Force-directed Method Research Articles

Multivariate Network Layout Using Force-Directed Method with Attribute Constraints

Graph visualization with proper layout is widely applied to understand the relationship between entities in a complex system and the topological structure information is mainly used. Real-world graphs often have the community structures property which is ignored in many existing graph layout methods. Thus, we propose a multivariate network layout method using the force-directed method with attribute constraints. This method can effectively take into account the hierarchical structure, connection strength, and quantitative comparison between communities. First, the layout of community centers is generated by a force-directed algorithm in which node count of the community is taken as constraints to enable area balance of community; Second, community force based on node attribute is added in the force-directed algorithm to maintain the community clarity. A visualization system is also developed to allow users to interactively generate community structure-aware layout results. qualitative and quantitative evaluation of the results verifies the usability and effectiveness of the proposed method by comparing it with other methods.

Effects of View Layout on Situated Analytics for Multiple-View Representations in Immersive Visualization.

Multiple-view (MV) representations enabling multi-perspective exploration of large and complex data are often employed on 2D displays. The technique also shows great potential in addressing complex analytic tasks in immersive visualization. However, although useful, the design space of MV representations in immersive visualization lacks in deep exploration. In this paper, we propose a new perspective to this line of research, by examining the effects of view layout for MV representations on situated analytics. Specifically, we disentangle situated analytics in perspectives of situatedness regarding spatial relationship between visual representations and physical referents, and analytics regarding cross-view data analysis including filtering, refocusing, and connecting tasks. Through an in-depth analysis of existing layout paradigms, we summarize design trade-offs for achieving high situatedness and effective analytics simultaneously. We then distill a list of design requirements for a desired layout that balances situatedness and analytics, and develop a prototype system with an automatic layout adaptation method to fulfill the requirements. The method mainly includes a cylindrical paradigm for egocentric reference frame, and a force-directed method for proper view-view, view-user, and view-referent proximities and high view visibility. We conducted a formal user study that compares layouts by our method with linked and embedded layouts. Quantitative results show that participants finished filtering- and connecting-centered tasks significantly faster with our layouts, and user feedback confirms high usability of the prototype system.

Comparing the network structure of ICD-11 PTSD and complex PTSD in three African countries

BackgroundSymptom network analysis has become an essential tool for researchers and clinicians investigating the structure of mental disorders. Two methods have been used; one relies on partial correlations, and the second relies on zero order correlations with forced-directed algorithm. This combination was used to examine symptom connections for ICD-11 Posttraumatic Stress Disorder (PTSD) and Complex PTSD (CPTSD) as the symptoms for these disorders have been known to be organized in a multi-dimensional and hierarchical fashion. We aimed to examine whether networks of ICD-11 CPTSD symptoms reproduced across samples from three African countries. MethodsWe produced network models based on data from 2524 participants in Nigeria (n = 1018), Kenya (n = 1006), and Ghana (n = 500). PTSD and CPTSD symptoms were measured using the International Trauma Questionnaire (Cloitre et al., 2018). ResultsThe CPTSD network analysis using force-directed method alongside partial correlations based on Gaussian Graphical Models (GGM) revealed the multidimensional-hierarchal structure of CPTSD. The within-cluster symptoms of Disturbances in Self Organization (DSO) and PTSD were strongly correlated with each other in all networks, and the cross-cluster symptoms were lower. The most central symptom was ‘feelings of worthlessness’, a symptom of Negative Self-Concept that is part of the CPTSD cluster. The networks were very similar across the three countries. ConclusionsFindings support the ICD-11 model of PTSD and CPTSD in three African countries.

Representing Social Influencers and Influence using Power-Law Graphs

This paper focuses on semantic networks that represent the user opinions expressed by social media users on a given set of topics. These networks are found to follow a power-law degree distribution of nodes, with a few hub nodes and a long tail of peripheral nodes. While there exist consolidated approaches supporting the identification and characterization of hu b nodes, research on the analysis of the multi-layered distribution of periph eral nodes is limited. In social media, hub nodes represent social influencers. However, the literature provides evidence of the multi-layered structure of influence networks, emphasizing the disti nction between influencers and influence. The latter seems to spread followi ng multi-hop paths across nodes in peripheral network layers. This paper proposes a visual approach to the graphical representation of peripheral layers. The core concept of our approach is to partition the node set of a graph into hub and peripheral nodes. Then, a modified force-directed method is applied to c learly display local multi-layered neighborhood clusters around hub nodes. Our approach is tested on a large sample of tweets from tourism domain. Our algorithm is visually compared with state-of-the-art network drawing techniques.

Comparing the Network Structure of ICD-11 PTSD and Complex PTSD in Three African Countries

Background: Symptom network analysis has become an essential tool for researchers and clinicians investigating the structure of mental disorders. Two common methods have been used; one relies on partial correlations, and the second relies on zero order correlations with forced-directed algorithm. The combination enables a multi-dimensional view of mental disorders and provide complimentary information. This combination was used to examine symptom connections for ICD-11 Posttraumatic Stress Disorder (PTSD) and Complex PTSD (CPTSD) as the symptoms for these disorders have been known to be organized in a multi-dimensional and hierarchical fashion. We aimed to examine whether networks of ICD-11 CPTSD symptoms reproduced across samples from three African countries. Methods: We produced network models based on data from 2,524 participants in Nigeria (n = 1006), Kenya (n = 1018), and Ghana (n = 500). PTSD and CPTSD symptoms were measured using the International Trauma Questionnaire1. Outcomes: The CPTSD network analysis using force-directed method alongside partial correlations based on Gaussian Graphical Models (GGM) revealed the multidimensional-hierarchal structure of CPTSD. The within-cluster symptoms of Disturbances in Self Organization (DSO) and PTSD were strongly correlated with each other in all networks, and the cross-cluster symptoms were lower. The most central symptom was ‘feelings of worthlessness’, a symptom of Negative Self-Concept that is part of the CPTSD cluster. The networks were very similar across the three countries. Interpretation: Findings support the ICD-11 model of PTSD and CPTSD in three African countries Funding: An internal research grant was awarded to MBE from Ariel University (grant no. RA1700000037). Declaration of Interests: None. Ethics Approval Statement: The study complied with the Helsinki declaration regarding human experimentation. All procedures involving human subjects were approved by Ariel’s University IRB [AU-MBE-2018-1029].

A Method of Node Layout of a Complex Network Based on Community Compression

As the theory of complex networks is further studied, the scale of nodes in the network is increasing, which makes it difficult to find useful patterns from only the analysis of nodes. Therefore, this paper proposes a complex network node layout method based on community compression, which can effectively display the mesoscale structure characteristics of the network, making it more convenient for users to analyze the status and function of a single node or a class of nodes in the whole complex network. To begin with, the whole network is divided into communities with different granularity by the Louvain algorithm. Secondly, the method of nodes importance analysis based on topological potential theory is extended from the network to the community structure, and the internal nodes of the community are classified into three types, namely important nodes, relatively important nodes, and fringe nodes. Furthermore, a compression algorithm for the community structure is designed to realize the compression of the network by retaining important nodes and merging fringe nodes. Finally, the compression network is laid out by the traditional force-directed layout method. Experimental results show that, compared with the compression layout methods of a complex network based on degree or PageRank, the method in this paper can retain the integrated community composition and its internal structure, which is convenient for users to effectively analyze the topology structure of a complex network.

Architecture‐aware routability‐driven placer for large‐scale mixed‐size designs

In this study, the authors have presented a simple but robust routability-driven placement for the mixed-size designs. The proposed technique is implemented through (i) look-ahead legalisation-based global placement, (ii) congestion removal and (iii) detailed placement stages. A balanced clustering technique has been proposed to group the circuit blocks into clusters based on the types of circuit blocks and their connectivity. A 0-1 integer programming-based global placement method is framed, which performs look-ahead legalisation. A new site information table concept is introduced to keep the information about each placement cell. Based on the divide conquer strategy, placement area is divided into a region to reduce problem size. A force-directed method has been conceived to select an appropriate region for global placement for the blocks of a cluster. A new congestion removal approach substitutes the legalisation stage to remove circuit block congestion and pin density in different regions. Finally, a gain-based strategy has been introduced for routability-driven detailed placement. The proposed technique is implemented and tested on ICCAD 2012 benchmark circuits. It achieves 1.92 and 0.13% improvements in terms of half perimeter wirelength and routing congestion w.r.t. recent placers.

Expectation-based 3D edge bundling

In the visualization of the node-link graph, it is common to use edge-bundling algorithms to reduce the visual clutter caused by the increase in nodes and connections while reflecting the high-level structure of the graph. However, the traditional force-directed edge-bundling method has unstable gravitation when applied in three dimensions. To address this issue, we propose an edge-bundling algorithm based on the expectation model, and the edge-bundling rules can be modularized to support the addition of calculation rules. The stability of the proposed method is improved. Our experimental results with 2D and 3D scenarios demonstrate that our algorithm produces superior results that unclutter complex graphs.

Methods and tools for automated production of origin-destination flow maps

Abstract. Origin-destination flow maps represent movement between locations using lines of optionally varying width connecting points or areas. When flow lines intersect or overlap, legibility can be improved by curving flows to avoid each other, which is a time-consuming process to do by hand when there are many flows.We present a tool for ArcGIS Pro that implements a force-directed method developed by Jenny et al. (2017) for curving flows. This method reduces overlaps and intersections by curving flows away from nodes, other flows, and arrowheads, taking flow map design principles into account (Jenny et al., 2018). Users provide node coordinates and ids, and a table describing the volume of movement between the nodes. The tool produces two map layers, one containing curved flow lines, and another containing points that includes data about the total quantity of movement to and from each point. The new line and point layers are then added to a map in ArcGIS Pro. The width of each line represents the relative quantity of movement represented, and the diameter of each node represents the total movement in and out of that location. Users can opt to produce either net flows (the difference in movement between points) or total flows (the sum of movement between points in both directions). In the case of net flows, arrowheads are added to flows to indicate flow direction, and the ends of flows are clipped to prevent arrowheads from overlapping destination points. Arrowheads of smaller flows are made slightly larger to improve visibility. Users have several options to help reduce map clutter, including modifying the maximum width of flows and nodes, creating additional space between flows and their endpoints, and displaying only a selected number of the largest flows.We also introduce more advanced experimental features that we implemented in standalone prototype software. Our prototype can create parallel flow lines for bidirectional flows. This avoids inconsistently spaced opposing flow lines between a pair of origin and destination nodes. The prototype can shorten flow lines to reduce overlaps with other flows, nodes and arrowheads, and keep a minimum distance between flow lines. We will also discuss placing flow lines between areas instead of nodes and demonstrate an algorithmic implementation for creating flows between areas. Our prototype provides an easy-to-use graphical user interface and will be released as free and open-source software.

ILP-Based Optimal PMU Placement with the Inclusion of the Effect of a Group of Zero-Injection Buses

Zero-injection buses (ZIBs) can reduce the number of phasor measurement units (PMUs) required to be installed for complete observability. It has been demonstrated that a group of neighboring ZIBs can further reduce this required number of PMUs. In contrast to a single ZIB, the effect of a group of ZIBs has not been incorporated into the model of optimal PMU placement (OPP) using mathematical approaches, except for some heuristics methods. In this paper, a novel methodology to incorporate the effect of a group of ZIBs into the OPP model is proposed, using the integer linear programming approach. Two common contingencies—line outage and PMU loss—are also considered. Moreover, two visualization techniques are used for illustrating the locations of PMUs obtained from OPP: (1) using a graph-based force-directed method and (2) on a map using the geographic information system. The proposed method is verified using several small- and large-scale test systems and compared with other related studies.

GPU-Based Parallel Particle Swarm Optimization Methods for Graph Drawing

Particle Swarm Optimization (PSO) is a population-based stochastic search technique for solving optimization problems, which has been proven to be effective in a wide range of applications. However, the computational efficiency on large-scale problems is still unsatisfactory. A graph drawing is a pictorial representation of the vertices and edges of a graph. Two PSO heuristic procedures, one serial and the other parallel, are developed for undirected graph drawing. Each particle corresponds to a different layout of the graph. The particle fitness is defined based on the concept of the energy in the force-directed method. The serial PSO procedure is executed on a CPU and the parallel PSO procedure is executed on a GPU. Two PSO procedures have different data structures and strategies. The performance of the proposed methods is evaluated through several different graphs. The experimental results show that the two PSO procedures are both as effective as the force-directed method, and the parallel procedure is more advantageous than the serial procedure for larger graphs.

Automated layout of origin–destination flow maps: U.S. county-to-county migration 2009–2013

ABSTRACTVisualizing large movement datasets with flow maps is difficult because overlapping flows create significant graphical conflicts that make accurate interpretation difficult or impossible. Interactive flow mapping applications allow users to explore large movement datasets by automatically generating flow maps from subsets of the data in response to queries by the user. However, even a small number of flows can overlap and cross each other in a way that impedes accurate interpretation. We introduce an interactive flow map of migration in the United States from 2009 to 2013 that uses a force-directed method to automatically lay out migration flows at the county-to-county and state levels. This map, available at http://usmigrationflowmapper.com/, aims at improving readability by automatically creating origin–destination flow layouts according to identified cartographic design principles. Map users explore high-level state-to-state migration patterns as well as detailed county-to-county movements through a custom user interface and interactive map features. We show migration flows between counties of different states by representing other states as nodes with a circular arrangement around the selected state, and connect county flows to those nodes. This constrains the map layout to a smaller area, reducing clutter and the amount of interaction required to view flows.

Ivga: A fast force-directed method for interactive visualization of complex networks

Complex networks play a very important role in various fields of science as data structures, which aggregate information about mutual relationships between numerous objects. The structural properties of these large graphs can be scrutinized throughout their interactive visualization. However, visual analysis of complex networks consisting of |V|∼106+ vertices represents a great challenge for nowadays computer systems both from computational and storage perspective. Therefore, the existing graph drawing methods involving greater than O(|V|) time and space complexity cannot be regarded as promising tools in the advent of the Big Data era. We present here a new and very fast graph drawing method with O(|V|) time and space complexity – ivga (interactive visualization of graphs). We evaluate its usefulness and performance by testing ivga on the large complex networks from the Stanford Large Network Dataset Collection. We demonstrate that ivga allows for very fast interactive visualization of large graphs consisting of up to a few million vertices on a regular laptop what makes it very competitive to other state-of-art graph drawing methods. Particularly, we recommend ivga method for interactive visualization of large non-planar complex networks such as small-world and scale-free social networks. The main concept of ivga can be seriously considered in developing tools for visualization and analysis of really huge networks, with billions of vertices and edges, on Big Data systems.

Fracture Mechanics Method for Word Embedding Generation of Neural Probabilistic Linguistic Model

Word embedding, a lexical vector representation generated via the neural linguistic model (NLM), is empirically demonstrated to be appropriate for improvement of the performance of traditional language model. However, the supreme dimensionality that is inherent in NLM contributes to the problems of hyperparameters and long-time training in modeling. Here, we propose a force-directed method to improve such problems for simplifying the generation of word embedding. In this framework, each word is assumed as a point in the real world; thus it can approximately simulate the physical movement following certain mechanics. To simulate the variation of meaning in phrases, we use the fracture mechanics to do the formation and breakdown of meaning combined by a 2-gram word group. With the experiments on the natural linguistic tasks of part-of-speech tagging, named entity recognition and semantic role labeling, the result demonstrated that the 2-dimensional word embedding can rival the word embeddings generated by classic NLMs, in terms of accuracy, recall, and text visualization.

Discovering social influencers with network visualization: evidence from the tourism domain

Identifying influential users and predicting their network impact on social networks have attracted tremendous interest from both academia and industry. Social networks follow a power-law degree distribution of nodes, with a few hub nodes and a long tail of peripheral nodes. While there exist consolidated approaches supporting the identification and characterization of hub nodes, research on the analysis of the multi-layered distribution of peripheral nodes is limited. In social media, hub nodes represent social influencers. However, the literature provides evidence of the multi-layered structure of influence networks, emphasizing the distinction between influencers and influence. Information seems to spread following multi-hop paths across nodes in peripheral network layers. This paper proposes a visual approach to the graphical representation and exploration of peripheral layers and clusters by exploiting the theory of k-shell decomposition analysis. The core concept of the proposed approach is to partition the node set of a graph into pre-defined hub and peripheral nodes. Then, a power-law based modified force-directed method is applied to clearly display local multi-layered neighborhood clusters around hub nodes based on a characterization of the content of message that we refer to as content specificity. We put forward three hypotheses that allow the graphical identification of the peripheral nodes that are more likely to be influential and contribute to the spread of information. Hypotheses are tested on a large sample of tweets from the tourism domain.

Improved Force-Directed Method of Graph Layout Generation with Adaptive Step Length

Abstract We present an improvement of the force-directed method of undirected graph layout generation by maximizing the step length of the iterative optimization process. We show that the upper bound on the step length value depends only on graph characteristics and remains constant throughout the optimization process. Our algorithm finds the largest possible step length that does not result in divergence of the process, therefore it reduces the number of iterations needed to achieve the optimal graph layout.

An Effective Cell Spreading Method for Force-Directed Global Placement

Force-directed placement method for large scale integration physical design is a very effective and fast method to spread the cell uniformly in the placement region. But this kind of method also create large amount of cell overlap in initial placement. In this paper, we present an effective method to cope with cell spreading and add additional force without damaging the wire length. It mainly takes the following method: Firstly, in the prior period of iteration n we keep limit the cell moving distance using a rectangle structure .Because the prior iteration play a decisive role in the final placement quality. Secondly, after the cell relative order determined we can use a new method to compute the weight of additional force to accelerate converge. Thirdly, a strategy called iterative local refinement is added in the well-distributed placement to further reduce the total wire length.

Scalable Visualization of Semantic Nets using Power-Law Graphs

Scalability and performance implications of semantic net visualization techniq ues are open research challenges. This paper focuses on developing a visualization technique that mitigates these challeng es. We present a novel approach that exploits the underlying concept of power-law degree distribution as many realistic semantic nets seems to possess a power law degree distribution and present a small world phenomenon. The core concept is to partition the node set of a graph into power and non-power nodes and to apply a modified force-directed method that emphasizes the power nodes whic h results in establishing local neighborhood clusters among power nodes. We also made refinements in conventional force-directe d method by tuning the temperature cooling mechanism in order to resolve 'local-minima' problem. To avoid cluttered view, we applied semantic filtration on nodes, ensuring zero loss of semantics. Results show that our technique handles very large scale semantic nets with a substantial performance improvement while producing aesthetically pleasant layouts. A visualization tool, NavigOWL, is developed by using this technique which has been ported as a plug-in for Protege, a famous ontology editor.

A new force-directed graph drawing method based on edge–edge repulsion

The conventional force-directed methods for drawing undirected graphs are based on either vertex–vertex repulsion or vertex–edge repulsion. In this paper, we propose a new force-directed method based on edge–edge repulsion to draw graphs. In our framework, edges are modelled as charged springs, and a final drawing can be generated by adjusting positions of vertices according to spring forces and the repulsive forces, derived from potential fields, among edges. Different from the previous methods, our new framework has the advantage of overcoming the problem of zero angular resolution, guaranteeing the absence of any overlapping of edges incident to the common vertex. Given graph layouts probably generated by previous algorithms as the inputs to our algorithm, experimental results reveal that our approach produces promising drawings not only preserving the original properties of a high degree of symmetry and uniform edge length, but also preventing zero angular resolution and usually having larger average angular resolution. However, it should be noted that exhibiting a higher degree of symmetry and larger average angular resolution does not come without a price, as the new approach might result in the increase in undesirable overlapping of vertices as some of our experimental results indicate. To ease the problem of node overlapping, we also consider a hybrid approach which takes into account both edge–edge and vertex–vertex repulsive forces in drawing a graph.

Force-Directed Method in Mirror Frames for Graph Drawing

The most widely used algorithms for graph drawing are force-directed algorithms. We should modify a hybrid force model that is coupling a traditional spring force model and a novel repulsive force model will be proposed to solve the graph drawing problems in 2-D space. Especially, regular triangle drawing frame can be applied to binary tree drawing problems that on an important contribution to computer science. And apply circle drawing frame to normal graph drawing problems, we get satisfactory and aesthetic criteria graphics.