Complex Graph Research Articles

The effect of graph complexity in an energy-based FDI approach

This paper introduces a structured approach for creating node signature graphs in energy graph-based visualization for industrial systems, focusing on anomaly detection. It examines the relationship between graph cardinality and the singular value decomposition analysis applied in the energy graph-based visualization method. The results reveal a trade-of between graph complexity and singular value resolution. The study highlights how graph structure affects energy flow monitoring and anomaly detection. It notably enables fault detection in components not represented as nodes, enhancing the methodology in energy-based system monitoring.

On the weight zero compactly supported cohomology of

Abstract For $g\ge 2$ and $n\ge 0$ , let $\mathcal {H}_{g,n}\subset \mathcal {M}_{g,n}$ denote the complex moduli stack of n-marked smooth hyperelliptic curves of genus g. A normal crossings compactification of this space is provided by the theory of pointed admissible $\mathbb {Z}/2\mathbb {Z}$ -covers. We explicitly determine the resulting dual complex, and we use this to define a graph complex which computes the weight zero compactly supported cohomology of $\mathcal {H}_{g, n}$ . Using this graph complex, we give a sum-over-graphs formula for the $S_n$ -equivariant weight zero compactly supported Euler characteristic of $\mathcal {H}_{g, n}$ . This formula allows for the computer-aided calculation, for each $g\le 7$ , of the generating function $\mathsf {h}_g$ for these equivariant Euler characteristics for all n. More generally, we determine the dual complex of the boundary in any moduli space of pointed admissible G-covers of genus zero curves, when G is abelian, as a symmetric $\Delta $ -complex. We use these complexes to generalize our formula for $\mathsf {h}_g$ to moduli spaces of n-pointed smooth abelian covers of genus zero curves.

Force-Directed Graph Layouts Revisited: A New Force Based on the T-Distribution.

In this article, we propose the t-FDP model, a force-directed placement method based on a novel bounded short-range force (t-force) defined by Student's t-distribution. Our formulation is flexible, exerts limited repulsive forces for nearby nodes and can be adapted separately in its short- and long-range effects. Using such forces in force-directed graph layouts yields better neighborhood preservation than current methods, while maintaining low stress errors. Our efficient implementation using a Fast Fourier Transform is one order of magnitude faster than state-of-the-art methods and two orders faster on the GPU, enabling us to perform parameter tuning by globally and locally adjusting the t-force in real-time for complex graphs. We demonstrate the quality of our approach by numerical evaluation against state-of-the-art approaches and extensions for interactive exploration.

A network model of social contacts with small-world and scale-free features, tunable connectivity, and geographic restrictions.

Small-world networks and scale-free networks are well-known theoretical models within the realm of complex graphs. These models exhibit "low" average shortest-path length; however, key distinctions are observed in their degree distributions and average clustering coefficients: in small-world networks, the degree distribution is bell-shaped and the clustering is "high"; in scale-free networks, the degree distribution follows a power law and the clustering is "low". Here, a model for generating scale-free graphs with "high" clustering is numerically explored, since these features are concurrently identified in networks representing social interactions. In this model, the values of average degree and exponent of the power-law degree distribution are both adjustable, and spatial limitations in the creation of links are taken into account. Several topological metrics are calculated and compared for computer-generated graphs. Unexpectedly, the numerical experiments show that, by varying the model parameters, a transition from a power-law to a bell-shaped degree distribution can occur. Also, in these graphs, the degree distribution is most accurately characterized by a pure power-law for values of the exponent typically found in real-world networks.

Who Let the Guards Out: Visual Support for Patrolling Games.

Effective security patrol management is critical for ensuring safety in diverse environments such as art galleries, airports, and factories. The behavior of patrols in these situations can be modeled by patrolling games. They simulate the behavior of the patrol and adversary in the building, which is modeled as a graph of interconnected nodes representing rooms. The designers of algorithms solving the game face the problem of analyzing complex graph layouts with temporal dependencies. Therefore, appropriate visual support is crucial for them to work effectively. In this paper, we present a novel tool that helps the designers of patrolling games explore the outcomes of the proposed algorithms and approaches, evaluate their success rate, and propose modifications that can improve their solutions. Our tool offers an intuitive and interactive interface, featuring a detailed exploration of patrol routes and probabilities of taking them, simulation of patrols, and other requested features. In close collaboration with experts in designing patrolling games, we conducted three case studies demonstrating the usage and usefulness of our tool. The prototype of the tool, along with exemplary datasets, is available at https://gitlab.fi.muni.cz/formela/strategy-vizualizer.

Frequency Domain-Oriented Complex Graph Neural Networks for Graph Classification.

Graph neural networks (GNNs) could directly deal with the data of graph structure. Current GNNs are confined to the spatial domain and learn real low-dimensional embeddings in graph classification tasks. In this article, we explore frequency domain-oriented complex GNNs in which the node's embedding in each layer is a complex vector. The difficulty lies in the design of graph pooling and we propose a mirror-connected design with two crucial problems: parameter reduction problem and complex gradient backpropagation problem. To deal with the former problem, we propose the notion of squared singular value pooling (SSVP) and prove that the representation power of SSVP followed by a fully connected layer with nonnegative weights is exactly equivalent to that of a mirror-connected layer. To resolve the latter problem, we provide an alternative feasible method to solve singular values of complex embeddings with a theoretical guarantee. Finally, we propose a mixture of pooling strategies in which first-order statistics information is employed to enrich the last low-dimensional representation. Experiments on benchmarks demonstrate the effectiveness of the complex GNNs with mirror-connected layers.

SubLinearForce: Fully Sublinear-Time Force Computation for Large Complex Graph Drawing

Recent works in graph visualization attempt to reduce the runtime of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">repulsion</i> force computation of force-directed algorithms using sampling. However, they fail to reduce the runtime for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">attraction</i> force computation to sublinear in the number of edges. We present the <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SubLinearForce</monospace> framework for a fully sublinear-time <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">force computation</i> algorithm for drawing large complex graphs. More precisely, we present new sublinear-time algorithms for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">attraction force</i> computation of force-directed algorithms. We then integrate them with sublinear-time repulsion force computation to give a fully sublinear-time force computation. Extensive experiments show that our algorithms compute layouts on average 80% faster than the existing linear-time force computation algorithm, while obtaining significantly better quality metrics such as edge crossing and shape-based metrics.

Statistical Analysis of Complex Shape Graphs.

This paper provides developments in statistical shape analysis of shape graphs, and demonstrates them using such complex objects as Retinal Blood Vessel (RBV) networks and neurons. The shape graphs are represented by sets of nodes and edges (articulated curves) connecting some nodes. The goals are to utilize nodes (locations, connectivity) and edges (edge weights and shapes) to: (1) characterize shapes, (2) quantify shape differences, and (3) model statistical variability. We develop a mathematical representation, elastic Riemannian metrics, and associated tools for shape graphs. Specifically, we derive tools for shape graph registration, geodesics, statistical summaries, shape modeling, and shape synthesis. Geodesics are convenient for visualizing optimal deformations, and PCA helps in dimension reduction and statistical modeling. One key challenge in comparing shape graphs with vastly different complexities (in number of nodes and edges). This paper introduces a novel multi-scale representation to handle this challenge. Using the notions of (1) "effective resistance" to cluster nodes and (2) elastic shape averaging of edge curves, it reduces graph complexity while retaining overall structures. This allows shape comparisons by bringing graphs to similar complexities. We demonstrate these ideas on 2D RBV networks from the STARE and DRIVE databases and 3D neurons from the NeuroMorpho database.

The stable cohomology of self-equivalences of connected sums of products of spheres

Abstract We identify the cohomology of the stable classifying space of homotopy automorphisms (relative to an embedded disk) of connected sums of ${\mathrm {S}^{k}} \times {\mathrm {S}^{l}}$ , where $3 \le k &lt; l \le 2k - 2$ . The result is expressed in terms of Lie graph complex homology.

Visual Branding of Sikapak Timur Village Pariaman as Media Promotion Based on Visual Complexity Effect on Social Media

Visual Complexity Effect is a term used in psychology to describe how people react to complex visual information. Typically, the more complicated or complex the visual information, the more difficult it is for people to process and understand it. The effects of visual complexity can also affect reaction times, cognitive abilities, and decision making. In everyday life, data visualization and complex graphs can be a challenge for many people, especially if they are not used to that type of information. Therefore, graphic designers and application developers try to minimize visual complexity so that it can be understood and used easily by users.

A simplicial epidemic model for COVID-19 spread analysis.

Networks allow us to describe a wide range of interaction phenomena that occur in complex systems arising in such diverse fields of knowledge as neuroscience, engineering, ecology, finance, and social sciences. Until very recently, the primary focus of network models and tools has been on describing the pairwise relationships between system entities. However, increasingly more studies indicate that polyadic or higher-order group relationships among multiple network entities may be the key toward better understanding of the intrinsic mechanisms behind the functionality of complex systems. Such group interactions can be, in turn, described in a holistic manner by simplicial complexes of graphs. Inspired by these recently emerging results on the utility of the simplicial geometry of complex networks for contagion propagation and armed with a large-scale synthetic social contact network (also known as a digital twin) of the population in the U.S. state of Virginia, in this paper, we aim to glean insights into the role of higher-order social interactions and the associated varying social group determinants on COVID-19 propagation and mitigation measures.

Towards physics-informed explainable machine learning and causal models for materials research

From emergent material descriptions to estimation of properties stemming from structures to optimization of process parameters for achieving best performance – all key facets of materials science and related fields have experienced tremendous growth with the introduction of data-driven models. This gradual progression goes at par with developments of machine learning workflows, from purely data-driven shallow models to those that are well-capable in encoding more complex graphs, symbolic representations, invariances, and positional embeddings. This perspective aims at summarizing strategic aspects of such transitions while providing insights into the requirements of bringing in explainable, interpretable predictive models, and causal learning to aid in materials design and discovery. Although the focus remains on a variety of functional materials by providing a handful of case studies, the applications of such integrated methodologies are universal to facilitate fundamental understandings of materials physics while enabling autonomous experiments.

Global disentangled graph convolutional neural network based on a graph topological metric

Graph convolutional networks (GCNs) are powerful tools for analyzing structured data with entities based on messages passing between a node and its surrounding nodes; these networks exhibit exceptional capabilities in diverse complex graph learning tasks. However, despite GCNs being capable of incorporating information from entities, they often neglect the structural connections between the entities generated by latent factors. In this study, we propose a global disentangled graph convolutional neural network based on a graph topological metric to identify these latent factors and perform graph-level disentanglement learning. In the proposed framework, a simple graph is accepted as the input and disentangled into several factorized graphs. Each factorized graph represents a latent factor and the disentangled relationship among the nodes. Specifically, our approach decouples the message passing process in GCNs into two distinct flows, feature and structural information flow. Importantly, a topological metric, named mean average distance, is introduced to promote the disentanglement among the factor graphs. Furthermore, we utilize the Jensen–Shannon MI estimator to promote disentanglement through feature information flow. Experiments on synthetic and real-world datasets demonstrated the superiority of our framework over state-of-the-art GNN networks. This work introduces a novel approach, preserving independence among latent factors while ensuring each factor maintains a consistent and interpretable meaning. We anticipate that this research can provide theoretical and technical analysis to further advance the understanding of graph disentanglement learning.

Research on Traditional Chinese Medicine: Domain Knowledge Graph Completion and Quality Evaluation.

Knowledge graphs (KGs) can integrate domain knowledge into a traditional Chinese medicine (TCM) intelligent syndrome differentiation model. However, the quality of current KGs in the TCM domain varies greatly, related to the lack of knowledge graph completion (KGC) and evaluation methods. This study aims to investigate KGC and evaluation methods tailored for TCM domain knowledge. In the KGC phase, according to the characteristics of TCM domain knowledge, we proposed a 3-step "entity-ontology-path" completion approach. This approach uses path reasoning, ontology rule reasoning, and association rules. In the KGC quality evaluation phase, we proposed a 3-dimensional evaluation framework that encompasses completeness, accuracy, and usability, using quantitative metrics such as complex network analysis, ontology reasoning, and graph representation. Furthermore, we compared the impact of different graph representation models on KG usability. In the KGC phase, 52, 107, 27, and 479 triples were added by outlier analysis, rule-based reasoning, association rules, and path-based reasoning, respectively. In addition, rule-based reasoning identified 14 contradictory triples. In the KGC quality evaluation phase, in terms of completeness, KG had higher density and lower sparsity after completion, and there were no contradictory rules within the KG. In terms of accuracy, KG after completion was more consistent with prior knowledge. In terms of usability, the mean reciprocal ranking, mean rank, and hit rate of the first N tail entities predicted by the model (Hits@N) of the TransE, RotatE, DistMult, and ComplEx graph representation models all showed improvement after KGC. Among them, the RotatE model achieved the best representation. The 3-step completion approach can effectively improve the completeness, accuracy, and availability of KGs, and the 3-dimensional evaluation framework can be used for comprehensive KGC evaluation. In the TCM field, the RotatE model performed better at KG representation.

Towards Adaptive Information Fusion in Graph Convolutional Networks

Graph Convolutional Networks (GCNs) have gained great popularity in tackling various analytic tasks on graph and network data. However, some recent studies raise concerns about whether GCNs can optimally integrate node features and topological structures in a complex graph. In this paper, we first present an experimental investigation. Surprisingly, our experimental results clearly show that the capability of the state-of-the-art GCNs in fusing node features and topological structures is distant from optimal or even satisfactory. The weakness may severely hinder the capability of GCNs in some classification tasks, since GCNs may not be able to adaptively learn some deep correlation information between topological structures and node features. Can we remedy the weakness and design a new type of GCNs that can retain the advantages of the state-of-the-art GCNs and, at the same time, enhance the capability of fusing topological structures and node features substantially? We tackle the challenge and propose an <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</b> daptive <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</b> ulti-channel <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</b> raph <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</b> onvolutional <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</b> etwork for semi-supervised classification ( <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AM-GCN</b> ). The central idea is that we extract the specific and common embeddings from node features, topological structures, and their combinations simultaneously, and use the attention mechanism to learn adaptive importance weights of the embeddings. However, considering that the input topology and feature structure in AM-GCN are still predefined and fixed, once the properties of graph structures are not consistent with tasks, the fusion performance of AM-GCN will be hindered from the beginning. Therefore, we need to adjust the structure and further propose the <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</b> abel <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</b> ropagation guided <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</b> ulti-channel <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</b> raph <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</b> onvolutional <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</b> etwork ( <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LPM-GCN</b> ). LPM-GCN introduces edge weights learning on both topology and feature spaces to improve structural homophily, which can better promote the fusion process of graph convolutional networks. Our extensive experiments on benchmark data sets clearly show that our proposed models extract the most correlated information from both node features and topological structures substantially, and improves the classification accuracy with a clear margin.

The Italian colour lexicon in Tuscany: elicited lists, cognitive salience, and semantic maps of colour terms

We investigated the Tuscan Italian colour inventory, with the aim of establishing the cognitive salience of the basic colour terms (BCTs) and most frequent non-BCTs. Native speakers from Tuscany (N = 89) completed a colour-term elicitation task lasting for 5 min. In total, 337 unique terms were elicited, with an average list length of 30.06. The frequency of each term, its mean list position and cognitive salience index (S) were calculated. The CTs with the highest S (ranked 1–13) included 10 counterparts of the Berlin and Kay BCTs listed in their 1969 seminal work and three basic ‘blue’ terms, blu, azzurro, celeste, estimated for Tuscan respondents by Del Viva et al. in 2022. S-index and Zipf-function (the terms’ “popularity”) indicated that fucsia (rank 14) is conceivably an emerging BCT in (Tuscan) Italian. Other cognitively salient non-BCTs are lilla, magenta, ocra and beige. The terms’ 3D semantic map (conceptual closeness), assessed using multidimensional scaling and cluster analysis, revealed that in the lists, closely associated CTs were arranged along three competing criteria: the term’s salience gradient; word length; and clustering of fully chromatic concepts with those defined primarily by lightness or desaturation. We also consider salient Italian non-BCTs as indicators of the ongoing process of lexical refinement in certain areas of the colour space. In conclusion, measures of elicitation productivity, as well as the augmented BCT inventory, including the Tuscan ‘triple blues’, and abundant hyponyms and derived forms all indicate (Tuscan) Italian speakers’ “cultural competence” in the colour domain and the need to communicate nuanced information about colour shades.

Diktyo: Network-Aware Scheduling in Container-Based Clouds

Containers have revolutionized application deployment and life-cycle management in current cloud platforms. Applications have evolved from single monoliths to complex graphs of loosely-coupled microservices. However, the efficient allocation of microservice-based applications is challenging due to their complex inter-dependencies. Further, recent applications are becoming even more delay-sensitive, demanding lower latency between dependent microservices. Scheduling policies in popular container orchestration platforms mainly aim to increase the resource efficiency of the infrastructure, insufficient for latency-sensitive applications. Application domains such as the Internet of Things and multi-tier web services would benefit from network-aware policies that consider network latency and bandwidth in the scheduling process. Previous works have studied network-aware scheduling via theoretical formulations or heuristic-based methods evaluated via simulations or small testbeds, making their full applicability in popular platforms difficult. This paper proposes a novel network-aware framework for the popular Kubernetes (K8s) platform named Diktyo that determines the placement of dependent microservices in long-running applications focused on reducing the application’s end-to-end latency and guaranteeing bandwidth reservations. Simulations show that Diktyo can significantly reduce the network latency for various applications across different infrastructure topologies compared to default K8s scheduling plugins. Also, experiments in a K8s cluster with microservice benchmark applications show that Diktyo can increase database throughput by 22% and reduce application response time by 45%.

Monocular Depth Estimation for Glass Walls with Context: A New Dataset and Method.

Traditional monocular depth estimation assumes that all objects are reliably visible in the RGB color domain. However, this is not always the case as more and more buildings are decorated with transparent glass walls. This problem has not been explored due to the difficulties in annotating the depth levels of glass walls, as commercial depth sensors cannot provide correct feedbacks on transparent objects. Furthermore, estimating depths from transparent glass walls requires the aids of surrounding context, which has not been considered in prior works. To cope with this problem, we introduce the first Glass Walls Depth Dataset (GW-Depth dataset). We annotate the depth levels of transparent glass walls by propagating the context depth values within neighboring flat areas, and the glass segmentation mask and instance level line segments of glass edges are also provided. On the other hand, a tailored monocular depth estimation method is proposed to fully activate the glass wall contextual understanding. First, we propose to exploit the glass structure context by incorporating the structural prior knowledge embedded in glass boundary line segment detections. Furthermore, to make our method adaptive to scenes without structure context where the glass boundary is either absent in the image or too narrow to be recognized, we propose to derive a reflection context by utilizing the depth reliable points sampled according to the variance between two depth estimations from different resolutions. High-resolution depth is thus estimated by the weighted summation of depths by those reliable points. Extensive experiments are conducted to evaluate the effectiveness of the proposed dual context design. Superior performances of our method is also demonstrated by comparing with state-of-the-art methods. We present the first feasible solution for monocular depth estimation in the presence of glass walls, which can be widely adopted in autonomous navigation.

Functional network properties in schizophrenia and bipolar disorder assessed with high-density electroencephalography

BackgroundThe study of the cortical functional network properties in schizophrenia (SZ) may benefit from the use of graph theory parameters applied to high-density electroencephalography (EEG). Connectivity Strength (CS) assesses global synchrony of the network, and Shannon Graph Complexity (SGC) summarizes the network distribution of link weights and allows distinguishing between primary and secondary pathways. Their joint use may help in understanding the underpinnings of the functional network hyperactivation and task-related hypomodulation previously described in psychoses. MethodsWe used 64-sensor EEG recordings during a P300 oddball task in 128 SZ patients (96 chronic, CR, and 32 first episodes, FE), as well as 46 bipolar disorder (BD) patients, and 92 healthy controls (HC). Pre-stimulus and modulation (task-response minus pre-stimulus windows values) of CS and SGC were assessed in the theta band (4–8 Hz) and the broadband (4–70 Hz). ResultsCompared to HC, SZ patients (CR and FE) showed significantly higher pre-stimulus CS values in the broadband, and both SZ and BD patients showed lower theta-band CS modulation. SGC modulation values, both theta-band and broadband, were also abnormally reduced in CR patients. Statistically significant relationships were found in the theta band between SGC modulation and both CS pre-stimulus and modulation values in patients. CS altered measures in patients were additionally related to their cognitive outcome and negative symptoms. A primary role of antipsychotics in these results was ruled out. ConclusionsOur results linking SGC and CS alterations in psychotic patients supported a hyperactive and hypomodulatory network mainly involving connections in secondary pathways.

QALD-10 – The 10th challenge on question answering over linked data

Knowledge Graph Question Answering (KGQA) has gained attention from both industry and academia over the past decade. Researchers proposed a substantial amount of benchmarking datasets with different properties, pushing the development in this field forward. Many of these benchmarks depend on Freebase, DBpedia, or Wikidata. However, KGQA benchmarks that depend on Freebase and DBpedia are gradually less studied and used, because Freebase is defunct and DBpedia lacks the structural validity of Wikidata. Therefore, research is gravitating toward Wikidata-based benchmarks. That is, new KGQA benchmarks are created on the basis of Wikidata and existing ones are migrated. We present a new, multilingual, complex KGQA benchmarking dataset as the 10th part of the Question Answering over Linked Data (QALD) benchmark series. This corpus formerly depended on DBpedia. Since QALD serves as a base for many machine-generated benchmarks, we increased the size and adjusted the benchmark to Wikidata and its ranking mechanism of properties. These measures foster novel KGQA developments by more demanding benchmarks. Creating a benchmark from scratch or migrating it from DBpedia to Wikidata is non-trivial due to the complexity of the Wikidata knowledge graph, mapping issues between different languages, and the ranking mechanism of properties using qualifiers. We present our creation strategy and the challenges we faced that will assist other researchers in their future work. Our case study, in the form of a conference challenge, is accompanied by an in-depth analysis of the created benchmark.