Wang et al

*Wenwen Li. School of Geographical Sciences and Urban Planning, Arizona State University, Tempe, AZ, ASU.

# GeoGraphViz: Geographically Constrained 3D Force-Directed Graph for
Knowledge Graph Visualization

Sizhe Wang  Wenwen Li  Zhining Gu  School of Geographical Sciences and Urban
Planning, Arizona State University, Arizona, USA  School of Computing and
Augmented Intelligence, Arizona State University, Arizona, USA<EMAIL_ADDRESS>
(<day> <Month>, <year>; <day> <Month>, <year>; <day> <Month>, <year>)

###### Abstract

[Abstract]Knowledge graphs are a key technique for linking and integrating
cross-domain data, concepts, tools, and knowledge to enable data-driven
analytics. As much of the world’s data have become massive in size,
visualizing graph entities and their interrelationships intuitively and
interactively has become a crucial task for ingesting and better utilizing
graph content to support semantic reasoning, discovering hidden knowledge
discovering, and better scientific understanding of geophysical and social
phenomena. Despite the fact that many such phenomena (e.g., disasters) have
clear spatial footprints and geographical properties, their location
information is considered only as a textual label in existing graph
visualization tools, limiting their capability to reveal the geospatial
distribution patterns of the graph nodes. In addition, most graph
visualization techniques rely on 2D graph visualization, which constraints the
dimensions of information that can be presented and lacks support for graph
structure examination from multiple angles. To tackle the above challenges, we
developed a novel 3D map-based graph visualization algorithm to enable
interactive exploration of graph content and patterns in a spatially explicit
manner. The algorithm extends a 3D force directed graph by integrating a web
map, an additional geolocational force, and a force balancing variable that
allows for the dynamic adjustment of the 3D graph structure and layout. This
mechanism helps create a balanced graph view between the semantic forces among
the graph nodes and the attractive force from a geolocation to a graph node.
Our solution offers a new perspective in visualizing and understanding spatial
entities and events in a knowledge graph.

###### keywords:

knowledge graph; force-directed graph; visualization; graph patterns; linked
data; location-aware

††articletype: Research Article

##  1 Introduction

Knowledge graphs are a machine-parsable graph technology that interlinks world
entities, both physical and digital, and provides formal descriptions of each
entity to enhance information consumption, support query answering, and
semantic inference and reasoning for deriving new knowledge 1, 2. As the data
volume in geospatial and other domains continue to hit exponential growth,
organizations and data holders have increasingly used knowledge graphs to
organize massive amounts of domain data. The IT giants, such as Google, have
created a knowledge graph by integrating information from a variety of sources
to support better search and information retrieval. Statistics have shown that
by May 2020, Google’s knowledge graph has grown to contain 5 billion entities
and over 500 billion facts, and it has supported over 1/3 of 100 billion
queries made to Google each month.

In the geospatial domain, progress in building spatial data infrastructures,
such as the European Union’s INSPIRE (Infrastructure for Spatial Information
in the European Community) portal, has been in creating data and metadata
schemas to annotate data in the broad Earth and environmental science domains
3. In the US, the National Science Foundation (NSF) has started a new program
called Convergence Accelerator. One of its aims is to develop cutting-edge
knowledge graph technologies for linking cross-domain data for building an
open knowledge network that fosters convergence research. A key research
advancement in spatial sciences is the creation of KnowWhereGraph 4, a
knowledge graph that connects environmental datasets related to natural
disasters, agriculture, and soil properties to understand the environment
impacts on the society. Semantic enrichment services are provided to support
semantic reasoning and question answering on top of its data store of over 12
billion facts 5.

As the domain data in various knowledge graphs proliferate in the research
community, challenges also arise for non-developers as well as knowledge
engineers to access and understand massive graph-ready datasets 6 7 8. In
particular, it has become increasingly challenging to enable open access to
the right graph data in the right form for the right end users. As human
brains are especially good at visual inspection, providing an intuitive
presentation of the knowledge graphs are critical for the understanding of the
graph, its entities, and interconnections among them. Knowledge graph
visualization, which enables interactive exploration and information filtering
of graph data and structure, has become an important means to facilitate data
consumption and sense making of big, linked data.

Popular graph visualization tools, such as those provided as part of a triple
store platform (e.g., GraphDB 9 or AllegroGraph 10), mainly support 2D graph
visualization. In the graph, nodes are used to represent the entities, and
edges represent interrelationships between the entities. To allow real-time
rendering, especially in handling large graph data, nodes expansion or
clustering functions are provided such that the graph starts from a summarized
view and can be gradually expanded according to end user interest. One major
limitation in such solutions is the lack of geographical reference for the
graph data, especially for data that are geospatial, such as hurricane tracks
that have originated in the North Atlantic Ocean and moved westward to hit the
US coastal communities, or an interruption of a food supply chain caused by a
wildfire event that has occurred near the farmlands in Southern California. In
existing visualization tools—even if the location information, which could be
a point, line, or polygon—is encoded in the graph, they are treated as regular
text and there are very few tools that support the visualization of this
special graph information in a virtual geographical space, such as a map.

In comparison, traditional GISs (Geographic Information Systems) provide
powerful solutions for overlaying multiple geospatial data on a base map, and
they often adopt flow maps to support graph data visualization 11, 12. In such
systems, when presenting interrelationships among entities, each entity must
be pinned to a fixed geographic location on the map, regardless of whether an
entity possesses multiple geographical properties or is a moving target (e.g.,
hurricane events). The relationships between the entities are visualized
through straight or curved lines between two locations on a map. Although
these map-based graph visualizations offer a geographical reference, the graph
patterns, such as local clusters, are significantly altered as strengths of
the edges connecting the nodes are not considered. This limitation hinders the
dynamic exploration of graph structure and patterns.

To overcome this limitation, this paper presents a new “Graph Above the Map”
solution to enable interactive graph exploration from both the graph and map
perspectives. A geographically constrained 3D force-directed graph
visualization algorithm is developed to dynamically render the graph layout by
considering the interrelations among the graph nodes and their geolocations.
This way, both the location property and graph properties can be visualized in
a coherent web interface, supporting knowledge discovery within a geospatial
context. The rest of the paper is organized as follows: Section 2 reviews
existing techniques for graph visualization, Section 3 introduces our proposed
algorithm in detail, Section 4 describes the data and experiments to
quantitatively measure the graph and geographical presentation of linked data,
Section 5 introduces the GeoGraphViz user interface, and Section 6 concludes
the paper with a discussion of future research directions.

##  2 Literature Review

###  2.1 Map-based visualization

Flow maps are a prominent approach that uses map-based visualization to
display linkages and relationships between two entities. It is a combination
of a 2D or 3D map with a flow diagram. For instance, the Sankey diagram 13 is
type of flow diagram to illustrate a flow trend from the start node to the end
node. In the flow diagram, the arrow on the edges shows the flow direction and
the width of edges connecting each pair of nodes indicates the intensity
between the connections. The edges can also be assigned with different colors
to show different types of connections. When the start and end nodes are
associated with some locations and are placed on a map, the diagram becomes a
flow map. Relying on distinctive flow styles and node symbolization, a flow
map can exhibit common and unique properties of different locations 11. It can
also intuitively demonstrate the patterns of flow, be it local, regional, or
global. Because of the intuitive manner for displaying flows and connections,
flow map visualization has received widespread adoptions in several
applications, such as mapping traffic patterns, migration routes, trade
patterns, disease spread, and other geospatial data with linkage information
14, 15, 16. To further improve the visual effect, Yang et al. 17 proposed a 3D
flow map to incorporate a height dimension of the arrows to display additional
data attributes that 2D flow maps are not capable of. Ardissono et al. 18
developed a novel model using colored shapes and interactive functions to
assist entity filtering based on selected categories to better support map-
based visualization. Because of its ability in presenting connections between
points, flow maps can be leveraged to support graph visualization,
particularly when location is the most prominent property of a graph node,
such as a city. However, because a flow map needs to pinpoint the graph nodes
to a fixed location on the map, it suppresses the display of some graph
patterns, such as clustering patterns of the graph nodes measured by the
strengths of their interconnections rather than the geographic proximity among
the nodes. The flow map has also shown limitation in visualizing the
spatiotemporal evolution of dynamic entities.

###  2.2 Graph visualization methods

Recently, several graph visualization tools have also been developed to
visualize linked data in a knowledge graph 19, 20. WebVOWL is a web-based
visualization tool for ontologies 21. It can directly load ontologies (a
logical representation of knowledge graph) in an RDF (Resource Description
Framework) format to visualize the interrelationships among the graph nodes.
Different line styles and node colors are applied to differentiate entities,
their properties and relationships. Several semantic graph databases, such as
GraphDB 22, Neo4j 23, and ArangoDB 24, also provide visual graph interfaces
along with data query support to allow visualization of graph data. Similar to
WebVOWL, these graph databases also provide 2D visual graphs to display nodes
and their connections; some provide additional statistical functions to show
counts of nodes and relationships belonging to different categories while
others support filtering operation to visualize a subgraph of interest. In
ArangoDB, graph visualization is combined with timeline visualization for
identifying events and relationships with a temporal pattern. These built-in
visualization solutions are based on drawing information on a 2D visual graph,
limiting the multi-dimensional exploration of the graph.

Besides these built-in tools for knowledge graph visualization, customized
tools that support different graph exploration needs have also been developed.
For instance, Heim et al. 25, 26 developed RelFinder to support the
identification and visualization of node relationships. This is achieved
through highlighting a path connecting two nodes of interests in a 2D graph.
He et al. 27 developed an interactive graph platform to support knowledge
discovery on dietary supplements. The graph can also be dragged and panned,
and a node’s visibility can be configured. Noel et al. 28 developed CyGraph, a
unified graph-based system for network security monitoring and improvement.
CyGraph provides multiple functions to allow visual interactions with the
graph, including node and edge property filtering and color configuration.
Most interestingly, it can also show a cluster view of graph nodes that share
the same property. Similar works that allow display of clustering patterns can
also be found in 29. All these graph solutions are based on 2D visualizations.

There are also works integrating map visualization and graph visualization for
linked data exploration. Liu et al. 30 developed a web portal that uses
multiple visualization methods, such as 2D graph visualization, streamgraph
visualization, map visualization, and circular flow charts, to showcase
patterns of research collaboration, popular research topics, and other
information from publications. Regalia et al. 31 developed a linked data
browser called Phuzzy.link to use hyperlinks to hop among connected graph
nodes. If a graph node has geographic information, a map will be displayed on
the side to enrich the visualization 32. This is a way to visualize graph data
in a non-graph form. A similar visualization portal was developed by Mai et
al. 33. In addition to visualizing graph data in a non-graph form, the authors
employ a narrative cartography to map geographic information with timestamps
on the map to tell a story, such as one describing an expedition path.

Recently, 3D graph visualization has become a trending technique. Open-source
JavaScript (JS) libraries, such as ThreeJS 34 and Gephi 35, have become
popular tools to provide 3D rendering engines using WebGL (Web Graphic
Language) to visualize and explore graph data in 3D on the Web. Powered by
ThreeJS, a force-directed 3D graph drawing mechanism can be implemented to
place nodes in a visually 3D space to avoid node cluttering problems. The 3D
forced-directed graph supports multiple ways of graph interactions and visual
effects. For instance, users can drag the graph nodes and place them in a
different position on the screen; they can also rotate the entire graph to
observe patterns from different viewpoints (e.g., to view the graph from the
front, the top, and the back, as well as in any other 3D angle). When a user
clicks on a node, the information about it pops up, and the clicked node will
be enlarged or highlighted. The nodes and edges can also be colored according
to the types of connections. Text, images, and customized geometries can be
used to render the nodes. These 3D visualization libraries offer an efficient
way to explore graph data interactively in a web-based environment.

Existing visualization tools or libraries provide visual displays for users to
interact and explore interested data, relationships, and knowledge within a
graph. To allow real-time rendering of large graph data, node
folding/expansion or clustering functions are often provided so that the
visual graph will start from a summarized view and can be gradually expanded
according to end user interest in certain subgraphs. However, in almost all
these tools, location information is rendered as text information (e.g., as an
annotation indicating the placename). This limitation makes it difficult to
examine the geospatial relationships among the graph nodes or exploring the
spatial contexts of semantically relevant information. As a result, it is
difficult to intuitively exhibit the knowledge connections between spatial
information and semantic relationships among entities.

To address the aforementioned limitations in both the more traditional map-
based visualization (which lacks the flexibility in presenting semantic
relationships of the graph nodes) and 2D graph visualization (which lacks the
intuitive representation of location information and spatial context), we
propose in a new “Graph Above the Map” solution, the GeoGraphViz. In this, 3D
web-based graph visualization is enabled in combination with a 2D map view to
allow a more coherent spatial-semantic visual presentation of knowledge graph
data. In particular, a geographically constrained 3D force-directed graph
visualization algorithm is developed. The algorithm is described in detail in
the next section.

##  3 GeoGraphViz Visualization Algorithm

The intuition behind our proposed algorithm is that current graph
visualization strategies almost entirely visualize nodes and links based on
their semantic relationships. The weights on the relationships are often
ignored in existing solutions. As such, nodes are placed close to each other
not because they are similar, but because there are linkages among them.
Force-directed graphs are capable of simulating the graph layout by the
strengths of connections among nodes. Therefore, they are very suitable for
visualizing graphs which have quantitative weights (such as similarities) on
the edges. However, the graph can only visualize based on one kind of force;
the algorithm is not capable of visualizing a graph when multiple forces
present, such as the semantic similarity 36 among graph nodes, and the
geographical force that a node receives based on its own geolocation
properties. However, we argue that the semantic connections among the nodes
and the geographical distribution patterns of the nodes are both important for
inspecting graph patterns, especially when the graph nodes are geospatially
related (e.g., each node represents a geographical entity, such as a natural
feature) 3738. Hence, in our paper, we are looking to “blend in” different
amounts of semantic and geographical forces to demonstrate multi-faceted
characteristics of graph patterns in a single view to enable a new kind of
geospatial knowledge discovery.

The GeoGraphViz visualization algorithm derives from and extends the force-
directed graph placement algorithm 39. A force-directed graph simulates the
graph layout with two forces: attractive and repulsive force among graph
nodes. Attractive force is used to place connected nodes visually close to
each other; it exists when there is an edge connecting two nodes. Repulsive
force exists universally among all node pairs in the graph, regardless of
whether a connection is presented. It prevents the nodes from becoming too
close to each other in the visual graph. With a joint effect of attractive and
repulsive forces, the position of the graph nodes is dynamically adjusted
until the graph reaches a stable state, in which all forces are at
equilibrium. The resultant graph layout is capable of presenting node
clustering patterns based on their interconnectivity. It also maintains
sufficient distance among the nodes to ensure graph readability and
interpretability.

However, when the nodes contain location information, which is important to
understand the spatial context of the graph patterns, this algorithm no longer
fulfills the requirement. Our algorithm addresses this limitation by adding
the third force, which we call the “geo-force,” to the original force-directed
graph placement algorithm to support location-aware graph visualization. The
geo-force is a type of attractive force from a specific geolocation to a graph
node. The geolocation can be a point location unique to a geographic entity,
such as a city; it could also be the location property of other named
entities, such as an expert who is related to a location (e.g., through
his/her affiliation). Integrating the three forces- the attractive force
($f^{A}$), repulsive force ($f^{R}$), and the geo-force ($f^{G}$)-the
visualization algorithm can not only reveal the interrelationships among the
graph nodes, but also the geographic distribution of the nodes.
Mathematically, the three forces can be computed as follows:

$\displaystyle f^{A}(u,v)$
$\displaystyle=\frac{\left\|C(u)-C(v)\right\|^{2}}{k}\cdot\frac{C(u)-C(v)}{\left\|C(u)-C(v)\right\|}$
$\displaystyle=\frac{\left\|C(u)-C(v)\right\|(C(u)-C(v))}{k}$ (1)

$\displaystyle f^{R}(u,v)$
$\displaystyle=-\frac{k^{2}}{\left\|C(u)-C(v)\right\|}\cdot\frac{C(u)-C(v)}{\left\|C(u)-C(v)\right\|}$
$\displaystyle=-\frac{k^{2}(C(u)-C(v))}{\left\|C(u)-C(v)\right\|^{2}}$ (2)

$\displaystyle f^{G}(u)$
$\displaystyle=K\cdot\frac{\left\|G(u)-C(u)\right\|^{2}}{k}\cdot\frac{G(u)-C(u)}{\left\|G(u)-C(u)\right\|}$
$\displaystyle=K\cdot\frac{\left\|G(u)-C(u)\right\|(G(u)-C(u))}{k}$ (3)

where $u$ and $v$ are two nodes between which the forces apply. $C(\cdot)$
indicates the coordinate vector of a graph node in a virtual 3D space in which
the graph is placed. $G(\cdot)$ refers to the geographical coordinate vector
(e.g., latitude and longitude) representing the geolocation property of a
graph node. Note that, before calculation, the geographic coordinates need to
be projected into the aforementioned virtual 3D space in which the graph
layout is updated. $||\cdot||$ computes the magnitude of a vector.
$f^{A}(u,v)$ and $f^{R}(u,v)$ respectively define the attractive and repulsive
forces that $v$ receives from $u$. $k(>0)$ is a parameter that balances
between the attractive and repulsive forces. The larger the $k$ is, the
smaller attractive force is, and thus the stronger repulsive force a node will
receive, resulting in a less localized layout. Parameter $K(\geq 0)$ controls
the relative strength of the geo-force compared with the two other forces. The
larger the $K$ is, the closer a graph node will be placed toward its actual
geolocation on a map.

To simulate the final graph layout, the location of each node will be updated
through an iterative process until the 3D graph reaches a stable state: a
graph-level force equilibrium. Below, we provide the pseudocode of our
proposed algorithm. The input of the algorithm includes the graph $G$, an
initial system temperature $T$, and a cooling parameter $\alpha$. Here the
system temperature and cooling factor are introduced to simulate the annealing
process in which a solid is being heated up by a high temperature so that all
particles of the solid can be transferred into the liquid state. This is
followed by a cooling process that slowly lowers the temperature until all
particles reach a low energy ground state 40. These parameters are also often
used in a heuristic-based optimization algorithm to apply more aggressive
search/move (a high initial $T$) at the beginning of the process and a careful
fine-tuning (smaller $\alpha$) at a later stage to find the near-optimal
solution. Here in the algorithm, the system temperature $T$ determines the
maximal distance $d_{T}$ that a node can move at each iteration. There are
five main steps at each iteration. Steps 1-3 calculate three individual forces
that act on each node from all the other nodes according to Equations 3, 3,
and 3. The net force jointly determined by the three forces are saved in
$F(v)$ as a vector. Step 4 updates a node’s position. The moving direction of
the node is along the direction given by the net force $F(v)$ and its moving
distance is co-decided by the strength of the net force $||F(v)||$ and a
maximum moving distance $d_{T}$. The system temperature $T$ decreases (Step 5)
as the process goes on so that, just as with the annealing process, the graph
layout is updated fast at the beginning and slower later for fine-tuning to
eventually reach a stable state, when an optimal or a near-optimal graph
layout is found.

Input: Graph $G=(V,E)$

Input: Initial temperature $T$

Input: Cooling parameters $\alpha$

Output: Graph $G$ with updated layout

1 for  _$i\leftarrow 1$ to $n\\_iterations$_ do

2 _// Step 0: Initialize the net force $F$ for each vertex_

3 foreach  _vertex $v\in V$_ do

4 let $F(v)\leftarrow 0$

5 end foreach

6

7  _// Step 1: Calculate accumulated attractive force_

8 foreach  _edge $e\in E$_ do

9

10 let $u$ and $v$ be the two vertices of $e$ and $u$, $v\in V$

11 $F(v)\leftarrow F(v)+f^{A}(u,v)$

12 $F(u)\leftarrow F(u)+f^{A}(v,u)$

13 end foreach

14

15  _// Step 2: Calculate accumulated repulsive force_

16 foreach  _vertex $v\in V$_ do

17 foreach  _vertex $u\in V$_ do

18 if  _$u\neq v$_ then $F(v)\leftarrow F(v)+f^{R}(u,v)$;

19

20 end foreach

21

22 end foreach

23  _// Step 3: Calculate the geo-force_

24 foreach  _vertex $v\in V$_ do

25 $F(v)\leftarrow F(v)+f^{G}(v)$

26 end foreach

27

28  _// Step 4: Update the coordinates of each vertex in the virtual 3D space_

29 let $d_{T}\leftarrow T$

30 foreach  _vertex $v\in V$_ do

31 $C(v)\leftarrow C(v)+\frac{F(v)}{||F(v)||}\cdot\min(d_{T},||F(v)||)$

32 end foreach

33

34  _// Step 5: cooling function (temperature decay)_

35 $T\leftarrow(1-\alpha)\cdot T$

36

37 end for

Algorithm 1 Geographically Constrained Force-Directed Graph Simulation

##  4 Data and Experiments

###  4.1 Graph Data

To test our proposed 3D geographically constrained force-directed graph
rendering algorithm, we use expert network data from Direct Relief, a non-
profile organization dedicated to providing disaster relief and humanitarian
aid. This expert network contains 41 worldwide experts with infectious disease
related expertise (e.g., COVID-19) that the Direct Relief staff works with to
distribute medical and other supplies to help vulnerable and COVID-19 affected
populations. Each expert has properties that include a name, research
interest, affiliation and its geolocation, as well as a public research
profile. The experts are linked through a semantic similarity measure of their
research interests, generating a similarity graph. The similarity scores
between two experts have a value range (0,1] and they are computed from a
semantic analysis of the experts’ most representative publications. Figure 1
shows the profile of an infectious disease expert (left) and her potential
collaboration network with researchers sharing similar expertise (right).

Figure 1: An example expert node in the expert graph.

###  4.2 Force balancing and graph presentation

To investigate the effect of the added geo-force to the visual presentation of
the 3D graph, we conducted an experiment to measure the graph layout changes
when the forces are assigned with different weights (parameter $K$ in equation
3, which is also known as the forcing balancing parameter). Here we propose
two quantitative metrics to evaluate the degree to which the graph structure
can be preserved and how well the spatial patterns can be revealed with an
added geo-force. To measure the layout changes of a rendered graph, we adopt
edge length variation (ELV), which provides a normalized measure of average
edge length changes of a graph. This measure has been increasingly adopted in
recent studies to determine the quality of a graph layout 41, 42. The metric
$M_{ELV}$ is defined as follows:

$\displaystyle M_{ELV}=\frac{l_{v}}{\sqrt{n_{E}-1}}$ (4)

with:

$\displaystyle l_{v}=\sqrt{\sum\limits_{e\in
E}\frac{(l_{e}-l_{\mu})^{2}}{n_{E}\cdot l^{2}_{\mu}}}$ (5)

Where $E$ is the set of edges in the graph, $n_{E}$ is the number of edges,
and $l_{\mu}$ is the mean length of all edges. Terms $\sqrt{n_{E}-1}$ and
$l_{\mu}^{2}$ are added for normalization purposes. The intuition behind our
choice of this metric is that the location of nodes and length of edges tend
to reach a near static state in a 3D force-directed graph when the attractive
and repulsive forces are being balanced. But after adding the geo-force, the
nodes which are originally clustered together may be stretched far apart if
their geolocations are distant from each other, resulting in an increase in
the ELV.

We also introduce the mean locational offset (MLO) to measure the location
accuracy in the visual presentation of the graph nodes. The metric $M_{MLO}$
is defined as follows:

$\displaystyle M_{MLO}=\sum\limits_{v\in
V}\frac{\left\|C(v)-G(v)\right\|}{n_{V}\cdot d_{GC}}$ (6)

Where $V$ is the set of nodes in the graph, $n_{V}$ is the number of nodes,
$C(v)$ indicates coordinate vector of a node in the final graph layout. $G(v)$
is the coordinate vector of the projected geolocation of a node. The offset is
computed as the horizontal distance that a node moves in the 2D map plane. The
distance between the North Pole and the South Pole on the map, $d_{GC}$,
measured in the viewport coordinate system, is used to normalize the MLO. When
every node is placed right above its exact geolocation, $M_{MLO}=0$.

Table 1: Quantitative measures for graph structure change of expert data under different force balancing parameter $K$ Scenario | $K$ | $M_{ELV}$ | $M_{MLO}$
---|---|---|---
(a) | 0 | 0.0555 | 0.554
(b) | 5 | 0.0731 | 0.119
(c) | 10,000 | 0.0941 | 0.001

((a))

((b))

((c))

Figure 2: Graph layout at the force balancing parameter $K$. (a) $K=0$, (b)
$K=5$, and (c) $K=10,000$

Table 1 presents the values of $M_{ELV}$ and $M_{MLO}$ at different settings
of the forcing balancing parameter $K$. The resultant graph layouts visualized
by the GeoGraphViz are shown in Figure 2. To more clearly present the 3D graph
through a 2D snapshot, less prominent nodes (nodes with fewer connections) are
set to be invisible, but their interactions through the three forces are still
considered. In practice, we recommend setting the parameter $K$ between 3 and
20. Graphs created with $K$ falling in this value range can better preserve
location representation of each node, as well as important graph structures,
such as local clusters. In this experiment, we use $K=5$ to present a balanced
graph layout. Figure 2(a) shows the scenario in which the geo-force is
excluded when drawing the graph. In this case, $K=0$ and $M_{ELV}$ reaches its
lower bound and $M_{MLO}$ reaches at its upper bound for this test dataset in
which experts are distributed very broadly with a strong international
perspective. In the Figure 2(a) graph, we can clearly observe a local cluster
near the center of the graph. However, it is almost impossible to correctly
infer the geographic distribution pattern of these experts, especially for the
two experts from India, if we consider only the information in the graph layer
(white nodes and white links). Here, because GeoGraphViz implements the new
“Graph Above the Map” strategy and uses the green lines to connect the nodes
with its geolocation on the map layer, the spatial context can still be
captured.

Figure 2(c) presents a scenario when $K$ is set to be a very large number
(Table 1), where the geo-force dominates the graph layout simulation. The
graph nodes in Figure 2(c) locate nearly exactly on top of their actual
geolocation, showing a clear geographic distribution pattern. Hence, the
$M_{MLO}$ is at a near-zero value. However, the graph structure is
significantly varied with the local cluster presented in Figure 2(a) almost
completely gone. It is therefore very difficult to analyze the graph patterns
through the graph’s visual topological presentation. $M_{ELV}$ in this case
reaches its upper bound due to the significant relocation of graph nodes.

In comparison, Figure 2(b) presents a more balanced view in location-aware
graph visualization (with $K=5$). While the nodes are moving closer to reflect
their geolocation, we can still observe a highly densely connected subgraph
near the center of the view. This graph view can also better present the
international perspective of the clustered nodes of experts with similar
research expertise. Quantitatively, $M_{ELV}$ reduces from when $K=0$ and
falls near the middle of its value range, meaning that nodes move but not
dramatically. We also found that $M_{MLO}$ has reduced substantially compared
to when $K=0$, meaning that the location offset is much reduced so the spatial
context can be better presented.

Observing value changes in the two metrics ($M_{ELV}$ and $M_{MLO}$) can also
help reveal the joint effects of the attractive force, repulsive force, and
the geo-force to the graph layout. Ideally, if the nodes of each densely
connected subgraphs (clusters) in a graph are all located within a local
geographical region, the algorithm is capable of generating a graph layout
with both a clear graph pattern and spatial pattern. In such a scenario,
$M_{ELV}$ and $M_{MLO}$ will remain low with varying $K$. However, when a
moderate $K$ value (e.g., between 3 and 20) results in a large edge length
variation (with $M_{ELV}$ at close to its upper bound), this means adding geo-
force will significantly change the graph structure. For applications that
focus on investigating the graph patterns, the use of geo-force is not
recommended. Instead, the users can still rely on the GeoGraphViz’s unique
“Graph Above the Map” feature (e.g., green lines connecting graph nodes with
their geolocations) to understand the spatial distribution patterns.

###  4.3 Algorithm generalizability test

To further test the generalizability of the proposed algorithm, we created a
simulated dataset with distinctive graph and geographical distribution
patterns and more nodes (>200) than the real dataset used in Section 4.2. The
graph can be considered as a large collaboration network of researchers with
international perspectives. It can also be used to model semantic
relationships for other types of data (e.g., publications, images, and
commercial products), among which their similarity can be measured.

This simulated dataset contains three major clusters. The number of nodes
distributed to each cluster are about the same ($\sim$70). The similarity
values among each pair of nodes were randomly generated, following normal
distributions. The existence of a linkage between two nodes, whether they are
in the same cluster or not, is based on a predefined probability. More
connections (edges) with stronger strengths (higher similarity values) will be
assigned to nodes within the same cluster, and the number of edges and
similarity values are lower for between-cluster nodes. The white nodes and
white links in Figure 3(a) illustrate the clusters. This figure also shows
when no geographical force is applied to each node. Hence, the clusters are
solely semantic. To assess the effect of location awareness in graph
visualization, each node in the simulated dataset was assigned with a geo-
location. In general, nodes in each of the three clusters are geographically
distributed in the United States (US), Europe, and Asia, respectively. From
west to east, let us call the three main clusters observed (in Figure 3(a))
the U.S., the European, and the Asian cluster. However, outliers also exist.
The green linkages in Figure 3(a) show nodes which "travel" a long distance.
For instance, several nodes whose geolocations are in the U.S. (the New York
region) belong semantically to the European cluster. When there are no
geographical constraints, these nodes will be placed near nodes to which they
are akin. Similar cases also include (1) a few nodes geographically located in
Germany but semantically belong to the Asian cluster; and (2) three nodes in
Norway, Sweden, and Thailand moved westward to be close to the clusters to
which they belong. Nodes with significant geographical movements are
highlighted in greenlinks in Figure 3(a).

((a))

((b))

((c))

Figure 3: Graph layout of simulated dataset at the force balancing parameter $K$. (a) $K=0$, (b) $K=5$, and (c) $K=10,000$ Table 2: Quantitative measures for graph structure change of simulated data under different force balancing parameter $K$ Scenario | $K$ | $M_{ELV}$ | $M_{MLO}$
---|---|---|---
(a) | 0 | 0.0241 | 0.315
(b) | 5 | 0.0445 | 0.0576
(c) | 10,000 | 0.0519 | 5.68e-5

The visualization results of the simulated graph under different force
balancing parameter $K$ are shown in Figure 3. While Figure 3(a) demonstrates
the visualized graph without a geo-force, Figure3(c) shows when a very strong
geo-force is applied ($K$=10,000) and has become the dominant force. In such a
case, all nodes are placed very close to their geo-locations, so it is easy to
observe the geographical properties of the graph nodes, but the graph’s
semantic structure can hardly be inspected. A visualization result that
balances between the two forces is shown in Figure 3(b), which presents a
clear spatial distribution as well as the semantic clustering pattern. In
particular, the nodes from New York and Germany are dragged close to their
actual clusters, but their geo-locations are still recognizable in the given
parameter settings.

The statistics of the above three configurations, measured by $M_{ELV}$ and
$M_{MLO}$, are listed in Table 2. It demonstrates a similar pattern as that in
Table 1. When $K$ increases from 0 to 5, the node’s semantic distance
($M_{ELV}$) becomes twice as great, but the geographical distance $M_{MLO}$
drops significantly, reaching a balanced view between graph and spatial
patterns.

###  4.4 Algorithm Efficiency Test

To assess system efficiency in visualizing graphs with an increasing size, we
simulated graph data with two types of patterns. In Type I graphs, the total
number of graph edges are in proportion to that of a complete, undirected
graph (i.e., for any two nodes in the graph, there is an edge connecting
them). The number of edges $N_{e}$ in such graphs can be represented as:

$N_{e}=p\cdot\frac{n\cdot(n-1)}{2}$ (7)

Where $n$ is the number of nodes in the graph. It can be seen that $N_{e}$ is
proportional to $n^{2}$ controlled by a parameter $p\in(0,1]$.

Type II graphs share the characteristic of the total number of edges, being
proportional to the number of graph nodes. Hence, $N^{\prime}_{e}$ can be
represented as:

$N^{\prime}_{e}=\frac{c\cdot n}{2}\;,\;\;(c\leq n-1)$ (8)

Where $n$ is the number of nodes in the graph. In graphs with such patterns,
the total number of edges, $N^{\prime}_{e}$ is proportional to the number of
the nodes. This proportion is controlled by a parameter $c\in[0,n-1]$. This
strategy emulates real-world scenarios, such as social networks wherein each
person maintains a certain number of (social) connections on average,
regardless of the size of the network/graph.

We further generated graphs with different sizes (with $n$ = 100, 200, 400,
800, and 1600) and different graph density parameters ($p$=0.05, $p$=0.5, and
$c$=50) following the two graph types. The graph visualization time counted
from loading the graph data, and simulating the positions of nodes in the
graph, to finishing rendering it in the web browser, as reported in Figure 4.

Figure 4: Efficiency of graph visualization as graph size increases

The X axis shows the number of nodes in the graph. The Y axis provides the
graph visualization time (in sec). In Type I graphs, the number of edges is
proportional to the square of number of nodes. The larger the parameter $p$,
the denser the graph. In Type II graphs, the number of edges is proportional
to the number of nodes. The larger the parameter $c$, the denser the graph.
The dashed blue line demonstrates the result of a graph simulation using the
second strategy (Type II graph) with $c$=50. The solid green line with
triangular markers indicates the visualization time for Type I graphs with
$p$=0.05. The solid orange line with square markers shows the results of Type
I graphs with $p$=0.5. It also presents an edge case (rare in real-world
scenarios) where the graphs are very densely connected (the number of edges
equal to half of that in a undirected, complete graph). The green and blue
lines show similar results. As the number of nodes increases, there is a
linear relationship between visualization efficiency and the number of graph
nodes. The orange line, in comparison, shows almost a quadratic growth per
number of nodes. This result reflects the time complexity of $O(n^{2})$
indicated in the algorithm presented in Section 3.

As seen in Figure 4, the performance of the GeoGraphViz algorithm in terms of
time efficiency is good and can serve near real-time visualization purposes
when the number of graph nodes is below 800. As shown in both the dashed blue
and solid green lines, the visualization time will be less than 3 sec. For the
orange line, the visualization can be completed within 7 sec. There are some
lags but considering the density of the graph, this visualization time is
acceptable. When the number of graph nodes reaches a very high number, such as
1600, the lags become longer. In such cases, further optimization is required
to improve both the visualization efficiency and the visual effect, as it will
be difficult to examine the pattern of a very large graph with dense
connections.

##  5 GeoGraphViz User Interface

Figure 5 demonstrates the interface for our graph visualization tool (with
expert data). As seen, there are two layers shown in the interface: (1) the 3D
graph layer showing connections of disease experts (white lines connecting
white nodes); and (2) a map layer connecting experts to their locations (i.e.,
geolocations of their affiliations) by using green lines connecting white
nodes to the red dots. These two layers together could demonstrate the
clusters of disease experts who share similar research interests from the
graph perspective. They can also reveal the spatial patterns of the potential
collaboration network, be it local, regional, or international. Several
supporting functions are developed to allow (1) clicking on a graph node to
view the profile information of an expert (see an example in Figure 1), (2)
filtering the graph to present subgraphs with different degrees of node
connections (Figure 2), (3) turning on and off the “KnowWhere” feature to
display purely a graph view or the “Graph Above the Map” view, and (4) a word
cloud view showing collective expertise of the experts in a selected subgraph.
Many graph features (e.g., connections among the graph nodes and connections
across graph and geolocations) can be set to invisible to allow examination of
different facets of the graph. The graph can also be rotated, panned, and
zoomed to improve user experience.

Figure 5: The GeoGraphViz user interface for location-aware knowledge graph
visualization

##  6 Conclusion

This paper presents GeoGraphViz, a location-aware knowledge graph
visualization tool to allow end users, both domain experts and the general
public, to interactively explore graph data, to identify hidden patterns, and
most importantly, to support discovery of new (geospatial) knowledge from
massive cross-domain datasets. GeoGraphViz is empowered by a novel
geographically constrained, 3D force-directed, graph visualization algorithm
and it addresses the limitations of general graph visualization methods and
map-based visualizations and is capable of (1) intuitively visualizing
location properties of the graph nodes, (2) performing multi-dimensional graph
visualization for heuristic knowledge search, and (3) achieving dynamic,
interactive, and context-aware graph visualization. Currently, our GeoGraphViz
tool is being used in combination with one of the largest geospatial knowledge
graphs, the KnowWhereGraph, to empower environmental intelligence applications
in the areas of disaster response and humanitarian aid, climate change, and
agricultural production to food supply chain management.

Leveraging a three-dimensional dynamic graph visualization and a strategy of
“Graph Above the Map,” our GeoGraphViz tool has the unique strength of
“knowing where.” We described the mathematical formulation of the algorithm in
Section 3, as well as conducted a series of experiments in Section 4 to verify
the efficiency and generalizability of the algorithm in visualizing graphs
with different patterns. In Section 4.3, we simulated graph data in which the
geographical and semantic distribution patterns share some similarities (i.e.,
three main semantic clusters reside mainly in three regions: US, Europe, and
Asia), but there are exceptions – while a certain number of nodes reside in
one main geographical region, they belong semantically to another semantic
cluster(s). In such cases, as the geo-force is gradually applied, we can
observe a change in the graph pattern where a node can move a very long
distance (examples shown in Figure 3(a)) to where a balanced view is achieved
between the proximity of this node to its geographical location and the
proximity of this node to the other nodes semantically similar to it (examples
shown in Figure 3(b)), and to where an edge case is reached, where every node
is located right above its location and the semantic pattern be barely
observable (Figure 3(c)).

As seen in Figure 3(b), our algorithm is capable of stretching out each
cluster (EU, Asia, and US) over the map real-estate and highlighting nodes
that have a high level of connectivity to another cluster. This way, the mixed
semantic and geographical patterns can be clearly presented. In fact, this
graph layout and every other layout are simulated based on the overall
attractive and repulsive force among all nodes, and the layout becomes stable
when a global force equilibrium is achieved. However, when a dataset contains
different similarity patterns, the graph will show different patterns. For
instance, if the EU cluster receives an equal amount of total attractive force
from the two edge clusters (US and Asia), the nodes in the EU cluster will not
move significantly towards either. Instead, the Asia and US nodes will likely
move toward the EU nodes, and the distance of movement will depend on the
overall forces they receive.

In an extreme case, when the geographical clustering and semantic clustering
are completely different, meaning that nodes in a semantic cluster do not have
any geographic proximity, and can come from any place on the Earth’s surface,
then mixing the two forces (geographical and semantic) will not present a
clear visual effect. In such cases, we recommend applying either the semantic
or the geographical force in the visualization. Our GeoGraphViz tool provides
functions to allow for such configurations. As known, visualizing multiple
dimensions of information simultaneously helps us gain a more comprehensive
view of a dataset, but it can become more challenging from a visualization
standpoint. Our research aims to solve this problem. Although not all cases
are suitable for being visualized using mixed force, we were able to offer a
new way to present multi-dimensional information in the same visual space, and
developed strategies to separately visualize the two patterns (geographical
and semantic) in complex cases.

In Section 4.4, we also conducted experiments to examine the efficiency of the
graph visualization algorithm. We observed that when the graph size becomes
very large (with the number of nodes above 800), the visualization lag time
will become long, and this will affect the user’s experience. With a large
graph, the nodes will likely be cluttered together. To address this, further
optimization strategies will be needed to accelerate rendering efficiency and
to improve the visualization effectiveness. Node clustering strategies, such
as geometry-based edge bundling 43 and multi-level edge agglomeration 44, are
to be exploited and integrated. In addition, converting from CPU-based
visualization to GPU (Graphics Processing Unit) visualization 456 could also
be an effective means to help the algorithm reduce graph layout computation
time and achieve desired real-time rendering performance.

Our research has broader implications for advances in GIScience. First, the
“Graph on the Map” solution offers a new way of presenting multi-dimensional
information and has the potential to spark the development of more innovative
geovisualization methods. Second, this new visualization strategy allows for a
more visual, intuitive, and interactive way to explore geospatially enabled
graph data, contributing to a better understanding of complex patterns and
relationships, especially in a geographical context. Third, the visualization
tool helps to provide a comprehensive and nuanced view of linked data, making
it easier to communicate scientific information with stakeholders to make
informed decisions. Finally, this work emphasizes the importance of “location-
awareness” in knowledge graph research, which can further foster cross-domain
knowledge exchange between the Semantic Web community and the GIS community.

In the future, we will continue to refine the visualization algorithm to
enhance its spatial-semantic visual presentation and develop more search and
filtering functions to better support graph knowledge exploration and
intelligent scientific question answering. The data and code will be openly
shared to benefit the broader research community.

##  7 Data and code

The data and code used for the GeoGraphVis system and the experiments can be
accessed through: https://github.com/ASUcicilab/GeoGraphViz.

##  8 Acknowledgements

This work is supported in part by the National Science Foundation under awards
number 2033521, 1853864, and 2120943. Any opinions and findings expressed in
this material are those of the authors and do not necessarily reflect the
views of the National Science Foundation.

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