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Journal articles on the topic 'Unweighted graph'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Shi, Xiaolong, Saira Hameed, Sadia Akhter, Aysha Khan, and Maryam Akhoundi. "Conversion of Unweighted Graphs to Weighted Graphs Satisfying Properties R and −SR." Axioms 12, no. 11 (2023): 1043. http://dx.doi.org/10.3390/axioms12111043.

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Spectral graph theory is like a special tool for understanding graphs. It helps us find patterns and connections in complex networks, using the magic of eigenvalues. Let G be the graph and A(G) be its adjacency matrix, then G is singular if the determinant of the adjacency matrix A(G) is 0, otherwise it is nonsingular. Within the realm of nonsingular graphs, there is the concept of property R, where each eigenvalue’s reciprocal is also an eigenvalue of G. By introducing multiplicity constraints on both eigenvalues and their reciprocals, it becomes property SR. Similarly, the world of nonsingul

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Panda, Swarup, and Dr Sukanta Pati. "On The Inverse Of A Class Of Bipartite Graphs With Unique Perfect Matchings." Electronic Journal of Linear Algebra 29 (September 20, 2015): 89–101. http://dx.doi.org/10.13001/1081-3810.2865.

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Let G be a simple, undirected graph and Gw be the weighted graph obtained from G by giving weights to its edges using a positive weight function w. A weighted graph Gw is said to be nonsingular if its adjacency matrix A(Gw) is nonsingular. In [9], Godsil has given a class $\mathcal{G }$of connected, unweighted, bipartite, nonsingular graphs G with a unique perfect matching, such that A(G)â1 is signature similar to a nonnegative matrix, that is, there exists a diagonal matrix D with diagonal entries Â±1 such that DA(G)â1D is nonnegative. The graph associated to the matrix DA(G)â1D is call

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Carlson, W., A. Ford, E. Harris, J. Rosen, C. Tamon, and K. Wrobel. "Universal Mixing of Quantum Walk on Graphs." Quantum Information and Computation 7, no. 8 (2007): 738–51. http://dx.doi.org/10.26421/qic7.8-4.

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We study the set of probability distributions visited by a continuous-time quantum walk on graphs. An edge-weighted graph $G$ is {\em universal mixing} if the instantaneous or average probability distribution of the quantum walk on $G$ ranges over all probability distributions on the vertices as the weights are varied over non-negative reals. The graph is {\em uniform} mixing if it visits the uniform distribution. Our results include the following: 1) All weighted complete multipartite graphs are instantaneous universal mixing. This is in contrast to the fact that no {\em unweighted} complete

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4

Trigo, Macarena. "On Harary energy and Reciprocal distance Laplacian energies¹." Journal of Physics: Conference Series 2090, no. 1 (2021): 012102. http://dx.doi.org/10.1088/1742-6596/2090/1/012102.

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Abstract Let G be an graph simple, undirected, connected and unweighted graphs. The Reciprocal distance energy of a graph G is equal to the sum of the absolute values of the reciprocal distance eigenvalues. In this work, we find a lower bound for the Harary energy, reciprocal distance Laplacian energy and reciprocal distance signless Laplacian energy of a graph. Moreover, we find relationship between the Harary energy and Reciprocal distance Laplacian energies.

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Braga, R. O., V. M. Rodrigues, and R. O. Silva. "Locating Eigenvalues of a Symmetric Matrix whose Graph is Unicyclic." Trends in Computational and Applied Mathematics 22, no. 4 (2021): 659–74. http://dx.doi.org/10.5540/tcam.2021.022.04.00659.

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We present a linear-time algorithm that computes in a given real interval the number of eigenvalues of any symmetric matrix whose underlying graph is unicyclic. The algorithm can be applied to vertex- and/or edge-weighted or unweighted unicyclic graphs. We apply the algorithm to obtain some general results on the spectrum of a generalized sun graph for certain matrix representations which include the Laplacian, normalized Laplacian and signless Laplacian matrices.

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MIZUTA, Haruka, Takehiro ITO, and Xiao ZHOU. "Reconfiguration of Steiner Trees in an Unweighted Graph." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E100.A, no. 7 (2017): 1532–40. http://dx.doi.org/10.1587/transfun.e100.a.1532.

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7

Demange, Marc, and Vangelis Paschos. "Improved Approximations for Weighted and Unweighted Graph Problems." Theory of Computing Systems 38, no. 6 (2004): 763–87. http://dx.doi.org/10.1007/s00224-004-1162-6.

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8

Spricer, Kristoffer, and Tom Britton. "An SIR epidemic on a weighted network." Network Science 7, no. 4 (2019): 556–80. http://dx.doi.org/10.1017/nws.2019.54.

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AbstractWe introduce a weighted configuration model graph, where edge weights correspond to the probability of infection in an epidemic on the graph. On these graphs, we study the development of a Susceptible–Infectious–Recovered epidemic using both Reed–Frost and Markovian settings. For the special case of having two different edge types, we determine the basic reproduction numberR0, the probability of a major outbreak, and the relative final size of a major outbreak. Results are compared with those for a calibrated unweighted graph. The degree distributions are based on both theoretical cons

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9

SUN, YACHYANG, and KOK-HOO YEAP. "EDGE COVERING OF COMPLEX TRIANGLES IN RECTANGULAR DUAL FLOORPLANNING." Journal of Circuits, Systems and Computers 03, no. 03 (1993): 721–31. http://dx.doi.org/10.1142/s0218126693000435.

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Rectangular dual graph approach to floorplanning is based on the adjacency graph of the modules in a floorplan. If the input adjacency graph contains a cycle of length three which is not a face (complex triangle), a rectangular floorplan does not exist. Thus, complex triangles have to be eliminated before applying any floorplanning algorithm. This paper shows that the weighted complex triangle elimination problem is NP-complete, even when the input graphs are restricted to 1-level containment. For adjacency graph with 0-level containment, the unweighted problem is optimally solvable in O(c1.5

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10

Burkett, David, David Hall, and Dan Klein. "Optimal Graph Search with Iterated Graph Cuts." Proceedings of the AAAI Conference on Artificial Intelligence 25, no. 1 (2011): 12–17. http://dx.doi.org/10.1609/aaai.v25i1.7829.

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Informed search algorithms such as A* use heuristics to focus exploration on states with low total path cost. To the extent that heuristics underestimate forward costs, a wider cost radius of suboptimal states will be explored. For many weighted graphs, however, a small distance in terms of cost may encompass a large fraction of the unweighted graph. We present a new informed search algorithm, Iterative Monotonically Bounded A* (IMBA*), which first proves that no optimal paths exist in a bounded cut of the graph before considering larger cuts. We prove that IMBA* has the same optimality and co

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11

Biermann, Jennifer, Selvi Kara, Kuei-Nuan Lin, and Augustine O’Keefe. "Toric ideals of weighted oriented graphs." International Journal of Algebra and Computation 32, no. 02 (2022): 307–25. http://dx.doi.org/10.1142/s0218196722500151.

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Given a vertex-weighted oriented graph, we can associate to it a set of monomials. We consider the toric ideal whose defining map is given by these monomials. We find a generating set for the toric ideal for certain classes of graphs which depends on the combinatorial structure and weights of the graph. We provide a result analogous to the unweighted, unoriented graph case, to show that when the associated simple graph has only trivial even closed walks, the toric ideal is the zero ideal. Moreover, we give necessary and sufficient conditions for the toric ideal of a weighted oriented graph to

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12

Rosenfeld, Vladimir R. "Eigenvalue −1 of the Vertex Quadrangulation of a 4-Regular Graph." Axioms 13, no. 1 (2024): 72. http://dx.doi.org/10.3390/axioms13010072.

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The vertex quadrangulation QG of a 4-regular graph G visually looks like a graph whose vertices are depicted as empty squares, and the connecting edges are attached to the corners of the squares. In a previous work [JOMC 59, 1551–1569 (2021)], the question was posed: does the spectrum of an arbitrary unweighted graph QG include the full spectrum {3,(−1)3} of the tetrahedron graph (complete graph K4)? Previously, many bipartite and nonbipartite graphs QG with such a subspectrum have been found; for example, a nonbipartite variant of the graph QK5. Here, we present one of the variants of the non

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13

Willson, James, and Tandy Warnow. "Axioms for clustering simple unweighted graphs: No impossibility result." PLOS Complex Systems 1, no. 2 (2024): e0000011. http://dx.doi.org/10.1371/journal.pcsy.0000011.

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In 2002, Kleinberg proposed three axioms for distance-based clustering, and proved that it was impossible for a clustering method to satisfy all three. While there has been much subsequent work examining and modifying these axioms for distance-based clustering, little work has been done to explore axioms relevant to the graph partitioning problem when the graph is unweighted and given without a distance matrix. Here, we propose and explore axioms for graph partitioning for this case, including modifications of Kleinberg’s axioms and three others: two axioms relevant to the “Resolution Limit” a

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Koana, Tomohiro, Viatcheslav Korenwein, André Nichterlein, Rolf Niedermeier, and Philipp Zschoche. "Data Reduction for Maximum Matching on Real-World Graphs." ACM Journal of Experimental Algorithmics 26 (July 8, 2021): 1–30. http://dx.doi.org/10.1145/3439801.

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Finding a maximum-cardinality or maximum-weight matching in (edge-weighted) undirected graphs is among the most prominent problems of algorithmic graph theory. For n -vertex and m -edge graphs, the best-known algorithms run in Õ( m √ n ) time. We build on recent theoretical work focusing on linear-time data reduction rules for finding maximum-cardinality matchings and complement the theoretical results by presenting and analyzing (thereby employing the kernelization methodology of parameterized complexity analysis) new (near-)linear-time data reduction rules for both the unweighted and the pos

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15

FENG, YING, ROBERT L. GOLDSTONE, and VLADIMIR MENKOV. "A GRAPH MATCHING ALGORITHM AND ITS APPLICATION TO CONCEPTUAL SYSTEM TRANSLATION." International Journal on Artificial Intelligence Tools 14, no. 01n02 (2005): 77–99. http://dx.doi.org/10.1142/s0218213005002004.

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ABSURDIST II, an extension to ABSURDIST, is an algorithm using attributed graph matching to find translations between conceptual systems. It uses information about the internal structure of systems by itself, or in combination with external information about concept similarities across systems. It supports systems with multiple types of weighted or unweighted, directed or undirected relations between concepts. The algorithm exploits graph sparsity to improve computational efficiency. We present the results of experiments with a number of conceptual systems, including artificially constructed r

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16

Bérczi, Kristóf, and András Frank. "Supermodularity in Unweighted Graph Optimization I: Branchings and Matchings." Mathematics of Operations Research 43, no. 3 (2018): 726–53. http://dx.doi.org/10.1287/moor.2017.0881.

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Bérczi, Kristóf, and András Frank. "Supermodularity in Unweighted Graph Optimization III: Highly Connected Digraphs." Mathematics of Operations Research 43, no. 3 (2018): 763–80. http://dx.doi.org/10.1287/moor.2017.0883.

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18

Guo, Ying, Yanyan Feng, and Guihua Zeng. "Quantum anonymous voting with unweighted continuous-variable graph states." Quantum Information Processing 15, no. 8 (2016): 3327–45. http://dx.doi.org/10.1007/s11128-016-1349-1.

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Akhtar, Adil, and Tazid Ali. "Analysis of Unweighted Amino Acids Network." International Scholarly Research Notices 2014 (December 16, 2014): 1–6. http://dx.doi.org/10.1155/2014/350276.

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The analysis of amino acids network is very important to studying the various physicochemical properties of amino acids. In this paper we consider the amino acid network based on mutation of the codons. To analyze the relative importance of the amino acids we have discussed different measures of centrality. The measure of centrality is a powerful tool of graph theory for ranking the vertices and analysis of biological network. We have also investigated the correlation coefficients between various measures of centrality. Also we have discussed clustering coefficient as well as average clusterin

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20

SAVITA S SHINDE, VIJAY. M.P, and SHIVAKUMAR MD. "Exploring Graph Theory For Practical Solutions." Innovative Research Thoughts 4, no. 8 (2018): 85–94. https://doi.org/10.36676/irt.v4.i8.1556.

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Graph theory is widely used to prove many mathematical theorems and models. This paper present the various applications and techniques of graph theory to solve problems in different fields of science and technology in addition to mathematics. A graph can be used to represent almost any physical situation involving discrete objects and a relationship among them. This abstract provides a concise overview of graph theory’s foundational principles, including graph types(such as directed, undirected, weighted, and unweighted graphs), basics terminologies( vertices, edges, paths, cycles), and essent

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21

Shan, Xiaohuan, Haihai Li, Chunjie Jia, Dong Li, and Baoyan Song. "Supergraph Topology Feature Index for Personalized Interesting Subgraph Query in Large Labeled Graphs." Complexity 2021 (June 29, 2021): 1–18. http://dx.doi.org/10.1155/2021/9274429.

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Interesting subgraph query aims to find subgraphs that are isomorphic to the given query graph from a data graph and rank the subgraphs according to their interestingness scores. However, the existing subgraph query approaches are inefficient when dealing with large-scale labeled data graph. This is caused by the following problems: (i) the existing work mainly focuses on unweighted query graphs, while ignoring the impact of query constraints on query results. (ii) Excessive number of subgraph candidates or complex joins between nodes in the subgraph candidates reduce the query efficiency. To

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22

Farhadi, Alireza, Jacob Gilbert, and MohammadTaghi Hajiaghayi. "Generalized Stochastic Matching." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 9 (2022): 10008–15. http://dx.doi.org/10.1609/aaai.v36i9.21239.

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In this paper, we generalize the recently studied stochastic matching problem to more accurately model a significant medical process, kidney exchange, and several other applications. Up until now the stochastic matching problem that has been studied was as follows: given a graph G= (V,E), each edge is included in the realized sub-graph of G independently with probability pe, and the goal is to find a degree-bounded sub-graph Q of G that has an expected maximum matching that approximates the expected maximum matching of G. This model does not account for possibilities of vertex dropouts, which

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23

Bérczi, Kristóf, and András Frank. "Supermodularity in Unweighted Graph Optimization II: Matroidal Term Rank Augmentation." Mathematics of Operations Research 43, no. 3 (2018): 754–62. http://dx.doi.org/10.1287/moor.2017.0902.

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24

Sebastian, Arya, John N. Mordeson, and Sunil Mathew. "Generalized Fuzzy Graph Connectivity Parameters with Application to Human Trafficking." Mathematics 8, no. 3 (2020): 424. http://dx.doi.org/10.3390/math8030424.

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Graph models are fundamental in network theory. But normalization of weights are necessary to deal with large size networks like internet. Most of the research works available in the literature have been restricted to an algorithmic perspective alone. Not much have been studied theoretically on connectivity of normalized networks. Fuzzy graph theory answers to most of the problems in this area. Although the concept of connectivity in fuzzy graphs has been widely studied, one cannot find proper generalizations of connectivity parameters of unweighted graphs. Generalizations for some of the exis

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25

Cohen-Addad, Vincent, Éric Colin De Verdière, Dániel Marx, and Arnaud De Mesmay. "Almost Tight Lower Bounds for Hard Cutting Problems in Embedded Graphs." Journal of the ACM 68, no. 4 (2021): 1–26. http://dx.doi.org/10.1145/3450704.

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We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut problem. A cut graph of a graph G embedded on a surface S is a subgraph of G whose removal from S leaves a disk. We consider the problem of deciding whether an unweighted graph embedded on a surface of genus G has a cut graph of length at most a given value. We prove a time lower bound for this problem of n Ω( g log g ) conditionally to the ETH. In other words,

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Jiang, Yingchun, and Ting Li. "Local Measurement and Diffusion Reconstruction for Signals on a Weighted Graph." Mathematical Problems in Engineering 2018 (July 19, 2018): 1–8. http://dx.doi.org/10.1155/2018/3264294.

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Bandlimited graph signals on an unweighted graph can be reconstructed by its local measurement, which is a generalization of decimation. Since most signals are weighted in real life, we extend and improve the iterative local measurement reconstruction (ILMR) by introducing the diffusion operators to reconstruct bandlimited signals on a weighted graph. We prove that the proposed reconstruction converges to the original signal. Moreover, the simulation results demonstrate that the improved algorithm has better convergence and has robustness against noise.

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Eisner, Jason. "Time-and-Space-Efficient Weighted Deduction." Transactions of the Association for Computational Linguistics 11 (2023): 960–73. http://dx.doi.org/10.1162/tacl_a_00588.

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Abstract Many NLP algorithms have been described in terms of deduction systems. Unweighted deduction allows a generic forward-chaining execution strategy. For weighted deduction, however, efficient execution should propagate the weight of each item only after it has converged. This means visiting the items in topologically sorted order (as in dynamic programming). Toposorting is fast on a materialized graph; unfortunately, materializing the graph would take extra space. Is there a generic weighted deduction strategy which, for every acyclic deduction system and every input, uses only a constan

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LYONS, RUSSELL. "Identities and Inequalities for Tree Entropy." Combinatorics, Probability and Computing 19, no. 2 (2009): 303–13. http://dx.doi.org/10.1017/s0963548309990605.

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The notion of tree entropy was introduced by the author as a normalized limit of the number of spanning trees in finite graphs, but is defined on random infinite rooted graphs. We give some new expressions for tree entropy; one uses Fuglede–Kadison determinants, while another uses effective resistance. We use the latter to prove that tree entropy respects stochastic domination. We also prove that tree entropy is non-negative in the unweighted case, a special case of which establishes Lück's Determinant Conjecture for Cayley-graph Laplacians. We use techniques from the theory of operators affil

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Panda, Swarup, and Sukanta Pati. "On the inverse of a class of weighted graphs." Electronic Journal of Linear Algebra 32 (February 6, 2017): 539–45. http://dx.doi.org/10.13001/1081-3810.3421.

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In this article, only connected bipartite graphs $G$ with a unique perfect matching $\c{M}$ are considered. Let $G_\w$ denote the weighted graph obtained from $G$ by giving weights to its edges using the positive weight function $\w:E(G)\ar (0,\ity)$ such that $\w(e)=1$ for each $e\in\c{M}$. An unweighted graph $G$ may be viewed as a weighted graph with the weight function $\w\equiv\1$ (all ones vector). A weighted graph $G_\w$ is nonsingular if its adjacency matrix $A(G_\w)$ is nonsingular. The {\em inverse} of a nonsingular weighted graph $G_\w$ is the unique weighted graph whose adjacency m

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30

Öztemiz, Furkan. "An Effective Algorithm for Edge Coloring: Malatya Edge Coloring Algorithm." Turkish Journal of Science and Technology 20, no. 1 (2025): 309–25. https://doi.org/10.55525/tjst.1633962.

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In this research, an algorithm offering effective and robust solutions for the edge coloring problem in graph theory is proposed. The edge coloring problem is identified as an NP-hard problem, known for its extensive resolution time and inability to be resolved within polynomial time. The proposed edge coloring algorithm emerges as an efficient greedy method that delivers effective solutions within polynomial time constraints. This developed algorithm employs Malatya centrality values as a decisive factor in the edge coloring process. The Malatya centrality algorithm, a current centrality meth

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Medina, Luis, and Macarena Trigo. "Spectral radius of the Harary matrix of the join product of regular graphs¹." Journal of Physics: Conference Series 2090, no. 1 (2021): 012103. http://dx.doi.org/10.1088/1742-6596/2090/1/012103.

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Abstract The distance between two vertices is equal to the number of edges on the shortest path connecting them. The Harary matrix of a simple, undirected, connected and unweighted graph of n vertices is an nonnegative matrix of order n, such that the (i, j)-entry is equal to the reciprocal distance between the vertices vi and Vj if the vertices are different and zero if are equal. In this work we found bounds for the spectral radius of the Harary matrix of the join product of regular graphs.

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B.Jothilakshmi. "Degree-Based Topological Indices of Modified Petersen Graph." Panamerican Mathematical Journal 35, no. 4s (2025): 235–46. https://doi.org/10.52783/pmj.v35.i4s.4673.

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Objectives:The Petersen graph is non-planar, meaning it cannot be drawn on a plane without edge crossings. This limits its use in applications requiring planar graphs, such as circuit board design, geographic mapping, or any domain where planar embeddings are essential. The Petersen graph is fixed with only 10 vertices and 15 edges. Its small size can make it unsuitable for modelling or analysing larger, more complex systems. The weakness of unsuitable for modelling or analysing larger, more complex systems estimation is the lack of consideration of the graph and it is not a function of the ov

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Madeo, Dario, Chiara Mocenni, Giulia Palma, and Simone Rinaldi. "A Game Theory Proof of Optimal Colorings Resilience to Strong Deviations." Mathematics 10, no. 15 (2022): 2781. http://dx.doi.org/10.3390/math10152781.

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This paper provides a formal proof of the conjecture stating that optimal colorings in max k-cut games over unweighted and undirected graphs do not allow the formation of any strongly divergent coalition, i.e., a subset of nodes able to increase their own payoffs simultaneously. The result is obtained by means of a new method grounded on game theory, which consists in splitting the nodes of the graph into three subsets: the coalition itself, the coalition boundary and the nodes without relationship with the coalition. Moreover, we find additional results concerning the properties of optimal co

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Koutrouli, Mikaela, Theodosios Theodosiou, Ioannis Iliopoulos, and Georgios A. Pavlopoulos. "The Network Analysis Profiler (NAP v2.0): a web tool for visual topological comparison between multiple networks." EMBnet.journal 26, no. 1 (2021): e943. http://dx.doi.org/10.14806/ej.26.1.943.

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In this article we present the Network Analysis Profiler (NAP v2.0), a web tool to directly compare the topological features of multiple networks simultaneously. NAP is written in R and Shiny and currently offers both 2D and 3D network visualisation, as well as simultaneous visual comparisons of node- and edge-based topological features as bar charts or scatterplot matrix. NAP is fully interactive, and users can easily export and visualise the intersection between any pair of networks using Venn diagrams or a 2D and a 3D multi-layer graph-based visualisation. NAP supports weighted, unweighted,

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Koutrouli, Mikaela, Theodosios Theodosiou, Ioannis Iliopoulos, and Georgios A. Pavlopoulos. "The Network Analysis Profiler (NAP v2.0): a web tool for visual topological comparison between multiple networks." EMBnet.journal 26 (May 13, 2021): e943. http://dx.doi.org/10.14806/ej.26.0.943.

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In this article we present the Network Analysis Profiler (NAP v2.0), a web tool to directly compare the topological features of multiple networks simultaneously. NAP is written in R and Shiny and currently offers both 2D and 3D network visualisation, as well as simultaneous visual comparisons of node- and edge-based topological features as bar charts or scatterplot matrix. NAP is fully interactive, and users can easily export and visualise the intersection between any pair of networks using Venn diagrams or a 2D and a 3D multi-layer graph-based visualisation. NAP supports weighted, unweighted,

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Sun, Yahui, Xiaokui Xiao, Bin Cui, Saman Halgamuge, Theodoros Lappas, and Jun Luo. "Finding group Steiner trees in graphs with both vertex and edge weights." Proceedings of the VLDB Endowment 14, no. 7 (2021): 1137–49. http://dx.doi.org/10.14778/3450980.3450982.

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Given an undirected graph and a number of vertex groups, the group Steiner trees problem is to find a tree such that (i) this tree contains at least one vertex in each vertex group; and (ii) the sum of vertex and edge weights in this tree is minimized. Solving this problem is useful in various scenarios, ranging from social networks to knowledge graphs. Most existing work focuses on solving this problem in vertex-unweighted graphs, and not enough work has been done to solve this problem in graphs with both vertex and edge weights. Here, we develop several algorithms to address this issue. Init

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Fomin, Fedor V., and Petr A. Golovach. "Subexponential Parameterized Algorithms and Kernelization on Almost Chordal Graphs." Algorithmica 83, no. 7 (2021): 2170–214. http://dx.doi.org/10.1007/s00453-021-00822-x.

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AbstractWe study algorithmic properties of the graph class $${\textsc {Chordal}}{-ke}$$ C H O R D A L - k e , that is, graphs that can be turned into a chordal graph by adding at most k edges or, equivalently, the class of graphs of fill-in at most k. It appears that a number of fundamental intractable optimization problems being parameterized by k admit subexponential algorithms on graphs from $${\textsc {Chordal}}{-ke}$$ C H O R D A L - k e . More precisely, we identify a large class of optimization problems on $${\textsc {Chordal}}{-ke}$$ C H O R D A L - k e solvable in time $$2^{{\mathcal{

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Krasanakis, Emmanouil, Symeon Papadopoulos, and Ioannis Kompatsiaris. "Universal Local Attractors on Graphs." Applied Sciences 14, no. 11 (2024): 4533. http://dx.doi.org/10.3390/app14114533.

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Being able to express broad families of equivariant or invariant attributed graph functions is a popular measuring stick of whether graph neural networks should be employed in practical applications. However, it is equally important to find deep local minima of losses (i.e., produce outputs with much smaller loss values compared to other minima), even when architectures cannot express global minima. In this work we introduce the architectural property of attracting optimization trajectories to local minima as a means of achieving smaller loss values. We take first steps in satisfying this prop

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Klemz, Boris, and Günter Rote. "Linear-Time Algorithms for Maximum-Weight Induced Matchings and Minimum Chain Covers in Convex Bipartite Graphs." Algorithmica 84, no. 4 (2022): 1064–80. http://dx.doi.org/10.1007/s00453-021-00904-w.

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AbstractA bipartite graph $$G=(U,V,E)$$ G = ( U , V , E ) is convex if the vertices in V can be linearly ordered such that for each vertex $$u\in U$$ u ∈ U , the neighbors of u are consecutive in the ordering of V. An induced matchingH of G is a matching for which no edge of E connects endpoints of two different edges of H. We show that in a convex bipartite graph with n vertices and mweighted edges, an induced matching of maximum total weight can be computed in $$O(n+m)$$ O ( n + m ) time. An unweighted convex bipartite graph has a representation of size O(n) that records for each vertex $$u\

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Ponten, S. C., L. Douw, F. Bartolomei, J. C. Reijneveld, and C. J. Stam. "Indications for network regularization during absence seizures: Weighted and unweighted graph theoretical analyses." Experimental Neurology 217, no. 1 (2009): 197–204. http://dx.doi.org/10.1016/j.expneurol.2009.02.001.

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Zheng, Xianwei, Yuan Yan Tang, Jiantao Zhou, et al. "Multi-Level Downsampling of Graph Signals via Improved Maximum Spanning Trees." International Journal of Pattern Recognition and Artificial Intelligence 33, no. 03 (2019): 1958005. http://dx.doi.org/10.1142/s0218001419580059.

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Graph signal processing (GSP) is an emerging field in the signal processing community. Novel GSP-based transforms, such as graph Fourier transform and graph wavelet filter banks, have been successfully utilized in image processing and pattern recognition. As a rapidly developing research area, graph signal processing aims to extend classical signal processing techniques to signals with irregular underlying structures. One of the hot topics in GSP is to develop multi-scale transforms such that novel GSP-based techniques can be applied in image processing or other related areas. For designing gr

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Liu, Peng, Zhuang Li, Yang Cong, and Yuheng Xu. "Sensor network prediction based on spatial and temporal GNN." ITM Web of Conferences 47 (2022): 01003. http://dx.doi.org/10.1051/itmconf/20224701003.

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Multi-sensor prediction is a hotspot for research and development in sensor management technologies. Thanks to artificial intelligence, researchers have been able to effectively use neural networks and traditional artificial intelligence approaches to multi-sensor prediction in recent years. In this model, we try to present the sensors network as an unweighted graph, based on the GNN with spatial and temporal features, combine the characteristics of the Gated recurrent unit with temporal context, and use the Graph Neural Network to predict sensor feature. We tackle the issue of poor sensor net

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IVANOV, DENIS, and ALEXANDER SEMENOV. "TOPOLOGICAL APPROACH TO BLACKHOLES ANOMALY DETECTION IN DIRECTED NETWORKS." Computational nanotechnology 7, no. 2 (2020): 49–57. http://dx.doi.org/10.33693/2313-223x-2020-7-2-49-57.

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In this paper we consider the problem of finding a blackhole pattern in directed unweighted graphs. The problem statement is the same as in an original paper by scientists from University of New-Jersey published in 2010. The paper contributes to the special graph pattern matching, the work results can be used for anomaly detection in finances, natural disasters, urban analysis. This paper aims to propose a novel algorithm for blackhole mining, which would take into account inner structure of the “blackhole” pattern and utilize this knowledge for more efficient mining. This paper reviews previo

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ASAHIRO, YUICHI, EIJI MIYANO, HIROTAKA ONO, and KOUHEI ZENMYO. "GRAPH ORIENTATION ALGORITHMS TO MINIMIZE THE MAXIMUM OUTDEGREE." International Journal of Foundations of Computer Science 18, no. 02 (2007): 197–215. http://dx.doi.org/10.1142/s0129054107004644.

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This paper studies the problem of orienting all edges of a weighted graph such that the maximum weighted outdegree of vertices is minimized. This problem, which has applications in the guard arrangement for example, can be shown to be [Formula: see text]-hard generally. In this paper we first give optimal orientation algorithms which run in polynomial time for the following special cases: (i) the input is an unweighted graph, and (ii) the input graph is a tree. Then, by using those algorithms as sub-procedures, we provide a simple, combinatorial, [Formula: see text]-approximation algorithm for

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Razvenskaya, Olga O. "On new algorithmic techniques for the weighted vertex coloring problem." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 22, no. 4 (2020): 442–48. http://dx.doi.org/10.15507/2079-6900.22.202004.442-448.

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The classical NP-hard weighted vertex coloring problem consists in minimizing the number of colors in colorings of vertices of a given graph so that, for each vertex, the number of its colors equals a given weight of the vertex and adjacent vertices receive distinct colors. The weighted chromatic number is the smallest number of colors in these colorings. There are several polynomial-time algorithmic techniques for designing efficient algorithms for the weighted vertex coloring problem. For example, standard techniques of this kind are the modular graph decomposition and the graph decompositio

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Jajcay, Lucia, David Tomeček, Jiří Horáček, Filip Španiel, and Jaroslav Hlinka. "Brain Functional Connectivity Asymmetry: Left Hemisphere Is More Modular." Symmetry 14, no. 4 (2022): 833. http://dx.doi.org/10.3390/sym14040833.

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Graph-theoretical approaches are increasingly used to study the brain and may enhance our understanding of its asymmetries. In this paper, we hypothesize that the structure of the left hemisphere is, on average, more modular. To this end, we analyzed resting-state functional magnetic resonance imaging data of 90 healthy subjects. We computed functional connectivity by Pearson’s correlation coefficient, turned the matrix into an unweighted graph by keeping a certain percentage of the strongest connections, and quantified modularity separately for the subgraph formed by each hemisphere. Our resu

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Skoda, A. "Complexity of inheritance of ℱ-convexity for restricted games induced by minimum partitions". RAIRO - Operations Research 54, № 1 (2020): 143–61. http://dx.doi.org/10.1051/ro/2019003.

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Let G = (N, E, w) be a weighted communication graph. For any subset A ⊆ N, we delete all minimum-weight edges in the subgraph induced by A. The connected components of the resultant subgraph constitute the partition 𝒫min(A) of A. Then, for every cooperative game (N, v), the 𝒫min-restricted game (N, v̅) is defined by v̅(A)=∑F∈𝒫min(A)v(F) for all A ⊆ N. We prove that we can decide in polynomial time if there is inheritance of ℱ-convexity, i.e., if for every ℱ-convex game the 𝒫min-restricted game is ℱ-convex, where ℱ-convexity is obtained by restricting convexity to connected subsets. This implie

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Talmaciu, Mihai, Luminita Dumitriu, Ioan Susnea, Victor Lepin, and Laszlo Barna Iantovics. "Recognition and Optimization Algorithms for P5-Free Graphs." Symmetry 12, no. 2 (2020): 304. https://doi.org/10.3390/sym12020304.

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<em>The weighted independent set problem on P5-free graphs has numerous applications, including data mining and dispatching in railways. The recognition of P5-free graphs is executed in polynomial time. Many problems, such as chromatic number and dominating set, are NP-hard in the class of P5-free graphs. The size of a minimum independent feedback vertex set that belongs to a P5-free graph with n vertices can be computed in O(n16) time. The unweighted problems, clique and clique cover, are NP-complete and the independent set is polynomial. In this work, the P5-free graphs using the weak decomp

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Asahiro, Yuichi, Jesper Jansson, Eiji Miyano, Hirotaka Ono, and T. P. Sandhya. "Graph Orientation with Edge Modifications." International Journal of Foundations of Computer Science 32, no. 02 (2021): 209–33. http://dx.doi.org/10.1142/s012905412150012x.

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The goal of an outdegree-constrained edge-modification problem is to find a spanning subgraph or supergraph [Formula: see text] of an input undirected graph [Formula: see text] such that either: (Type I) the number of edges in [Formula: see text] is minimized or maximized and [Formula: see text] can be oriented to satisfy some specified constraints on the vertices’ resulting outdegrees; or: (Type II) among all subgraphs or supergraphs of [Formula: see text] that can be constructed by deleting or inserting a fixed number of edges, [Formula: see text] admits an orientation optimizing some object

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KUNDETI, VAMSI, SANGUTHEVAR RAJASEKARAN, and HEIU DINH. "AN EFFICIENT ALGORITHM FOR CHINESE POSTMAN WALK ON BI-DIRECTED DE BRUIJN GRAPHS." Discrete Mathematics, Algorithms and Applications 04, no. 02 (2012): 1250019. http://dx.doi.org/10.1142/s179383091250019x.

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Sequence assembly from short reads is an important problem in biology. It is known that solving the sequence assembly problem exactly on a bi-directed de Bruijn graph or a string graph is intractable. However, finding a shortest double stranded DNA string (SDDNA) containing all the k-long words in the reads seems to be a good heuristic to get close to the original genome. This problem is equivalent to finding a cyclic Chinese Postman (CP) walk on the underlying unweighted bi-directed de Bruijn graph built from the reads. The Chinese Postman walk Problem (CPP) is solved by reducing it to a gene

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