An arbitrary segmentation method for loss allocation in power grids with distributed generation by Wenqiang Tao, Hongkun Chen, Lei Chen, Shengbin Chen

“…In response to this challenge, this paper proposes a novel network loss allocation method based on the arbitrary segmentation method and graph theory, applicable to complex transmission and distribution networks with distributed generation integration. …”
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Efficient and safe software defined network topology discovery protocol by Dong LI, Junqing YU, Yongpu GU, Pengcheng ZHAO

“…The network topology discovery in OpenFlow-based software-defined networks is mainly achieved by utilizing the OpenFlow discovery protocol (OFDP).However, it has been observed in existing research that OFDP exhibits low updating efficiency and is susceptible to network topology pollution attacks.To address the efficiency and safety concerns of the network topology discovery protocol, an in-depth investigation was conducted on the mechanism and safety of OFDP network topology discovery.The characteristics of network topology establishment and updating in OFDP were analyzed, and an improved protocol named Im-OFDP (improved OpenFlow discovery protocol) based on the minimum vertex covering problem in graph theory was proposed.In Im-OFDP, the switch port table and network link table were initially established using prior information obtained from OFDP network topology discovery.Subsequently, a graph model of the network topology was constructed, and the minimum vertex covering algorithm in graph theory was employed to select specific switches for the reception and forwarding of topology discovery link layer discovery protocol (LLDP) packets.Multi-level flow tables were designed based on the network topology structure, and these flow entries were installed on the selected switches by the controller to process LLDP packets.To address security issues, dynamic check code verification in LLDP packets was employed to ensure the safety of network links.Additionally, a network equipment information maintenance mechanism was established based on known network topologies to ensure the safety of the network equipment.Experimental results demonstrate a significant reduction in the number of network topology discovery messages, bandwidth overhead, and CPU overhead through the deployment of Im-OFDP.Moreover, the response time for node failures and link recovery time after mode failure is substantially reduced.Im-OFDP also effectively mitigates various network topology pollution attacks, such as link fabrication and switch forgery attacks.Overall, Im-OFDP has the capability to enhance the efficiency and safety of SDN topology discovery.…”
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Maximum Colored Cuts in Edge-Colored Complete Graphs by Huawen Ma

“…Max-Cut problem is one of the classical problems in graph theory and has been widely studied in recent years. …”
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Using Partial Directed Coherence to Study Alpha-Band Effective Brain Networks during a Visuospatial Attention Task by Zongya Zhao, Chang Wang

“…Effective connectivity pattern indicated that in response to targets, there existed obvious top-down connections from the frontal, temporal, and parietal cortexes to the visual cortex compared with in response to nontargets. Graph theory analysis was used to quantify the topographical properties of the brain networks, and results revealed that in response to targets, the brain networks were characterized by significantly smaller characteristic path length and larger global efficiency than in response to nontargets. …”
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Maximum Independent Sets Partition of (n,k)-Star Graphs by Fu-Tao Hu

“…The independent number and chromatic number of a graph are two important parameters in graph theory. However, we have not known the values of these two parameters of the (n,k)-star graph since it was proposed. …”
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A reconstruction algorithm of service path for mobile Ad Hoc network based on SDN by Fang DONG, Ou LI, Youquan MO

“…In view of the service path reconstruction for link failure in the mobile Ad Hoc network based on SDN,a hierarchical service path reconstruction method was proposed.The timeliness of service path reconstruction was improved through the combination of reconstruction on backup and calculation.At the same time,considering the possible path conflict caused by the service path reconstruction,the criterion of comprehensive determinant reconstruction was given based on the graph theory,and it also ensured the effectiveness of reconstruction service path.…”
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New methods of reconstruction of foundry production units by О. I. Ponomarenko, V. V. Torjanik

“…In the article there is offered the method of development and reconstruction of casting houses and their subsystems, based on using of the procedure of system analysis, theory of reliability, hierarchical structure of graph theory, probabalistic automatons, mathematical and simulation technique. …”
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MODELING MOVEMENT OF OBJECTS WITHOUT STOPS IN A NETWORK OF CROSSING ROUTES by I. V. Rubanov, M. S. Barketau, M. Y. Kovalyov

“…The problem is formulated in terms of disjunctive linear programming, mixed integer linear programming and graph theory. Several variants for representing constraints on convergence of objects are considered. …”
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Uncertainty analysis of linear and non-linear regression models in the modeling of water quality in the Caspian Sea basin: Application of Monte-Carlo method by Sahar Heidari Masteali, Mahmoud Bayat, Pete Bettinger, Mansour Ghorbanpour

“…These outcomes suggest that landscape indicators and graph theory continuity can be used to model water quality parameters with an acceptable level of uncertainty.…”
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Heterogeneous Information Networks Node Similarity Measurement Based on Feature Sub-Graph by Biao Zhang, Chuan Li, Hongyu Xu, Yanmei Li, Ning Yang, Qian Luo

“…The algorithm takes graph theory as its foundation, set different weight to different kinds of edges, considers nodes information as well as graph to topological information, and makes full use of the information in heterogeneous network. …”
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Computing Topological Indices and Polynomials of the Rhenium Trioxide by Shahid Imran, Muhammad Mudassar Raza, Niat Nigar, Syed Ajaz K. Kirmani, Fikre Bogale Petros

“…In the study of mathematical chemistry and chemical graph theory, a topological index, also known as a connectivity index, is the arithmetical framework of a graph that specifies its topology and also graph invariant. …”
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DEVELOPMENT OF COMPUTER MODEL AND INVESTIGATION OF HYDRAULIC OPERATIONAL MODES OF CIRCULATING SYSTEMS AT VAZ THERMAL POWER STATION by V. V. Dikop, A. V. Bukhtiarov, A. G. Kovalenko, V. V. Kotov, V. A. Kudinov

“…Results of investigations of fluid levels in capacitances of cooling towers and in a forebay are shown on a computer model developed with the help of graph theory.…”
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Upper bound of mean-square deviation of discrete linear consensus system by Quan-sheng DOU, Yu-rong LI, Ping JIANG

“…The consistency problem is the basis of cooperative control of multi-agents,and has wide application background.The previous research has given the sufficient condition for the linear consistency protocol to realize mean-square consistency problem .Based on graph theory and random analysis,the noise-deviation upper bound of linear discrete mean-square consistency problem was strictly proved further,at the same time,four different network were used as examples to explain the theoretical results.The conclusion provides theoretical basis for the noise evaluation and control of the linear discrete consistency system.…”
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THE ANALYSIS OF STUDENTS' ACTIVITY IN SOCIAL NETWORK by Vasiliy V. Krasil'shchikov, Mitrofan A. Osetrov

“…Methods of mathematical modeling of networks, Graph Theory, and Statistics were used. The research of the personal pages in the social network «VKontakte » of full-time courses students of Vladimir branch of the Russian University of Cooperation was conducted to illustrate the methods. …”
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Exponential Stability of Coupled Systems on Networks with Mixed Delays and Reaction-Diffusion Terms by Wenxue Li, Tianrui Chen, Ke Wang

“…By employing Lyapunov method and Kirchhoff's Theorem in graph theory, a systematic method is proposed to guarantee exponential stability of CSNMRs. …”
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Statistical Analyses of a Class of Random Pentagonal Chain Networks with respect to Several Topological Properties by Jia-Bao Liu, Qing Xie, Jiao-Jiao Gu

“…The purpose of this paper is to study the mathematical properties of the random pentagonal chain networks PECn with the help of graph theory. Based on the networks PECn, we first obtain the expected value expressions of the Gutman index, Schultz index, multiplicative degree-Kirchhoff index, and additive degree-Kirchhoff index, and then, we get the explicit expression formulas of their variances. …”
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Exploration and application of autonomous network based on network events by Weihong LI, Ying YANG, Kun HUANG, Chenglong ZHU, Tantao PAN, Xianzong HE

“…In order to achieve the goal of autonomous networks and improve the automation of network operation, an autonomous network model was explored.The model introduced algorithms such as multidimensional data automatic clustering, adaptive sliding time window mechanism, user traffic loss assessment model based on spatiotemporal sequence correlation, fault propagation graph based on graph theory and spatiotemporal clustering, and builded automation capabilities through network event management, fault self-identification, self-positioning, self-scheduling, and intelligent quality inspection.The goal is achieving L4 advanced intelligent network by 2025.…”
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Role-based fine-grained delegation constraint framework in collaborative environments by LIU Wei1, CAI Jia-yong1, HE Ye-ping1

“…An algorithm based on the graph theory for verifying the consistency of delegation constraints was presented, which had the time complexity of O（n2）.…”
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Fixation Probabilities of Evolutionary Graphs Based on the Positions of New Appearing Mutants by Pei-ai Zhang

“…Evolutionary graph theory is a nice measure to implement evolutionary dynamics on spatial structures of populations. …”
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More on Spectral Analysis of Signed Networks by Guihai Yu, Hui Qu

“…Spectral graph theory plays a key role in analyzing the structure of social (signed) networks. …”
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