Network Simplification and Visualization through
System Dynamics-based Network Centrality
Lukas Frannek, Haruko Nagaoka, Tadasuke Nakagawa
Hitachi Ltd., Global Center for Customer Co-Creation, Tokyo
Abstract
When developing innovative products in today’s business world, companies try to
optimize the process of indentifying and discussing customer problems, value and
opportunities as much as possible to advance faster to new business creation, proof of
concept and finally contract agreement. In this paper we use system dynamics as a
methodology that facilitates the modeling and visualization of causal business indicator
relationships in a compact and intuitive way that clearly points to business problems and
therefore leads to value and opportunity discovery. Specifically, we propose a technique
that automatically simplifies a given network of nodes based on node importance, such
that a fast understanding of interdependencies and problems in time-limited workshops
and other occasions can be assured.
We first state the principle algorithm used to determine node importance, and then
explain how the network is displayed based on node importance and user input. We
illustrate the usage of this simplification and visualization method with an example in
the field of visitor prediction.
1. Introduction
In the last decade the concept of customer co-creation became a widely used technique
to engage clients as a group of companies, where the companies work together to create
value that is specific to each client [1]. Companies want to find that specific value faster
in order to be able to faster advance to later stages in the business discussions that
propose a company’s products and services to the client. This requires
easy-to-understand ways to illustrate the client’s problems and the suitable measures
that fix those problems. It is vital to come to an agreement with all involved parties.
System dynamics proved to be able to provide valuable tools regarding group model
building in workshop-style meetings and the visualization of these models [2].
Specifically, the causal loop diagram (CLD) serves as a tool that can help to understand
complex relations between a multitude of business indicators all the way up to
management key performance indices (KPIs) such as profit, return on investment or
sales. In a workshop and in the following meetings when explaining the outcomes of the
workshop, time may be limited and understanding a large CLD is not feasible in that
case. However, we may want to gather opinions and comments from persons that did
not participate in the workshop, where we also may not be clear about what additions to
a CLD a person can offer. On the other hand we also may need to present the workshop
outcomes to various persons, where we may not know what kind of information a
person is looking for.
As a means to condense a given network into a form that makes a quick understanding
and exploration of that network possible, we propose a method that consists of two parts.
The first part of the method determines the importance of nodes in the network with a
novel calculation for the node importance. The second part of the method simplifies the
network by consolidating nodes that are less likely to be relevant to the specific
customer, i.e., nodes that likely have low importance to the customer.
A. Related Works
To find the importance of nodes in a network various techniques exist such as the
degree centrality [3], that is determined by incoming and outgoing edges, the
betweenness centrality [3], that is determined by the number of times a node acts as a
2
bridge between other nodes, or the page rank [4], that assesses how many nodes can be
connected via paths, where paths to high importance nodes add more importance. While
the degree and betweenness centralities are less useful to determine the importance of
nodes from a system dynamics viewpoint, the page rank takes also distant nodes and
their importance into account, and thus not only assesses the topological structure.
However, it still lacks the ability to grasp the main determining factors, such as
feedback, in networks such as the CLD.
In the proposed method, the importance for each node in a network is found by utilizing
two types of input. The first type is information based on system dynamics parameters
such as loop and pattern structures. We explain what a pattern constitutes in Chapter 2.
The second type of information is user input that is captured during workshops with
clients or otherwise. We explain what this user input specifically constitutes in C hapter
2. as well.
The display or consolidation of nodes is based on the importance. Consolidation means
that nodes that are less likely to be relevant disappear from the view of the person who
views the network. Similar to the network pruning explained in references [5,6], nodes
with an importance that is below some threshold are removed, but without taking any
meaning away from the main structure of the network and while preserving connectivity.
However, the removed nodes are not viewable after the pruning anymore, and the
importance of nodes may change in subsequent meetings, which requires the nodes to
be still accessible. A nother technique for network simplification is given in reference [7],
where nodes are rearranged in layers to represent their importance. Even though the
visualization becomes cleaner, the difficulty of reconstructing the mental models of the
participants of the CLD creation workshop during the workshop makes this approach
unfeasible. In reference [8] the geometrical structure of a network is not recreated from
scratch, but adjusted in order to preserve the mental map of a network. This approach is
more suitable, but for the previously stated purpose of preserving the mental models of
CLD workshop participants we refrain from any adjustments to node positions.
The display method in this paper consolidates, or hides, nodes based on importance,
such that they can still be found by expanding nodes in the network to allow for an
exploration of the network. In addition, the display method only adds or removes nodes
and edges at the exact same positions the initial nodes and edges were located in the
network. The way the consolidation works and the benefits of this approach compared
to other technique for rearranging networks are explained in Chapter 3.
B. Problem Definition
As mentioned above, one part of the problem that we tackle in this paper is the time
required to read and understand a CLD in time-limited meetings with unspecified
providers and recipients of information. The increased time requirement when
presenting the output of CLD workshops arises from the multitude of nodes and
overlapping edges which impede the understanding of a large CLD and in addition also
decrease aesthetics of the network as well as the patience and interest from participants
in time-limited meetings. This hinders the effective usage of CLDs as decision making
support and the adoption of system dynamics as a valid tool in business. Usually
post-processing is necessary, and even then the result leaves a lot to be desired,
practically making the extraction of the main information and creation of separate
content necessary. However, at an early stage in a project the creation of separate
content might not be feasible since there were not enough discussions or available key
members. In addition, we want to utilize the CLD directly since the way of thought of
the CLD creators can be often retraced from the CLD.
The second part of the problem we tackle in this paper is related to the possibility to use
the CLD as a story building board. To this end, the possibility to expand consolidated
nodes is very important since it allows for an exploration of the network and retracing
of the mental models of the CLD creators.
Note that the creation of the overall method for simplification and visualization was
developed as a direct response to business needs that arose during the usage of the CLD
in business situations.
2. Node Importance
A. Preamble
As a preamble to the introduction of the calculation method for node importance in this
chapter, we describe the general setting where this tool is intended to be used. The
4
creation of a CLD in a typical workshop uses paper as the main medium. Workshop
participants use post-its to write down their ideas and arrange them on a large piece of
paper or a white board. There are various drawbacks to this way of conducting
workshops, such as interruptions of the train of thought, unwieldy workshop utensils or
illegible writing. Hitachi Ltd. developed a framework that supports this process through
computerized tools, the NEXPERIENCE framework [9]. Within this framework, CLDs
can be created digitally, alleviating many drawbacks of creating CLDs on paper.
Furthermore, sharing and presenting digital CLDs becomes easier, and an automatic
analysis becomes possible. In this paper we deal with CLDs that have been created
digitally.
The points that can be leveraged to improve an insufficient visualization are three-fold.
First, many nodes that are not relevant are displayed too, and while they are necessary
to draw the CLD they are not necessary to quickly explain the gist of the CLD.
Secondly, the loops might not be sufficiently clear, and especially in larger CLDs this is
a challenge. Thirdly, we use certain common patterns in CLDs that consist of particular
arrangements of nodes and edges. These pattems are industry- independent and indicate
certain problems or situations in a business structure [10,11]. There exist various
patterns which were defined beforehand and stored in some sort of database, such that
they can be accessed and used as a reference to identify instances of these patterns ina
given CLD. Anexample of a pattern is the “Limits to Success” patter in Fig. 1.
Main pattern
component
for this
pattern type
Figure 1: ‘Limits to Success’ Pattern Structure
In this pattem a ‘Result’ node is increased by a reinforced loop through an ‘Effort’ that
can be contributed to directly, whereas the ‘Result’ can usually not be directly
5
influenced from a business point of view. Opposed to the ‘Effort’ is an ‘Activity that
hinders success’ that decreases the ‘Result’ through a negative feedback loop. The
‘Activity that hinders success’ can usually be directly influenced or indirectly through
the ‘Constraint’. Note that each node, except the ‘Result’ that is the main node and
defined as tha main pattern component, can consist of multiple nodes that were
summarized. There is always just one ‘Result’ node.
A more complex pattern is the ‘Success to the Successful’ pattern in Fig. 2.
A's Success
A’s Resources
Main pattern
component for this
pattern type
Figure 2: ‘Success to the Successful’ Pattern Structure
In this pattern two entities, A and B, use the same resources which means that the
success of the first entity leads to a higher share of the resource for the first and a lower
share of the resources for the second entity. The challenge when using patterns is that
they can also be considerably complex, which makes them even more difficult to find
and understand.
Note that, just as loops, patterns are created, or not created, naturally in the CLD
creation process, without any particular attention from, for instance, the CLD workshop
facilitator.
B. System Dynamics Centrality
In the calculation for the node importance we take the information regarding loop
membership, pattern membership and pattern main component membership of a node
and the average importance of nodes in a loop into account.
We define a loop as a set of edges and nodes that connects an arbitrary node with itself
6
with at least one other node in between. Patterns are defined as particular arrangements
of edges and nodes, such as in Fig. 1 and Fig. 2, and are stored in a data file to be
compared with a given CLD. The algorithm for the identification of loops and patterns
reads in a new CLD and assigns IDs to each node in the CLD. With a depth-first search
the algorithm finds node-edge-node combinations, such as Effort-edge-Result in Fig. 1
when searching for ‘Limits to Success’ patterns, and sets this not yet completely
identified pattem before continuing to the next node-edge-node combination, in this
case Result-edge-A ctivity that hinders success, until the pattern has been completely
identified or until the search ends due to preset conditions. Note that the
Effort-edge-Result combination in Fig. 1, for instance, can consist of more than 2 nodes
due the summary of multiple nodes. A more thorough explanation of the algorithm is
given in reference [12], while references [9,13] contain information on how the
algorithm is intended to be used.
The outputs of this algorithm are arrays for each loop and each pattern that contain the
IDs of the included nodes, where each ID in a pattern array is given the suitable label,
such as ‘Result’ in Fig. 1, thus identifying the main pattern components. We convert this
information into a form where each loop, pattem and main pattern component is given a
vector that has a length equal to the overall number of nodes ina given CLD. We denote
these vectors
Leb,
pie P,
m, € M,
for loops, patterns and main pattern components respectively, where i is an index, L is
the set of loops, P is the set of patterns and M_ is the set of main pattern components
in the network. If a node is a member of a loop or pattem, the corresponding entry in the
vector for that loop or pattern is set to 1.
Note that patterns, such as in Fig.1 and Fig. 2, include loops as well. In this paper we
make the assumption that loops that are used in a pattern, are not again included in the
set of loops L. This is assured when converting the output of the algorithm to the
vectors above.
Based on the information from the three matrices, we can define the intermediate
importance IM as
IM=) hat) pb+ ) mee,
Tel jer ke
where the parameters a, b and c are weights that indicate the importance we assign
to loops, patterns and main pattern components. Generally main pattern components are
more important in the overall network structure since they are by experience centrally
located and comnected to various loops. Nodes that are not main pattern components but
still members in pattems have a relatively high importance since they represent
important feedback structures, whereas loops are slightly less important. If a node in the
network is neither a member of a loop nor a member of a pattern it can be ignored
unless it was selected as a K PI node or a controllable node during the CLD creation. We
define a KPI node as a node that was identified to have significant impact on the
customer’s business and a controllable node as a node that was identified to have
significant potential to change the current business structure due to the customer’s
ability to change that node. The non-membership of nodes does not occur very often
since CLDs are commonly created around K PI nodes and controllable nodes in order to
understand interdependencies and problems better.
After the calculation of the intermediate importance we calculate the system dynamics
centrality (SDC) with
. IM
spc = M+] —— ip
" sum (Ij)
ie€L
In this equation we calculate the average loop importance for each loop by summing up
the importance of each node in the loop and then dividing that sum by the number of
nodes in that specific loop. We add the resulting number to each node in that loop. After
conducting this operation for each loop in the CLD we receive the SDC.
The reason for this calculation is that we want to emphasize the few loops that have a
very big impact on the business. Nodes may not receive a high importance only based
on the IM, since they are not part of patterns. However, if other very high importance
nodes are contained in the same loop as the low importance nodes, the low importance
nodes have an impact on the high importance nodes, thus becoming more important
themselves. This relationship is reflected in the SDC and is related to the page rank
algorithm. The elements of the SDC vector are the values for each node’s importance.
The second type of input used to determine importance is user input. This user input
consists of KPI node designations and controllable node designations. KPI nodes and
controllable nodes are decided before or in a workshop for CLD creation. These
designations do not change the SDC but are considered during the drawing of the
consolidated CLD.
3. Node Consolidation
Taking the SDC vector as the input, the decision of whether a node should be visible or
not is made based on the average node importance, given by
SDC
Average Node Importance = =
N
i=1
where the total number of nodes in the CLD is denoted as N. Depending on the use case,
the average node importance is multiplied by a factor that increases or decreases the
threshold that determines if a node is displayed or not. If a node’s importance is below
that threshold it is not displayed. Instead, it is replaced by a symbol such as a dot at the
exact position in the diagram where the node was before, Fig. 3.
Before Consolidation After Consolidation
dati
Figure 3: C: by Repr ing Nodes with Low Im portance as a Dot
After conducting this check for all nodes, the actual consolidation of dots starts.
Starting at the dot with the lowest importance, all directly connected dots are
consolidated into one dot, pair by pair, Fig. 4.
1 2
Figure 4: Step-by-Step Consolidation of Nodes
The edges between dots are hidden as well, while the edges between dots and nodes
10
remain. In the end this creates several clusters that are each represented by one dot and
separated by nodes with above-average importance. The idea is then to expand dots that
are connected to nodes of interest pair by pair, where the expansion starts with the node
that has the highest importance, such that a meaningful exploration of clusters of
interest can take place. An illustration of this exploration is given in Appendix 1-3. The
important part is that nodes and dots are not moved from their position, only hidden,
such that the CLD creators’ train of thought can be better understood.
The user of this visualization simplification can, after the initial consolidation, expand
and contract dots at will, by using the appropriate symbols in the user interface.
4, Example Case
A. Network Simplification Process
As an illustrating example for the simplification technique proposed in this paper we
chose the example of visitor prediction for a department store. Assume the output of an
initial workshop is given in Fig. 5.
External Factors] [Financial Indices | |
| Sales }->{_ Profit, }——_
Customer
Internal Factors] “\
(Consecutive Holidays
KPI
Waiting Time
‘Season Specialty }—} i
*---{Out-of Stock Produets
} IN
ie Pye (Admission Regulation]
Traffic Congestion } (nie Ret
Controllab} fiotel {|
External Brand Events) ——
Product z
Advertisement t
et coven
Hours of Sunshine «~~
Figure 5: CLD for Understanding Department Store Visitor Prediction
The CLD in Fig. 5 is not very complex but sufficient to illustrate how the proposed
i
simplification method works. During the CLD workshop it was found that the client in
this specific case is interested in implementing measures that reduce the waiting time
for various shop related activities, such that the overall satisfaction of customers who
come to the department store is increased. Hence, the waiting time and the satisfaction
are set as KPIs. As a controllable node external brand events were identified, thus
marking the corresponding node as controllable. In this example we can discover two
system patterns. One of them is ‘Limit to Success’ as given in Fig. 6.
Constraint
Activity that
/ hinders success node
Result node
Frequent Visitor}
Figure 6: ‘Limit to Success’ Pattern in the Example CLD
Note that the ‘Effort’ can take other forms as well in this CLD, thus forming multiple
occurrences of the ‘Limit to Success’ pattern. Also note that the satisfaction node is the
main pattern component in each of these occurrences.
The second pattern we can find is the ‘Success to the Successful’ pattern, given in Fig.
7.
12
B’ s Resources
A's Resources A’ s Success
Allocate to A
instead of B
Figure 7: ‘Success to the Successful’ Pattern in the Example CLD
This pattem also occurs multiple times, increasing the importance of the satisfaction
node even more. An example of a loop that is not used ina pattern, but includes very
important nodes, is given in Fig. 8.
Frequent Visitors
Figure 8: Increased Node Importance of Nodes outside Patterns through the
Assessment of the Average Loop Importance
Since satisfaction and visitors are both very important nodes, which can be seen in the
previously displayed patterns, noise receives a higher importance, increasing the
possibility of being displayed and not hidden.
To calculate the importance for each node we set the parameters a, b and c to 1,2
and 3 respectively. The importance numbers are given in Fig. 9.
13
External F actors]
[Financial Indices |
Customer
&
Figure 9: SDC Display and Representation of Unimportant Nodes as Dots
After consolidating all nodes the final CLD is given as displayed in Fig. 10.
External Factors]
[Financial Indices]
|
Customer
Internal Factors
KPI
{Waiting Time }e,
Frequent Visitors
**-+-{Qut-of-Stock Products}
Figure 10: Final Output of the Simplification Method
14
In this specific case the average node importance is multiplied by 1.2, setting the
threshold that determines if nodes are displayed or not to 27.1.
B. Evaluation
With regards to the reduction of time that is necessary to understand the CLD, persons
who view this CLD for the first time can quickly indentify KPI and controllable nodes,
and the nodes that influence them. From this basic understanding that acts as a platform,
other pathways can be easily explored, for instance, by management level staff who
want to get a more detailed picture of financial indices or department store layout
planners who are able to add important factors that could reduce waiting time. Since the
viewer of the network is confronted with less nodes and edges, compared to the original
view of the CLD, the positions in the network where the financial indices and waiting
time-related indices can be found, are easy to determine as well.
The majority of nodes that were consolidated are in the ‘External Factors’ category,
which mainly contains nodes that cannot be controlled or influenced such that the
satisfaction or waiting time would improve. This circumstance is represented by the fact
that these nodes are not part of any pattern or loop, which therefore results in a low
importance and the associated consolidation of these nodes, thus reducing
view-cluttering nodes and edges. ‘External brand events’ are an exception since they
were specifically identified as a controllable node because, even though external brand
events have little influence in the dynamics of the CLD, they are important to the
customer. It is easily imaginable that a subsequent meeting could update the CLD by
connecting the ‘Profit’ to ‘External brand events’, which would result in a different
view.
With regards to the usage of the simplified CLD as a story building board, related
persons can be easily led along story paths in the CLD after those persons gained a
basic understanding of KPI, controllable nodes and their interdependencies. As an
example, the path from ‘External brand events’ to ‘Visitors’ and ‘Satisfaction’ could be
explored by branching out the dot connected to ‘External brand events’. Expanding this
path would make it easier to understand the mental model of the CLD creators, and if
the mental model was understood, meaningful additions and changes could be made
such as the connection between ‘External brand events’ and ‘Profit’ mentioned above.
In the end, the time needed to understand the CLD and find nodes of interest,
consolidated or not, was reduced in the case of this explanatory CLD. CLDs that are
usually created in business situations contain significantly more nodes, increasing the
number of expandable clusters and their content to a great extent, thus making the
proposed method even more effective.
5. Conclusion
In this paper we proposed a method for simplifying the visualization of networks from a
system dynamics viewpoint. In Chapter 1 we gave the motivation for this research,
surveyed related techniques, and explained our contribution. We continued to give
details regarding the importance calculation in Chapter 2 and the network display in
Chapter 3. Chapter 4 contained an example case that was used to illustrate the usage of
the proposed method.
The main purpose of the proposed method is to simplify cluttered networks such that
less time needs to be spent to understand the network in a system dynamics sense, for
operators that may contribute to the network through their knowledge of low level
processes as well as for management staff that wants to receive a quick assessment of
the business situation. As the example case indicates, the gist of the customer’s business
structure can be assessed and discussed quicker with the simplified CLD, compared to
the CLD before the simplification. This can potentially lead to faster understanding of
the business structure, goals and problems by various parties, and an accelerated
consensus building, two important elements for achieving an effective customer
co-creation.
Another advantage the proposed method has is the ability to explore a network, an
ability that supports the story telling in a proposal process. This is best combined with
an appealing user interface that might add additional information to the view of the
network. From a business standpoint, further developments involve a more appealing
presentation with more information, and dynamic real time network changes that allow
for a better interaction with the customer and related persons.
16
6. References
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Business Review, 2000
[2] Sterman, J.D., Business Dynamics: Systems Thinking and Modeling for a Complex
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[4] Page, L., Brin, S., Motwani, R. and Winograd, T., “The PageRank citation ranking:
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[8] Misue, K. et al., “Layout Adjustment and the Mental Map”, J. Visual Languages and
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for visualizing customer value in terms of people and management”, Hitachi Review,
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[10] Wolstenholme, E., “Using generic system archetypes to support thinking and
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[12] Aoshima. Y., Nagaoka, H., Nakagawa, T., Tanaka, E., PREIS LO
FEU HEH HH 72 [Problem structure extraction apparatus and problem structure
extraction method], Japan patent application number 2014- 204903, October 2014
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Appendix
[foe
Appendix 1: Illustration of Node Expansion 1
Appendix 2: Illustration of Node Expansion 2
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Appendix 3: Illustration of Node Expansion 3
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Appendix : System Dynamics Modeling Overview
System dynamics helps analysts model and analyze critical behavior as it evolves over time within
complex socio-technical domains. It is one of several
ing methods applicable to insider threat
modeling
and has been used extensively in that domain [Moore 2016b, Cappelli 2012]. Figure 13 summarizes
the notation used in our system dynamics model.
Var1 Variable - anything of interest in the problem being
modeled
<WVarl> Ghost Variable - variable acting as a placeholder
for a variable occurring somewhere else
Positive Influence - values of variables move in the
Var1 —_* 4 Var2 same direction (e.g., source increases, target
increases)
. Negative Influence - values of variables move in
Varl —————-> Var2 the opposite direction (e.g., source increases, the
target decreases)
Stock1 Stock - special variable representing a pool of
materials, money, people, or other resources
YZ Flow - special variable representing a
Stock1 7. Stock2 process that directly adds to or subtracts from
Flow1 a stock
Oo Cloud - source or sink (represents a stock
outside the model boundary)
Figure 13: System Dynamics Notation
The primary elements are variables of interest, stocks (which represent collections of resources, such.
as dissatisfied employees), and flows (which represent the transition of resources between stocks, such
as satisfied employees becoming dissatisfied). Signed arrows represent causal relationships, where the
sign indicates how the variable at the arrow’s source influences the variable at the arrow’s target. A
positive (+) influence indicates that the values of the variables move in the same direction, and a
negative (—) influence indicates that they move in opposite directions.
A comnected group of variables, stocks, and flows can create a path that is referred to as a feedback
loop. At this stage in our modeling effort, we have not identified any significant feedback loops.
As a convention in our model, we format model input variables with italics, bold, and underline since
these variables can be dynamically manipulated during model execution.
21
