in the domain of domination in a fuzzy graph and a directed graph. Let GD*=V,A be a directed simple graph, where V is a finite nonempty set and A=x,y:x,y∈V,x≠y. A fuzzy digraph GD=σD,μD is a pair of two functions σD:V→0,1 and μD:A→0,1, such that μDx,y≤σDx∧σDy, where x,y∈V. An edge μDx,y of a fuzzy digraph is called an effective edge if μDx,y=σDx∧σDy. Let x,y∈V. The vertex σDx dominates σDy in GD if μDx,y is an effective edge. Let S⊆V, u∈V\S, and v∈S. A subset σDS⊆σD is a dominating set of GD if, for every σDu∈σD\σDS, there exists σDv∈σDS, such that σDv dominates σDu. The minimum dominating set of a fuzzy digraph GD is called the domination number of a fuzzy digraph and is denoted by γGD. In this paper, the concept of domination in a fuzzy digraph is introduced, the domination number of a fuzzy digraph is characterized, and the domination number of a fuzzy dipath and a fuzzy dicycle is modeled.

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47

Cruz, Roberto, Juan Monsalve, and Juan Rada. "Sombor index of directed graphs." Heliyon 8, no. 3 (March 2022): e09035. http://dx.doi.org/10.1016/j.heliyon.2022.e09035.

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48

Rameshkumar, A., and G. Kavitha. "Two Finite Simple Directed Graphs." Bulletin of Pure & Applied Sciences- Mathematics and Statistics 37e, no. 1 (2018): 223. http://dx.doi.org/10.5958/2320-3226.2018.00022.x.

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49

Portilla, Ana, José M. Rodríguez, José M. Sigarreta, and Eva Tourís. "Gromov Hyperbolicity in Directed Graphs." Symmetry 12, no. 1 (January 6, 2020): 105. http://dx.doi.org/10.3390/sym12010105.

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In this paper, we generalize the classical definition of Gromov hyperbolicity to the context of directed graphs and we extend one of the main results of the theory: the equivalence of the Gromov hyperbolicity and the geodesic stability. This theorem has potential applications to the development of solutions for secure data transfer on the internet.

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50

Apt, Krzysztof R., Sunil Simon, and Dominik Wojtczak. "Coordination Games on Directed Graphs." Electronic Proceedings in Theoretical Computer Science 215 (June 23, 2016): 67–80. http://dx.doi.org/10.4204/eptcs.215.6.

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Journal articles on the topic 'Directed graphs'

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