353 research outputs found
Visual Similarity Perception of Directed Acyclic Graphs: A Study on Influencing Factors
While visual comparison of directed acyclic graphs (DAGs) is commonly
encountered in various disciplines (e.g., finance, biology), knowledge about
humans' perception of graph similarity is currently quite limited. By graph
similarity perception we mean how humans perceive commonalities and differences
in graphs and herewith come to a similarity judgment. As a step toward filling
this gap the study reported in this paper strives to identify factors which
influence the similarity perception of DAGs. In particular, we conducted a
card-sorting study employing a qualitative and quantitative analysis approach
to identify 1) groups of DAGs that are perceived as similar by the participants
and 2) the reasons behind their choice of groups. Our results suggest that
similarity is mainly influenced by the number of levels, the number of nodes on
a level, and the overall shape of the graph.Comment: Graph Drawing 2017 - arXiv Version; Keywords: Graphs, Perception,
Similarity, Comparison, Visualizatio
The Impact of Shape on the Perception of Euler Diagrams
Euler diagrams are often used for visualizing data collected into sets. However, there is a significant lack of guidance regarding graphical choices for Euler diagram layout. To address this deficiency, this paper asks the question `does the shape of a closed curve affect a user's comprehension of an Euler diagram?' By empirical study, we establish that curve shape does indeed impact on understandability. Our analysis of performance data indicates that circles perform best, followed by squares, with ellipses and rectangles jointly performing worst. We conclude that, where possible, circles should be used to draw effective Euler diagrams. Further, the ability to discriminate curves from zones and the symmetry of the curve shapes is argued to be important. We utilize perceptual theory to explain these results. As a consequence of this research, improved diagram layout decisions can be made for Euler diagrams whether they are manually or automatically drawn
Degradation mechanism of tris(2-chloroethyl) phosphate (TCEP) as an emerging contaminant in advanced oxidation processes: a DFT modelling approach
As a typical toxic organophosphate and emerging contaminant, tris(2-chloroethyl) phosphate (TCEP) is resistant to conventional water treatment processes. Studies on advanced oxidation processes (AOPs) to degrade TCEP have received increasing attention, but the detailed mechanism is not yet fully understood. This study investigated the mechanistic details of TCEP degradation promoted by ·OH using the density functional theory (DFT) method. Our results demonstrated that in the initial step, energy barriers of the hydrogen abstraction pathways were no more than 7 kcal/mol. Cleavage of the P-O or C-Cl bond was verified to be possible to occur, whilst the C-O or C-C cleavage had to overcome an energy barrier above 50 kcal/mol, which was too high for mild experimental conditions. The bond dissociation energy (BDE) combined with the distortion/interaction energy (DIE) analysis disclosed origin of the various reactivities of each site of TCEP. The systematic calculations on the transformation of products generated in the initial step showed remarkable exothermic property. The systematic calculations on the transformation of products generated in the initial step showed remarkable exothermic property. The novel information at molecular level provides insight on how these products are generated and offers valuable theoretical guidance to help develop more effective AOPs to degrade TCEP or other emerging environmental contaminant
Convexity-Increasing Morphs of Planar Graphs
We study the problem of convexifying drawings of planar graphs. Given any
planar straight-line drawing of an internally 3-connected graph, we show how to
morph the drawing to one with strictly convex faces while maintaining planarity
at all times. Our morph is convexity-increasing, meaning that once an angle is
convex, it remains convex. We give an efficient algorithm that constructs such
a morph as a composition of a linear number of steps where each step either
moves vertices along horizontal lines or moves vertices along vertical lines.
Moreover, we show that a linear number of steps is worst-case optimal.
To obtain our result, we use a well-known technique by Hong and Nagamochi for
finding redrawings with convex faces while preserving y-coordinates. Using a
variant of Tutte's graph drawing algorithm, we obtain a new proof of Hong and
Nagamochi's result which comes with a better running time. This is of
independent interest, as Hong and Nagamochi's technique serves as a building
block in existing morphing algorithms.Comment: Preliminary version in Proc. WG 201
Compact Drawings of 1-Planar Graphs with Right-Angle Crossings and Few Bends
We study the following classes of beyond-planar graphs: 1-planar, IC-planar,
and NIC-planar graphs. These are the graphs that admit a 1-planar, IC-planar,
and NIC-planar drawing, respectively. A drawing of a graph is 1-planar if every
edge is crossed at most once. A 1-planar drawing is IC-planar if no two pairs
of crossing edges share a vertex. A 1-planar drawing is NIC-planar if no two
pairs of crossing edges share two vertices. We study the relations of these
beyond-planar graph classes (beyond-planar graphs is a collective term for the
primary attempts to generalize the planar graphs) to right-angle crossing (RAC)
graphs that admit compact drawings on the grid with few bends. We present four
drawing algorithms that preserve the given embeddings. First, we show that
every -vertex NIC-planar graph admits a NIC-planar RAC drawing with at most
one bend per edge on a grid of size . Then, we show that
every -vertex 1-planar graph admits a 1-planar RAC drawing with at most two
bends per edge on a grid of size . Finally, we make two
known algorithms embedding-preserving; for drawing 1-planar RAC graphs with at
most one bend per edge and for drawing IC-planar RAC graphs straight-line
Perception of Symmetries in Drawings of Graphs
Symmetry is an important factor in human perception in general, as well as in
the visualization of graphs in particular. There are three main types of
symmetry: reflective, translational, and rotational. We report the results of a
human subjects experiment to determine what types of symmetries are more
salient in drawings of graphs. We found statistically significant evidence that
vertical reflective symmetry is the most dominant (when selecting among
vertical reflective, horizontal reflective, and translational). We also found
statistically significant evidence that rotational symmetry is affected by the
number of radial axes (the more, the better), with a notable exception at four
axes.Comment: Appears in the Proceedings of the 26th International Symposium on
Graph Drawing and Network Visualization (GD 2018
GiViP: A Visual Profiler for Distributed Graph Processing Systems
Analyzing large-scale graphs provides valuable insights in different
application scenarios. While many graph processing systems working on top of
distributed infrastructures have been proposed to deal with big graphs, the
tasks of profiling and debugging their massive computations remain time
consuming and error-prone. This paper presents GiViP, a visual profiler for
distributed graph processing systems based on a Pregel-like computation model.
GiViP captures the huge amount of messages exchanged throughout a computation
and provides an interactive user interface for the visual analysis of the
collected data. We show how to take advantage of GiViP to detect anomalies
related to the computation and to the infrastructure, such as slow computing
units and anomalous message patterns.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Evaluation of two interaction techniques for visualization of dynamic graphs
Several techniques for visualization of dynamic graphs are based on different
spatial arrangements of a temporal sequence of node-link diagrams. Many studies
in the literature have investigated the importance of maintaining the user's
mental map across this temporal sequence, but usually each layout is considered
as a static graph drawing and the effect of user interaction is disregarded. We
conducted a task-based controlled experiment to assess the effectiveness of two
basic interaction techniques: the adjustment of the layout stability and the
highlighting of adjacent nodes and edges. We found that generally both
interaction techniques increase accuracy, sometimes at the cost of longer
completion times, and that the highlighting outclasses the stability adjustment
for many tasks except the most complex ones.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs
Fan-planar graphs were recently introduced as a generalization of 1-planar
graphs. A graph is fan-planar if it can be embedded in the plane, such that
each edge that is crossed more than once, is crossed by a bundle of two or more
edges incident to a common vertex. A graph is outer-fan-planar if it has a
fan-planar embedding in which every vertex is on the outer face. If, in
addition, the insertion of an edge destroys its outer-fan-planarity, then it is
maximal outer-fan-planar. In this paper, we present a polynomial-time algorithm
to test whether a given graph is maximal outer-fan-planar. The algorithm can
also be employed to produce an outer-fan-planar embedding, if one exists. On
the negative side, we show that testing fan-planarity of a graph is NP-hard,
for the case where the rotation system (i.e., the cyclic order of the edges
around each vertex) is given
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