Graph Connectivity Research Articles

Analysis of the impact effect of a piece of cotton with a flat surface with a multi-sided grates slope

In the cotton ginning unit recommended in the article, the impact effects of multi-faceted gutters on flat sloping surfaces of cotton pieces in large waste ginning zones have been theoretically studied and connection graphs have been constructed. The results of the numerical solution of the problem, based on the analysis of the obtained analytical solutions, recommended the appropriate values of system parameters to increase the efficiency of cleaning cotton from large wastes in all three zones of the cleaning unit.

Effective Connectivity Is A More Promising Biomarker for Brain Health in Middle‐Aged Adults Than Functional Connectivity: Bogalusa Heart Study

AbstractBackgroundEffective connectivity, the causal influence that functional activity in a source brain location exerts over functional activity in a target brain location, has the potential to provide richer information about brain networks than functional connectivity, which only quantifies activity synchrony between regions. However, head‐to‐head comparisons of effective and functional connectivity from functional MRI data are rare, especially among diverse cognitively healthy middle aged and older adults.Method100 Bogalusa Heart Study participants performed a Stroop task during functional MRI (Table 1). Effective connectivity and functional connectivity among 24 regions of interest (ROIs) previously identified as activated by this task [1] were calculated using deep stacking networks [2] and Pearson correlation, respectively. Graph metrics were then calculated from directed graphs resulting from effective connectivity and undirected graphs resulting from functional connectivity. Linear regression models related graph metrics to demographic, cardiometabolic, and cognitive measures.ResultFigure 1 shows the group‐consensus effective and functional connectivity graphs. Systolic blood pressure (SBP) was associated with effective connectivity based characteristic path length (Pearson’s r = 0.22, p‐value = 0.038) and modularity (r = 0.25, p‐value = 0.02) (Figure 2). Diastolic blood pressure (DBP) was associated with effective connectivity based degree, density, clustering coefficient, modularity, transitivity, characteristic path length, and global efficiency (|r| = 0.26 ‐ 0.35, maximum p‐value = 0.013) (Figure 2). Word reading and vocabulary scores from the Wide Range Achievement Test (WRAT) were associated with effective connectivity based degree, density, clustering coefficient, transitivity, characteristic path length, modularity, and global efficiency (|r| = 0.21 ‐ 0.27, maximum p‐value = 0.049). Logical Memory II Recognition scores associated with effective connectivity based assortativity (r = 0.24, p‐value = 0.025). Associations between functional connectivity based graph metrics and demographic, cardiometabolic, and cognitive measures were not significant.ConclusionIn a diverse, cognitively healthy, middle‐aged community sample, graph metrics derived from effective connectivity based directed graphs tracked more closely with recognized indicators of brain health than traditional functional connectivity based undirected graph metrics.

Characterization of component diagnosability of regular networks

Multiprocessor systems, which usually take interconnection network (or graph) as underlying topologies, are commonly deployed for big data analysis because of evolution in technologies such as cloud computing, IoT, social network and so on. Reliability evaluation is of significant importance to characterize fault tolerability for the topologies of multiprocessor systems, and system-level diagnosis is a primary strategy to identify the faulty processors in the systems. The g-component connectivity cκg(G) of a graph G is the size of a minimal vertex-set, whose removal will disconnect G to possess at least g components, which reflects the invulnerability of the topology graph. Based on g-component connectivity of graph G, the g-component diagnosability ctg(G) of regular networks has been proposed as a parameter to measure network fault-tolerability. The g-component diagnosability ctg(G) is the maximum t such that the graph G is g-component t-diagnosable. We first propose some general characterizations of the component diagnosability of regular networks under the classic PMC model and MM∗ model based on the component connectivity. And then we present some empirical analysis for some kinds of well-known regular networks, such as BC networks, star graphs, bubble-sort star graphs, alternating group graphs.

Substantiation of the parameters of modernized cotton bundle disassembler machine with the working drum with a curved peg and a flexible element

The article covers the results of research on substantiation of the parameters of the modernized cotton bundle disassembler machine with the working drum with a curved peg and a flexible element. The design scheme and working principle of the machine are described. Recommended values of the parameters because of full factor experiments in the production environment are given. The results of the calculations after processing in the article are presented in the form of connection graphs for raw cotton. In each graph, the first factor is presented at the minimum, the second at the intermediate, and the third at the maximum value. The figures show graphs of the dependence of the seed damage after the UHK unit on the input factors and the graphs of the dependence of the torque on the milling shaft on the input factors.

Functional Connectome of the Human Brain with Total Correlation.

Recent studies proposed the use of Total Correlation to describe functional connectivity among brain regions as a multivariate alternative to conventional pairwise measures such as correlation or mutual information. In this work, we build on this idea to infer a large-scale (whole-brain) connectivity network based on Total Correlation and show the possibility of using this kind of network as biomarkers of brain alterations. In particular, this work uses Correlation Explanation (CorEx) to estimate Total Correlation. First, we prove that CorEx estimates of Total Correlation and clustering results are trustable compared to ground truth values. Second, the inferred large-scale connectivity network extracted from the more extensive open fMRI datasets is consistent with existing neuroscience studies, but, interestingly, can estimate additional relations beyond pairwise regions. And finally, we show how the connectivity graphs based on Total Correlation can also be an effective tool to aid in the discovery of brain diseases.

Semihypergroup-Based Graph for Modeling International Spread of COVID-n in Social Systems

Graph theoretic techniques have been widely applied to model many types of links in social systems. Also, algebraic hypercompositional structure theory has demonstrated its systematic application in some problems. Influenced by these mathematical notions, a novel semihypergroup-based graph (SBG) of G=H,E is constructed through the fundamental relation γn on H, where semihypergroup H is appointed as the set of vertices and E is addressed as the set of edges on SBG. Indeed, two arbitrary vertices x and y are adjacent if xγny. The connectivity of graph G is characterized by xγ*y, whereby the connected components SBG of G would be exactly the elements of the fundamental group H/γ*. Based on SBG, some fundamental characteristics of the graph such as complete, regular, Eulerian, isomorphism, and Cartesian products are discussed along with illustrative examples to clarify the relevance between semihypergroup H and its corresponding graph. Furthermore, the notions of geometric space, block, polygonal, and connected components are introduced in terms of the developed SBG. To formulate the links among individuals/countries in the wake of the COVID (coronavirus disease) pandemic, a theoretical SBG methodology is presented to analyze and simplify such social systems. Finally, the developed SBG is used to model the trend diffusion of the viral disease COVID-n in social systems (i.e., countries and individuals).

A generalization of Petersen's matching theorem

One of the earliest results in graph theory is Petersen's matching theorem from 1891 which states that every bridgeless cubic graph contains a perfect matching. Since the vertex-connectivity and edge-connectivity in a connected cubic graph are equal, Petersen's theorem can be stated as follows: If G is a 2-connected 3-regular graph of order n, then α′(G)=12n, where α′(G) denotes the matching number of G. We generalize Petersen's theorem and prove that for k≥3 an odd integer, if G is a 2-connected k-regular graph of order n, then α′(G)≥(k2+k+6k2+2k+3)×n2. The case when k is even behaves differently. In this case, for k≥4 even, if G is a 2-connected k-regular graph of order n, then α′(G)≥(k2+4k2+k+2)×n2. For all k≥3, if G is a 2-connected graph of order n and maximum degree k that is not necessarily regular, then we show that α′(G)≥2nk+2. In all the above bounds, the extremal graphs are characterized.

Vertex Splitting, Coincident Realisations, and Global Rigidity of Braced Triangulations

We give a relatively short graph theoretic proof of a result of Jordán and Tanigawa that a 4-connected graph which has a spanning plane triangulation as a proper subgraph is generically globally rigid in \({\mathbb {R}}^3\). Our proof is based on a new sufficient condition for the so called vertex splitting operation to preserve generic global rigidity in \({\mathbb {R}}^d\).

Pure graph-guided multi-view subspace clustering

Multi-view subspace clustering approaches have shown outstanding performance in revealing similarity relationships and complex structures hidden in data. Despite the progress, previous multi-view clustering methods still face two challenges: (1) it is difficult to simultaneously achieve sparsity and connectivity of the affinity graph; (2) existing methods usually separate the graph learning step from the clustering process, which leads to unsatisfactory clustering performance as the final results critically rely on the learned graph. In this paper, we propose to achieve a structured consensus graph for multi-view subspace clustering by leveraging the sparsity and connectivity of each affinity graph. In the proposed method, the pure graph for each view is searched by finding the good neighbors. The multiple pure graphs are further fused into a consensus graph with a block-diagonal structure. That is, the consensus graph is enforced to contain exactly c connected components where c is the number of the clusters. Hence the label to each sample can be directly assigned since each connected component precisely corresponds to an individual cluster. As a result, the proposed model seamlessly accomplishes the subtasks including graph construction, pure graph learning (i.e., good neighbors searching), and cluster label allocation in a mutual reinforcement manner. Extensive experimental results demonstrate the superiority and reliability of our proposed method.

Connectivity of Triangulation Flip Graphs in the Plane

Given a finite point set P in general position in the plane, a full triangulation of P is a maximal straight-line embedded plane graph on P. A partial triangulation of P is a full triangulation of some subset P' of P containing all extreme points in P. A bistellar flip on a partial triangulation either flips an edge (called edge flip), removes a non-extreme point of degree 3, or adds a point in P setminus P' as vertex of degree 3. The bistellar flip graph has all partial triangulations as vertices, and a pair of partial triangulations is adjacent if they can be obtained from one another by a bistellar flip. The edge flip graph is defined with full triangulations as vertices, and edge flips determining the adjacencies. Lawson showed in the early seventies that these graphs are connected. The goal of this paper is to investigate the structure of these graphs, with emphasis on their vertex connectivity. For sets P of n points in the plane in general position, we show that the edge flip graph is lceil {n}/{2}-2rceil -vertex connected, and the bistellar flip graph is (n-3)-vertex connected; both results are tight. The latter bound matches the situation for the subfamily of regular triangulations (i.e., partial triangulations obtained by lifting the points to 3-space and projecting back the lower convex hull), where (n-3)-vertex connectivity has been known since the late eighties through the secondary polytope due to Gelfand, Kapranov, & Zelevinsky and Balinski’s Theorem. For the edge flip-graph, we additionally show that the vertex connectivity is at least as large as (and hence equal to) the minimum degree (i.e., the minimum number of flippable edges in any full triangulation), provided that n is large enough. Our methods also yield several other results: (i) The edge flip graph can be covered by graphs of polytopes of dimension lceil {n}/{2} -2rceil (products of associahedra) and the bistellar flip graph can be covered by graphs of polytopes of dimension n-3 (products of secondary polytopes). (ii) A partial triangulation is regular, if it has distance n-3 in the Hasse diagram of the partial order of partial subdivisions from the trivial subdivision. (iii) All partial triangulations of a point set are regular iff the partial order of partial subdivisions has height n-3. (iv) There are arbitrarily large sets P with non-regular partial triangulations and such that every proper subset has only regular triangulations, i.e., there are no small certificates for the existence of non-regular triangulations.

Rank connectivity and pivot-minors of graphs

The cut-rank of a set X in a graph G is the rank of the X×(V(G)−X) submatrix of the adjacency matrix over the binary field. A split is a partition of the vertex set into two sets (X,Y) such that the cut-rank of X is less than 2 and both X and Y have at least two vertices. A graph is prime (with respect to the split decomposition) if it is connected and has no splits. A graph G is k+ℓ-rank-connected if for every set X of vertices with the cut-rank less than k, |X| or |V(G)−X| is less than k+ℓ. We prove that every prime 3+2-rank-connected graph G with at least 10 vertices has a prime 3+3-rank-connected pivot-minor H such that |V(H)|=|V(G)|−1. As a corollary, we show that every excluded pivot-minor for the class of graphs of rank-width at most k has at most (3.5⋅6k−1)/5 vertices for k≥2. We also show that the excluded pivot-minors for the class of graphs of rank-width at most 2 have at most 16 vertices.

Diagnosis of Epilepsy with Functional Connectivity in EEG after a Suspected First Seizure.

Epilepsy is regarded as a structural and functional network disorder, affecting around 50 million people worldwide. A correct disease diagnosis can lead to quicker medical action, preventing adverse effects. This paper reports the design of a classifier for epilepsy diagnosis in patients after a first ictal episode, using electroencephalogram (EEG) recordings. The dataset consists of resting-state EEG from 629 patients, of which 504 were retained for the study. The patient's cohort exists out of 291 patients with epilepsy and 213 patients with other pathologies. The data were split into two sets: 80% training set and 20% test set. The extracted features from EEG included functional connectivity measures, graph measures, band powers and brain asymmetry ratios. Feature reduction was performed, and the models were trained using Machine Learning (ML) techniques. The models' evaluation was performed with the area under the receiver operating characteristic curve (AUC). When focusing specifically on focal lesional epileptic patients, better results were obtained. This classification task was optimized using a 5-fold cross-validation, where SVM using PCA for feature reduction achieved an AUC of 0.730 ± 0.030. In the test set, the same model achieved 0.649 of AUC. The verified decrease is justified by the considerable diversity of pathologies in the cohort. An analysis of the selected features across tested models shows that functional connectivity and its graph measures have the most considerable predictive power, along with full-spectrum frequency-based features. To conclude, the proposed algorithms, with some refinement, can be of added value for doctors diagnosing epilepsy from EEG recordings after a suspected first seizure.

MODL-37. DISCERNIBLE INTERINDIVIDUAL PATTERNS OF GLOBAL EFFICIENCY DECLINE DURING THEORETICAL BRAIN SURGERY

Abstract Resection of infiltrating brain tumors, such as diffuse gliomas, generally involves resecting a portion of a lobe of the brain. While the concept of localized functions, and the risk to removing these areas, is well established in neurosurgical thinking, the potential that the overall global efficiency of the connectome could be disproportionately disturbed by an intervention in ways which are not immediately obvious have not been formally studied. The current article provides evidence that structural patterns exist in the impact resection of various lobes of the brain has, which also differs between subjects. We utilized diffusion tractography to create structural connectivity graphs from the brains of 80 healthy adults, and then performed every plausible brain surgery in every gross anatomic region of the cerebrum by deleting every possible combination of nodes in the graph which were adjacent to each other, and measured the drop in global efficiency (GE) at each nodal deletion. Not surprisingly, the deletion of some nodes was worse than others, such that in every lobe we studied in every subject, there were combinations of deletions which were worse for GE than removing a greater number of nodes in a different part of the brain. Interestingly, while the worst nodes differed between subjects, there were specific nodes which typically showed up as particularly detrimental regardless of which node was the worst in that person, but that there were patterns of so-called ―connectotype, which could determine which nodes were the worst. Progressive removal of a lobe of the brain leads to patterns of global efficiency decline which are reasonably predictable, but which are not the same between subjects. Given evidence that global efficiency relates to specific neuro-cognitive abilities, this provides a path towards reducing the cognitive footprint of brain surgery.

Multi-label classification of Alzheimer's disease stages from resting-state fMRI-based correlation connectivity data and deep learning

Alzheimer's disease is a neurodegenerative condition that gradually impairs cognitive abilities. Recently, various neuroimaging modalities and machine learning methods have surfaced to diagnose Alzheimer's disease. Resting-state fMRI is a neuroimaging modality that has been widely utilized to study brain activity related to neurodegenerative diseases. In literature, the previous studies are limited to the binary classification of Alzheimer's disease and Mild Cognitive Impairment. The application of computer-aided diagnosis for the numerous advancing phases of Alzheimer's disease, on the other hand, remains understudied. This research analyzes and presents methods for multi-label classification of six Alzheimer's stages using rs-fMRI and deep learning. The proposed model solves the multi-class classification problem by extracting the brain's functional connectivity networks from rs-fMRI data and employing two deep learning approaches, Stacked Sparse Autoencoder and Brain Connectivity Graph Convolutional Network. The suggested models' results were assessed using the k-fold cross-validation approach, and an average accuracy of 77.13% and 84.03% was reached for multi-label classification using Stacked Sparse Autoencoders and Brain Connectivity Based Convolutional Network, respectively. An analysis of brain regions was also performed by using the network's learned weights, leading to the conclusion that the precentral gyrus, frontal gyrus, lingual gyrus, and supplementary motor area are the significant brain regions of interest.

Localizing epileptogenic network from SEEG using non-linear correlation, mutual information and graph theory analysis.

The key challenge in epilepsy surgery is precise localization and removal of the epileptogenic zone (EZ) from the brain. Localization of the epileptogenic network by visual analysis of intracranial EEG is extremely difficult. In this retrospective study, we used interictal connectivity and graph theory analysis on intracranial EEG to better delineate the epileptogenic zone. Patients who underwent surgery for drug-refractory mesial temporal and neocortical epilepsy were included. Computational measures, such as h2 nonlinear correlation and mutual information, were used to estimate the interdependency of intracranial EEGs. We observed that the Out-Degree, Out-Strength, and Betweenness centrality (graph properties) were the best predictors of EZ. From the results, we also found that graph properties with a normalized value above 0.75 were found to be a useful measure to localize the EZ with a sensitivity of 87.88 and a specificity of 87.13. Our results also validate that frequently occurring types of interictal fast discharges (IFD) with connectivity measures and graph properties can better localize the EZ. We foresee graph theory analysis of interictal intracranial EEG data can help precise localization of EZ for cortical resection as well as in minimally invasive radiofrequency ablation of epileptogenic hubs. Further, prospective validation is required for clinical use.

Graph-generative neural network for EEG-based epileptic seizure detection via discovery of dynamic brain functional connectivity

Dynamic complexity in brain functional connectivity has hindered the effective use of signal processing or machine learning methods to diagnose neurological disorders such as epilepsy. This paper proposed a new graph-generative neural network (GGN) model for the dynamic discovery of brain functional connectivity via deep analysis of scalp electroencephalogram (EEG) signals recorded from various regions of a patient’s scalp. Brain functional connectivity graphs are generated for the extraction of spatial–temporal resolution of various onset epilepsy seizure patterns. Our supervised GGN model was substantiated by seizure detection and classification experiments. We train the GGN model using a clinically proven dataset of over 3047 epileptic seizure cases. The GGN model achieved a 91% accuracy in classifying seven types of epileptic seizure attacks, which outperformed the 65%, 74%, and 82% accuracy in using the convolutional neural network (CNN), graph neural networks (GNN), and transformer models, respectively. We present the GGN model architecture and operational steps to assist neuroscientists or brain specialists in using dynamic functional connectivity information to detect neurological disorders. Furthermore, we suggest to merge our spatial–temporal graph generator design in upgrading the conventional CNN and GNN models with dynamic convolutional kernels for accuracy enhancement.

The thresholding problem and variability in the EEG graph network parameters

Graph thresholding is a frequently used practice of eliminating the weak connections in brain functional connectivity graphs. The main aim of the procedure is to delete the spurious connections in the data. However, the choice of the threshold is arbitrary, and the effect of the threshold choice is not fully understood. Here we present the description of the changes in the global measures of a functional connectivity graph depending on the different proportional thresholds based on the 146 resting-state EEG recordings. The dynamics is presented in five different synchronization measures (wPLI, ImCoh, Coherence, ciPLV, PPC) in sensors and source spaces. The analysis shows significant changes in the graph’s global connectivity measures as a function of the chosen threshold which may influence the outcome of the study. The choice of the threshold could lead to different study conclusions; thus it is necessary to improve the reasoning behind the choice of the different analytic options and consider the adoption of different analytic approaches. We also proposed some ways of improving the procedure of thresholding in functional connectivity research.

Towards Obtaining a 3-Decomposition From a Perfect Matching

A decomposition of a graph is a set of subgraphs whose edges partition those of $G$. The 3-decomposition conjecture posed by Hoffmann-Ostenhof in 2011 states that every connected cubic graph can be decomposed into a spanning tree, a 2-regular subgraph, and a matching. It has been settled for special classes of graphs, one of the first results being for Hamiltonian graphs. In the past two years several new results have been obtained, adding the classes of plane, claw-free, and 3-connected tree-width 3 graphs to the list.
 In this paper, we regard a natural extension of Hamiltonian graphs: removing a Hamiltonian cycle from a cubic graph leaves a perfect matching. Conversely, removing a perfect matching $M$ from a cubic graph $G$ leaves a disjoint union of cycles. Contracting these cycles yields a new graph $G_M$. The graph $G$ is star-like if $G_M$ is a star for some perfect matching $M$, making Hamiltonian graphs star-like. We extend the technique used to prove that Hamiltonian graphs satisfy the 3-decomposition conjecture to show that 3-connected star-like graphs satisfy it as well.

Extremal graphs of bipartite graphs of given diameter for two indices on resistance-distance

For a connected graph G , the Kirchhoff index is defined as K f ( G ) = ∑ 1 ≤ i < j ≤ n R G ( v i , v j ) and the multiplicative eccentricity resistance-distance index ξ R ∗ ( G ) = ∑ { v i , v j } ⊆ V G ɛ ( v i ) ɛ ( v j ) R G ( v i , v j ) , where R G ( v i , v j ) is the effective resistance-distance between v i and v j , and ɛ ( ⋅ ) is the eccentricity of the corresponding vertex, respectively. In this paper, among all the bipartite graphs with diameter 2, the graphs which have the smallest multiplicative eccentricity resistance-distance index are characterized. Among all the bipartite graphs with diameter 3 except 2-connected graphs with g ( G ) = 4 , the graphs which have the second largest, the third largest Kirchhoff index and the largest, the second largest multiplicative eccentricity resistance-distance index are also characterized, respectively.

Sun toughness and path-factor uniform graphs

A path-factor is a spanning subgraphFofGsuch that each component ofFis a path of order at least two. Letkbe an integer withk ≥ 2. AP≥k-factor is a spanning subgraph ofGwhose components are paths of order at leastk. A graphGis called aP≥k-factor covered graph if for any edgeeofG,Gadmits aP≥k-factor coveringe. A graphGis called aP≥k-factor uniform graph if for any two distinct edgese1ande2ofG,Ghas aP≥k-factor coveringe1and excludinge2. In this article, we claim that (1) a 4-edge-connected graphGis aP≥3-factor uniform graph if its sun toughnesss(G) ≥ 1; (2) a 4-connected graphGis aP≥3-factor uniform graph if its sun toughnesss(G)&gt;4/5.