Edge Removal Research Articles

Total outer connected vertex-edge domination

A vertex [Formula: see text] of a graph is said to [Formula: see text]-[Formula: see text] dominate every edge incident with [Formula: see text], as well as every edge incident to vertices adjacent to [Formula: see text]. A subset [Formula: see text] is a total outer connected vertex-edge dominating set of a graph [Formula: see text] if every edge in [Formula: see text] is [Formula: see text]-[Formula: see text] dominated by a vertex in [Formula: see text], the subgraph induced by [Formula: see text] has no isolated vertices and the subgraph induced by [Formula: see text] is connected. We initiate the study of total outer connected vertex-edge domination in graphs. We show that the decision problem for total outer-connected vertex-edge domination problem is [Formula: see text]-Complete even for bipartite graphs. We prove that for every tree of order [Formula: see text] with [Formula: see text] leaves, [Formula: see text] and characterize the trees attaining the lower bound. We also study the effect of edge removal, edge addition and edge subdivision on total outer connected vertex-edge domination number of a graph.

A New Method for Community Detection in the Complex Network on the Basis of Similarity

Introduction: Regarding complex network, to find optimal communities in the network has become a key topic in the field of network theory. It is crucial to understand the Structure and functionality of associated networks. In this paper, we propose a new method of community detection that works on the structural similarity of a network (SSN). Method: This method works in two steps, at the first step, it removes edges between the different groups of nodes which are not very similar to each other. As a result of edge removal, the network is divided into many small random communities, which are referred as main communities. Result: In the second step, we apply the evaluation method (EM), it chooses the best quality communities, from all main communities which already produced at the first step. At last, we apply evaluation metrics to our proposed method and benchmarking methods, which show that the SSN method can detect comparatively more accurate results than other methods in this paper. Conclusion: In this article, we proposed a novel method for community detection in networks, called structural similarity of network (SSN). It works in two steps. In the first step, it randomly removes low similarity edges from the network, which makes several small disconnected communities, called as main communities. Afterward, the main communities are merged to search for the final communities, which are near to actual existing communities of the network. Discussion: This approach is defined on the base of the unweighted network, so in Further research it could be used on weighted networks and can explore some new deep-down attributes. Furthermore, it will be used Facebook and twitter weighted data with the artificial intelligence approach.

Finite element modelling of the progressive collapse of post-and-beam mass timber building substructures under edge and corner column removal scenarios

The structural behaviour of mass timber buildings under a load bearing element removal scenario is complex. To well understand this phenomenon and ultimately develop scientifically based design guidelines against progressive collapse for this type of buildings, there is a need to develop a Finite Element model which accurately captures the non-linear response, load redistribution mechanisms (alternative load paths) and failure modes of such buildings. As such, this paper presents for the first time how mass timber post-and-beam systems can be accurately modelled using Finite Element under edge and corner column removal scenarios. The model was validated against published 2D and 3D experimental tests performed on scaled-down substructures. The non-linear structural responses of the main structural connections were experimentally quantified and inputted into the model using the component method. Results show that the model accurately replicated load redistribution mechanisms, ultimate loads, failure modes, and strain developments. The use of the model was then illustrated by running parametric studies to quantify (i) the influence of the Cross Laminated Timber (CLT) floor panels layout and (ii) one alternative load path, typically ignored in design, on the progressive collapse resistance capacity.

The Method of Braille Embossed Dots Segmentation for Braille Document Images Produced on Reusable Paper

Braille is the language of communication for blind and visually impaired people. Braille characters are embossed at points to convey the meaning. Typically, Braille documents can be produced on plain paper. Braille documents can be created on reusable paper, also known as a third-page paper; this reduces the paper cost, allowing more available documents to stimulate learning for blind or visually impaired persons. This research presents a method of Braille embossed dots segmentation for Braille document images produced on reusable paper to support the availability of cheaper learning material. Initially, Braille documents were imported with a calibrated scanner, Braille document image layer separation was then performed. Followed by edge removal, Braille embossed dot recovery, noise removal, and specify the embossed Braille point. This research was conducted by using four scanners, which scanned Braille documents images under four different lighting conditions. For each lighting condition, the Braille document image area was cropped to the desired size, considering the possible event conditions. They were used to create over 200,000 Braille cells, with over 12 billion patterns. When calculating the average performance under all lighting conditions, the values were Precision 1.0000, Recall 0.7817, Accuracy 0.8545, and F-Measure 0.8756. By effectively using Braille embossed dots segmentation, the process of Braille document recognition will also be efficient.

Optimizing edge sets in networks to produce ground truth communities based on modularity

We consider two new problems regarding the impact of edge addition or removal on the modularity of partitions (or community structures) in a network. The first problem seeks to add edges to enforce that a desired partition is the partition that maximizes modularity. The second problem seeks to find the sparsest representation of a network that has the same partition with maximum modularity as the original network. We present integer programming formulations, a row generation algorithm, and heuristic algorithms to solve these problems. Further, we demonstrate a counter-intuitive behavior of modularity that makes the development of heuristics for general networks difficult. We then present results on a selection of social and illicit networks from the literature.

An efficient method to improve the quality of tetrahedron mesh with MFRC

In this paper, we proposed a novel operation to reconstruction tetrahedrons within a certain region, which we call MFRC (Multi-face reconstruction). During the existing tetrahedral mesh improvement methods, the flip operation is one of the very important components. However, due to the limited area affected by the flip, the improvement of the mesh quality by the flip operation is also very limited. The proposed MFRC algorithm solves this problem. MFRC can reconstruct the local mesh in a larger range and can find the optimal tetrahedron division in the target area within acceptable time complexity. Therefore, based on the MFRC algorithm, we combined other operations including smoothing, edge removal, face removal, and vertex insertion/deletion to develop an effective mesh quality improvement method. Numerical experiments of dozens of meshes show that the algorithm can effectively improve the low-quality elements in the tetrahedral mesh, and can effectively reduce the running time, which has important significance for the quality improvement of large-scale mesh.

Criminal networks analysis in missing data scenarios through graph distances

Data collected in criminal investigations may suffer from issues like: (i) incompleteness, due to the covert nature of criminal organizations; (ii) incorrectness, caused by either unintentional data collection errors or intentional deception by criminals; (iii) inconsistency, when the same information is collected into law enforcement databases multiple times, or in different formats. In this paper we analyze nine real criminal networks of different nature (i.e., Mafia networks, criminal street gangs and terrorist organizations) in order to quantify the impact of incomplete data, and to determine which network type is most affected by it. The networks are firstly pruned using two specific methods: (i) random edge removal, simulating the scenario in which the Law Enforcement Agencies fail to intercept some calls, or to spot sporadic meetings among suspects; (ii) node removal, modeling the situation in which some suspects cannot be intercepted or investigated. Finally we compute spectral distances (i.e., Adjacency, Laplacian and normalized Laplacian Spectral Distances) and matrix distances (i.e., Root Euclidean Distance) between the complete and pruned networks, which we compare using statistical analysis. Our investigation identifies two main features: first, the overall understanding of the criminal networks remains high even with incomplete data on criminal interactions (i.e., when 10% of edges are removed); second, removing even a small fraction of suspects not investigated (i.e., 2% of nodes are removed) may lead to significant misinterpretation of the overall network.

Probabilistic measures of edge criticality in graphs: a study in water distribution networks

The issue of vulnerability and robustness in networks have been addressed by several methods. The goal is to identify which are the critical components (i.e., nodes/edges) whose failure impairs the functioning of the network and how much this impacts the ensuing increase in vulnerability. In this paper we consider the drop in the network robustness as measured by the increase in vulnerability of the perturbed network and compare it with the original one. Traditional robustness metrics are based on centrality measures, the loss of efficiency and spectral analysis. The approach proposed in this paper sees the graph as a set of probability distributions and computes, specifically the probability distribution of its node to node distances and computes an index of vulnerability through the distance between the node-to-node distributions associated to original network and the one obtained by the removal of nodes and edges. Two such distances are proposed for this analysis: Jensen–Shannon and Wasserstein, based respectively on information theory and optimal transport theory, which are shown to offer a different characterization of vulnerability. Extensive computational results, including two real-world water distribution networks, are reported comparing the new approach to the traditional metrics. This modelling and algorithmic framework can also support the analysis of other networked infrastructures among which power grids, gas distribution and transit networks.

Sentinel-1 EW mode dataset for Antarctica from 2014–2020 produced by the CASEarth Cloud Service Platform

ABSTRACT Antarctica plays an important role in research on global change, and its unique geography, ocean, climate, and environment provide an ideal place for humankind to understand Earth’s evolution. Remote sensing provides an effective means to monitor and observe large-scale processes on the continent. Synthetic aperture radar (SAR) in particular provides the capability for all-weather Earth observation. The Sentinel-1A and Sentinel-1B SAR satellites have ideal ground coverage and imaging frequency for observing Antarctica. This study developed a dataset of 69,586 Sentinel-1 EW mode satellite images of the Antarctic ice sheet from October 2014 to December 2020. The dataset was processed with the European Space Agency Sentinel Application Platform (SNAP) and a Python batch scheduling tool on the Big Earth Data Cloud Service Platform of the Chinese Academy of Sciences Big Earth Data Science Engineering Program (CASEarth). Several data processing operations were implemented to process the raw dataset, including radiometric calibration, invalid edge removal, geocoding, data re-projection to an Antarctic projection, data compression to TIFF format, and construction of image pyramids. The dataset is available at http://www.doi.org/10.11922/sciencedb.j00076.00085.

Hogyan befolyásolja a villamosenergia-hálózatról rendelkezésre álló információ a fizikai támadások által okozott sérülékenységről alkotott képet?

Összefoglaló. A villamosenergia-rendszerek fizikai támadásokkal szembeni ellenálló képessége a közelmúltban világszerte történt események ismeretében egyre nagyobb hangsúlyt kap a tématerület kutatásaiban. Az ilyen eseményekre való megfelelő felkészüléshez elengedhetetlen az üzemeltetett infrastruktúrának, elsősorban annak gyengeségeinek pontos ismerete. A cikkben Magyarország villamosenergia-hálózatának adatai alapján készített súlyozatlan és súlyozott gráfokon végzünk vizsgálatokat, hogy megértsük a különböző stratégia mentén kiválasztott célpontok elleni támadások milyen mértékben csökkentik a topológiai hatékonyságot. A cikk célja egyben a magyar hálózat sérülékenységének általános bemutatása is, mely hasznos bemeneti információ lehet a kockázati tervek elkészítésekor. Summary. Tolerance of the power grid against physical intrusions has gained importance in the light of various attacks that have taken place around the world. To adequately prepare for such events, grid operators have to possess a deep understanding of their infrastructure, more specifically, of its weaknesses. A graph representation of the Hungarian power grid was created in a way that the vertices are generators, transformers, and substations and the edges are high-voltage transmission lines. All transmission and sub-transmission elements were considered, including the 132 kV network as well. The network is subjected to various types of single and double element attacks, objects of which are selected according to different aspects. The vulnerability of the network is measured as a relative drop in efficiency when a vertex or an edge is removed from the network. Efficiency is a measure of the network’s performance, assuming that the efficiency for transmitting electricity between vertices i and j is proportional to the reciprocal of their distance. In this paper, simultaneous removals were considered, arranged into two scenarios (single or double element removal) and a total of 5 cases were carried out (single vertex removal, single edge removal, double vertex removal, double edge removal, single vertex and single edge removal). During the examinations, all possible removal combinations were simulated, thus the 5 cases represent 385, 504, 73920, 128271 and 193797 runs, respectively. After all runs were performed, damage values were determined for random and targeted attacks, and attacks causing maximal damage were also identified. In all cases, damage was calculated for unweighted and weighted networks as well, to enable the comparison of those two models. The aims of this paper are threefold: to perform a general assessment on the vulnerability of the Hungarian power grid against random and targeted attacks; to compare the damage caused by different attack strategies; and to highlight the differences between using unweighted and weighted graphs representations. Random removal of a single vertex or a single edge caused 0.3–0.4% drop in efficiency, respectively, which indicates a high tolerance against such attacks. Damage for random double attacks was still only in the range of 0.6–0.8%, which is acceptable. It was shown that if targets are selected by the attacker based on the betweenness rank of the element, damage would be below the maximal possible values. Comparison of the damage measured in the unweighted and the weighted network representations has shown that damage to the weighted network tends to be bigger for vertex attacks, but the contrary is observed for edge attacks. Numerical differences between the two representations do not show any trend that could be generalised, but in the case of the most vulnerable elements significant differences were found in damage measures, which underlines the importance of using weighted models.

Edge Control in the Computer-Controlled Optical Surface.

The computer-controlled optical surface (CCOS) can process good optical surfaces, but its edge effect greatly affects its development and application range. In this paper, based on the two fundamental causes of the CCOS’s edge effect—namely the nonlinear variation of edge pressure and the unreachable edge removal—a combined polishing method of double-rotor polishing and spin-polishing is proposed. The model of the combined polishing method is established and theoretically analyzed. Combined with the advantages of double-rotor polishing and spin-polishing, the combined polishing process can achieve full-aperture machining without pressure change. Finally, the single-crystal silicon sample with a diameter of 100 mm is polished by the combined polishing process. The results show that, compared with the traditional CCOS polishing, the residual error of the sample after the combined polishing process is more convergent, and the edge effect is effectively controlled.

Qualitative Regionalization of Bay of Bengal

Clustering is an essential statistical technique to find subgroups within a dataset. Clustering helps to uncover hidden relationships among the observational variables in the data. Many researchers have applied clustering techniques across a number of knowledge domains with success. Here we focus on application to ocean science, more particularly to the north region of the Indian Ocean, i.e., the Bay of Bengal. In this article, Regionalization is carried out for the Bay of Bengal to group the regions with similar characteristics using a graph-based clustering technique called SKATER (Spatial ‘K’luster Analysis by Tree Edge Removal). These subgroups are consistent with observations that characterize the near-surface features of the Bay of Bengal.

Critical concepts of restrained domination in signed graphs

A signed graph [Formula: see text] is a simple undirected graph in which each edge is either positive or negative. Restrained dominating set [Formula: see text] in [Formula: see text] is a restrained dominating set of the underlying graph [Formula: see text] where the subgraph induced by the edges across [Formula: see text] and within [Formula: see text] is balanced. The minimum cardinality of a restrained dominating set of [Formula: see text] is called the restrained domination number, denoted by [Formula: see text]. In this paper, we initiate the study on various critical concepts to investigate the effect of edge removal or edge addition on restrained domination number in signed graphs.

Election Manipulation on Social Networks: Seeding, Edge Removal, Edge Addition

We focus on the election manipulation problem through social influence, where a manipulator exploits a social network to make her most preferred candidate win an election. Influence is due to information in favor of and/or against one or multiple candidates, sent by seeds and spreading through the network according to the independent cascade model. We provide a comprehensive theoretical study of the election control problem, investigating two forms of manipulations: seeding to buy influencers given a social network and removing or adding edges in the social network given the set of the seeds and the information sent. In particular, we study a wide range of cases distinguishing in the number of candidates or the kind of information spread over the network.
 Our main result shows that the election manipulation problem is not affordable in the worst-case, even when one accepts to get an approximation of the optimal margin of victory, except for the case of seeding when the number of hard-to-manipulate voters is not too large, and the number of uncertain voters is not too small, where we say that a voter that does not vote for the manipulator's candidate is hard-to-manipulate if there is no way to make her vote for this candidate, and uncertain otherwise.
 We also provide some results showing the hardness of the problems in special cases. More precisely, in the case of seeding, we show that the manipulation is hard even if the graph is a line and that a large class of algorithms, including most of the approaches recently adopted for social-influence problems (e.g., greedy, degree centrality, PageRank, VoteRank), fails to compute a bounded approximation even on elementary networks, such as undirected graphs with every node having a degree at most two or directed trees. In the case of edge removal or addition, our hardness results also apply to election manipulation when the manipulator has an unlimited budget, being allowed to remove or add an arbitrary number of edges, and to the basic case of social influence maximization/minimization in the restricted case of finite budget.
 Interestingly, our hardness results for seeding and edge removal/addition still hold in a re-optimization variant, where the manipulator already knows an optimal solution to the problem and computes a new solution once a local modification occurs, e.g., the removal/addition of a single edge.

Regionalization for urban air mobility application in metropolitan areas: case studies in San Francisco and New York

In a new era of mobility where the transportation of persons or goods via flying vehicles over urban areas has garnered great interest in its application in urban space. With the anticipated utilization of sUAS in urban airspace, a multi-dimensional understanding of urban space is essential. As a first step to assess the feasibility of Urban Air Mobility (UAM) in urban areas, we conduct regionalization and correspondence analysis in highly urbanized areas – San Francisco, CA and Manhattan, NY – by incorporating population dataset and urban 3D airspace to delineate the regional boundaries. Regionalization is carried out using graph-based clustering technique called SKATER (Spatial ‘K’luster Analysis by Tree Edge Removal) to group the regions having similar characteristics and address the compound effect of both population and spatial information. By classifying the regions into five categories through correspondence analysis, the operational and economic feasibility of each region is evaluated. The results provide the region maps of each city with the most and least attractive regions for UAM application with the temporal notion, whether the clusters are daytime-intensive or nighttime-intensive areas. The outcomes have several unique information that can benefit drone delivery target area identification, landing location identification, demand prediction. Our approach can contribute to providing a useful basis for management for UAM in urban areas as well as the process of regulating airspace use.

Criminal networks analysis in missing data scenarios through graph distances.

Data collected in criminal investigations may suffer from issues like: (i) incompleteness, due to the covert nature of criminal organizations; (ii) incorrectness, caused by either unintentional data collection errors or intentional deception by criminals; (iii) inconsistency, when the same information is collected into law enforcement databases multiple times, or in different formats. In this paper we analyze nine real criminal networks of different nature (i.e., Mafia networks, criminal street gangs and terrorist organizations) in order to quantify the impact of incomplete data, and to determine which network type is most affected by it. The networks are firstly pruned using two specific methods: (i) random edge removal, simulating the scenario in which the Law Enforcement Agencies fail to intercept some calls, or to spot sporadic meetings among suspects; (ii) node removal, modeling the situation in which some suspects cannot be intercepted or investigated. Finally we compute spectral distances (i.e., Adjacency, Laplacian and normalized Laplacian Spectral Distances) and matrix distances (i.e., Root Euclidean Distance) between the complete and pruned networks, which we compare using statistical analysis. Our investigation identifies two main features: first, the overall understanding of the criminal networks remains high even with incomplete data on criminal interactions (i.e., when 10% of edges are removed); second, removing even a small fraction of suspects not investigated (i.e., 2% of nodes are removed) may lead to significant misinterpretation of the overall network.

How does the vulnerability of an evolving power grid change?

Topological robustness and fault tolerance of the power system are amongst the most studied topics when it comes to the assessment of grid vulnerability. The use of adequate methods and performance metric can greatly contribute to a number of actions, including operation planning, grid development and other specific measures. A shortcoming of several studies is that they fail to take the aspects of network evolution into consideration. In this paper the seven-decade historical dataset (1949–2019) of the Hungarian power system is used to perform vulnerability assessment applying a complex network approach. Damage tolerance of the network is examined against node and edge removals. The results show that the evolving grid has increased its tolerance against large disturbances very early, but vulnerability values show little variance from 1979, despite that the size of the network has increased significantly. It is also found that more efficient and more robust topologies impose slightly conflicting conditions for grid development planning.

Modeling and prediction of tool influence function under complex edge in sub-aperture optical polishing.

Edge mis-figures are regarded as one of the most difficult technical issues in optical fabrication. At present, only the near straight-line edge tool influence function (TIF) can be fitted by a polynomial function, but it is difficult to unify a 2-D analytical model suitable for complex edge workpieces and various tools, due to the lack of the scientific understanding of the edge removal behavior. In this paper, a comprehensive mathematical model is proposed to reveal the mechanism of the edge effect and accurately predict the complex edge TIF. The concept of a nonlinear edge kernel is first proposed and verified that the nonlinear pressure can be characterized by convoluting the kernel with the edge contour, which can be easily adapted to complex edge cases; besides, the edge kernel obtaining algorithm is established. The linear pressure part is verified to be constrained by the moment balance formula, which occurs in universal joint tool. Besides, the basic pressure distribution is presented to compensate the pressure distortion caused by the uneven form of the tool pad. The introducing of these three parts makes the complex edge pressure modeled efficiently and matched perfectly with the FEA results. In addition, a series of TIF experiments were carried out on various complex edge workpieces and different tools, which could be well predicted by the proposed model in 2-D view.

Network community detection via iterative edge removal in a flocking-like system

We present a network community-detection technique based on properties that emerge from a nature-inspired flocking system. Our algorithm comprises two alternating mechanisms: first, we control the particles alignment in higher dimensional space and, second, we present an iterative process of edge removal. These mechanisms together can potentially reduce accidental alignment among particles from different communities and, consequently, the model can generate robust community-detection results. In the proposed model, a random-direction unit vector is assigned to each vertex initially. A nonlinear dynamic law is established, so that neighboring vertices try to become aligned with each other. After some time, the system stops and edges that connect the least-aligned pairs of vertices are removed. Then, the evolution starts over without the removed edges, and after enough number of removal rounds, each community becomes a connected component. The proposed approach is evaluated using widely accepted benchmarks and real-world networks. Experimental results reveal that the method is robust and excels on a wide variety of networks. For large sparse networks, the edge-removal process runs in quasilinear time, which enables application in large-scale networks. Moreover, the distributed nature of the process eases the parallel implementation of the model.

Network permeability changes according to a quadratic power law upon removal of a single edge

We report a phenomenological power law for the reduction of network permeability in statistically homogeneous spatial networks upon removal of a single edge. We characterize this power law for plexus-like microvascular sinusoidal networks from liver tissue, as well as perturbed two- and three-dimensional regular lattices. We provide a heuristic argument for the observed power law by mapping arbitrary spatial networks that satisfy Darcy's law on a small-scale resistor network.