=Paper=
{{Paper
|id=Vol-2845/Paper_26.pdf
|storemode=property
|title=The use of Graph Theory in the Implementation of Psychodiagnostic Projects on the Example of Researching the Leadership Qualities of Participants in Software Development Teams
|pdfUrl=https://ceur-ws.org/Vol-2845/Paper_26.pdf
|volume=Vol-2845
|authors=Dmytro Lukianov,Oleg Radyuk,Hanna Charniauskaya,Irina Basinskaya
|dblpUrl=https://dblp.org/rec/conf/iti2/LukianovRCB20
}}
==The use of Graph Theory in the Implementation of Psychodiagnostic Projects on the Example of Researching the Leadership Qualities of Participants in Software Development Teams==
https://ceur-ws.org/Vol-2845/Paper_26.pdf
The Use of Graph Theory in the Implementation of
Psychodiagnostic Projects on the Example of Researching the
Leadership Qualities of Participants in Software Development
Teams
Dmytro Lukianova, Oleg Radyukb , Hanna Charniauskayac and Irina Basinskayad
a.
Interdisciplinary Institute for Advanced Studies and Retraining, Belarusian National Technical University, 77,
Partyzansky ave., Minsk, 220107, Belarus
b.
Individual Entrepreneur, Post office box 67, Minsk-134, 220134, Belarus
c.
Independent Researcher, HR in IT, Rogachyovskaya str. 7-36, 220056, Minsk, Belarus
d.
Belarusian State University, 4, Nezavisimosti Avenue, Minsk 220030, Belarus
Abstract
The article proposes consider the application of visual analysis of psychological testing
results through the use of directed graph representations. It is proposed to consider the
method of visual analysis by means of various representations based on the analysis of the
number of connections between the elements of the system, considered as the basis for the
formation of a directed graph. In the example considered in the article, it is proposed to
consider the scales of the integrated test technique used as the vertices of the graph. As the
main views, the application of calculating centrality properties based on the number of links,
the topological structure of links, and the Page Rank parameter is demonstrated. It is
proposed to use the method of visual analysis of the graph as an additional to the classical
method of correlation analysis used in processing the results of the application of
psychodiagnostic methods. The possibility of using visual analysis to form hypotheses about
the possible optimization of the structure of the scales used in the design of psychodiagnostic
techniques (test batteries) is shown. In parallel, the results of the analysis of the leadership
qualities of such a category of specialists as software developers (members of development
teams) are presented.
Keywords 1
leadership, psychodiagnostics, test methods design, correlation matrix, adjacency matrix,
directed graph, graph theory, centrality, visual analyzes
1. Introduction
Over the past few years, there has been a growing interest in developing professional leadership
skills. This is due to many reasons, however, one of the main ones is that business, technology,
communications, human values today function in an era of continuous change. The sphere of
professional project management is no exception. Organizations such as the International Project
Management Association (IPMA) [1], and the American Institute for Project Management (PMI) [2]
have incorporated "leadership" into their competency models. Many researchers have long been
talking about the importance of the role of leadership in the management system, confirming this both
by psychological research [3, 4] and by analyzing the structures of modern models of competencies
Information technology and interactions, December 02–04, 2020, Kyiv, Ukraine
EMAIL: dlukiano@gmail.com (D.Lukianov); 6311141@mail.ru (O.Radyuk); cbt1coach@gmail.com (H.Charniauskaya);
3075007@mail.ru (I.Basinskaya)
ORCID: 0000-0001-8305-2217 (D.Lukianov); 0000-0003-2888-9238 (O.Radyuk); 0000-0001-8778-5928 (H.Charniauskaya);
0000-0001-9640-2933 (I.Basinskaya)
© 2020 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
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[5, 6]. In modern practice of psychodiagnostics, various methods of assessing leadership qualities are
widely used, including such methods as the "Five-factor personality questionnaire NEO-PI-R" [7],
"Eight-factor personal leadership questionnaire 8FLQ" [8] and "Multifactorial leadership
questionnaire (form 5X) ”[9], which allow assessing personal qualities on a much larger number of
scales than the widely used“ role ”techniques, such as the famous tests by R. Belbin [10] and I.
Adizes [11]. Authors have more than ten years of experience in using such techniques in their work
and propose to consider their approach to the visual presentation of the results of such studies.
2. Problem
Today, a wide range of approaches to the development of professional leadership qualities are
being formed. Each organization, human resources specialists, consultants have their own preferred
approach to leadership. But, unfortunately, there are not enough studies, the results of which could
demonstrate which of the approaches is the most effective [12]. Understanding personality traits,
which, for example, may be associated with transformational and charismatic leadership, can provide
significant support in the selection of personnel for leadership positions. Accordingly, understanding
the importance of certain properties (in the terminology of competency models of professional project
managers - elements of competencies) can seriously help in choosing an approach to developing the
necessary qualities. For example, if transformational leadership or charisma are associated with
certain personality traits, then the organization can make a choice in the process of finding and hiring
personnel in favor of an individual with these traits [13], or initiate an appropriate program to develop
such abilities in the team.
A serious problem in solving such a problem is the professional choice of the concept of
"leadership" among many modern approaches - in modern psychology there are at least several dozen
such approaches. The presence of such a large number of theories hinders progress in practice and
research, in which case it becomes necessary to consolidate leadership theories. Emmanuel Mango,
author of the article "Rethinking Leadership Theories" [14] carried out a revision of 66 theories of
leadership, the result of which is 22 theories, according to the author, well representing this
phenomenon.
The existing methods of assessing and profiling personality traits are based both on standard tests
and on the creation of our own "test batteries", collection of primary data, their processing (including
using statistical methods) and interpretation of the results. This is not to say that the current state of
affairs is at the "initial" stage - rather, we can talk about many years of established practice.
Nevertheless, today more and more attention in the field of direct data analysis is paid to
visualization. There was even such a thing as "visual data analysis". One of the most effective ways to
represent data in complex integrated systems is to represent it in the form of graphs, which is
extremely rare in the field of data analysis in the field of engineering psychology.
An important problem, according to the authors, is that it is extremely rare to find in practice
attempts to create programs for the development of professional competencies based on the
relationship between the leader's character and personal characteristics, making it as individual as
possible, thereby increasing the rather low efficiency of personnel development programs, often based
on the idea of "development of all" in "all directions", regardless of the account of personal
characteristics.
3. Methods
As a possible approach to the construction of models of complex organizational, technical, socio-
economic and other systems, it is proposed to use the graph theory toolkit, which is a constituent
element of the general theory of systems in the representation of L. Bertalanffy [15]. Bertalanffy
includes engineering psychology in the “applied components” block of his presentation of general
systems theory, along with operations research and systems engineering.
This article proposes to consider the use of tools from another, theoretical block of the Bertalanffy
structure - the toolkit of graph theory in relation to classical methods of data processing of research
carried out in the field of practical psychology.
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The transformation of the classical correlation matrix into an adjacency matrix is proposed for the
analysis of the structure of the factors underlying some test methods, using the example of the
analysis of some results that were obtained in a real study.
The main methods used were the following:
1. Analysis of leadership theories and construction of a system of "scales" for the development
of test methods
2. Psychological testing
3. Methods of statistical data processing in the program IBM SPSS 23.0 [16]
4. Conversion of data to statistical processing into an adjacency matrix using the logic of
Markov models in MS Excel [17]
5. Visualization of the obtained adjacency matrix in the form of a directed graph in the yEd
environment [18]
The review and analysis of leadership theories in the work of E. Mango, as well as a broad
analysis of scientific literature on leadership, was carried out in terms of the presence of six
fundamental areas of leadership: the character of a leader as a whole (based on morality and ethics),
special individual characteristics (mental abilities , level of extraversion, emotional intelligence,
perseverance, courage, striving to achieve success) [19], leadership behavioral practices (exactly how
leaders build communication with followers to achieve organizational goals) [20], institutional
practices (consist in the activities of a leader to clarify goals organization or team, ways and directions
of organizational development) [21], the purposefulness of the leader's activities (what is expected
from leadership, and what the leader strives for) [22].
In the modern "managerial" approach (in particular, in the competency models of project
managers), "skill theory" and "behavioral theory" are very common. Behavioral theory is based on a
leader demonstrating certain behaviors to achieve desired goals. In behavioral practice, leaders are
people-oriented in the first place, create and maintain optimal conditions for the activities and
development of followers. In an organizational context, the behavior of a leader is aimed at tasks, the
effectiveness of processes in the organization, in this case, leaders rely on current research and
innovation [23]. Skills theory, which implies that a leader has specific skills for effective work. In the
field of behavioral practices, this theory is realized in the fact that a leader must have communication
skills with people. In the field of institutional practices - in the availability of technical and conceptual
skills [22]. This is a fairly effective approach, which, in our opinion, first of all prepares a potential
leader for “meaningful” situational leadership, which means that the leader's behavior style is
determined by the current situation. A person, in the position of a leader, sets the levels of
responsibilities and tasks of the followers, along with this, the development needs for the fulfillment
of tasks by the followers are established. In the future, the leader chooses the leadership style that will
contribute to the development of followers (coaching, support, delegation). Organizationally, leaders
must clearly understand what organizational means and tools can be used to achieve the goal of
developing followers [24].
In our opinion, the most effective approaches to the study of leadership are still transactional and
transformational theory. These theories are well developed and relevant today. In addition, there are
techniques for diagnosing the character of a leader in terms of transactional and transformational
leadership, the use of which is the standard for leadership research.
Transactional leadership involves the use of transactions, rewards, and punishment to motivate
followers to achieve organizational goals. In this approach, there are several ways: accompanying
reward, deviation management (search for violations of agreements and contracts, the leader suggests
punishment or fines), passive deviation management (the leader only takes steps to punish followers
in case of failure to achieve goals) [25].
Transformational leadership refers to situations in which followers are producing more results than
expected. A leader motivates followers beyond expectations. Within this theory, both the leader and
the followers work together to increase the level of productivity. The behavior of leaders is
characterized by ideological influence, inspiring motivation, intellectual stimulation, and an
individual approach to their followers [26].
This opinion is caused, in a practical sense, by the study by the authors of the combination of such
qualities as "controlling" and "leadership". The behavior of individuals with a high level of control is
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characterized by a high level of organization, persistence, purposefulness, and a low level of
impulsivity [27].
The "controlling" (synonym: “conscientiousness”) component includes a high level of self-
discipline, productivity, ethical behavior, and striving for achievements [28]. Controlling is also
positively associated with transformational leadership, although this contradicts findings from 2004
by Lim and Ployhart [29] and is supported by studies by Bono and Judge in the same year [30]. In
2014, a positive link was found between charisma (a combination of ideological influence and
inspiring motivation) and controlling. Within the framework of the same study, no connection was
found between controlling and individual approach (contrary to the study by Bono and Judge in
2004), this may be due to the fact that individuals with high control scores can adhere to a rational
approach in communication, be extremely honest with followers and being somewhat closed off to
emotional communication, which suggests that such leaders will not seek to care for their followers.
In addition, in the same study, negative associations were found between controlling and inspirational
motivation, as well as intellectual stimulation, that is, a controlling leader will tend to negatively
represent the future and its presentation, which will also reduce the leader's ability to stimulate
positive thinking about the future. from their followers [31].
Accordingly, despite the use of a number of techniques by the authors in their psychodiagnostic
projects, it is proposed to consider in this article the results of using the Eight-Factor Leadership
Questionnaire, which includes both the scale for assessing the factors of the "Big Five" and the scale
for assessing leadership qualities, including limited, transactional and transformational leadership
styles.
4. Results
As already mentioned in the Methods section, of particular interest is the analysis of the results
obtained in a sample of 58 specialists of an IT companies using the Eight-Factor Leadership
Questionnaire, which includes scales for assessing the Big Five factors and for assessing the limited ,
transactional and transformational leadership.
Table 1 shows the mean values on the Big Five scales of the eight-factor leadership questionnaire.
Based on the data obtained on the main scales of the "Big Five" of the eight-factor leadership
questionnaire, described in Table 2.4, it should be noted that the lowest level on the Emotionality (N)
scale was 3.96. The highest score belongs to the scale of Originality (O), 5.32.
Indicators on the scales of Emotionality (3.96), Energy (E) (4.74), Cooperation (A) (4.68),
Controlling (C) (4.87) are in the range of average values. It can be concluded that study participants
are able to control their impulses, cope with stress and negative emotions. In addition, the research
participants have the characteristic that they do not strive to constantly be in a team, they are not very
sociable individuals, however, being in a group of people, they do not experience much discomfort. If
it is possible to avoid making unpopular decisions in the group, research participants tend to act in this
way. In their work, research participants strive to follow the rules and requirements, but do not attach
much importance to them. They tend to feel uncomfortable in an environment where there are strict
rules and at the same time in an environment where there are no rules. The results of the study on the
Originality scale (5.32) are in the high range. This means that the subjects practice new methods and
approaches in their work, even when there are established standards, they feel comfortable in a
creative environment where there is freedom of decision-making.
It should be noted that the results of the study on the eight-factor leadership questionnaire coincide
with the results of the study on the NEO-PI-R questionnaire.
Table 2 presents the mean values for the leadership style scales of the eight-factor leadership
questionnaire.
Based on the data obtained on the scales of styles and consequences of leadership of the eight-
factor leadership questionnaire, described in Table 2.5, it should be noted that the lowest level on the
Laissez-Faire scale was 2.90. The highest score belongs to the Idealized Influence (behavior)
scale, 5.54.
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Table 1
Average values of the data obtained on the Big Five scales of the eight-factor leadership
questionnaire
Standard error Average deviation Factors for visual
Scale ID Average (M)
(m) (ϭ) analysis
O_8FLQ 5,32 0,07 0,50 F01
C_8FLQ 4,87 0,10 0,73 F02
E_8FLQ 4,74 0,11 0,79 F03
A_8FLQ 4,68 0,10 0,68 F04
N_8FLQ 3,96 0,14 0,97 F05
O1_8FLQ 5,44 0,15 1,10 -
O2_8FLQ 5,70 0,13 0,95 -
O3_8FLQ 5,46 0,13 0,91 -
O4_8FLQ 4,75 0,12 0,82 -
O5_8FLQ 5,10 0,14 1,00 -
O6_8FLQ 5,66 0,08 0,59 -
C1_8FLQ 5,21 0,12 0,85 -
C2_8FLQ 4,66 0,16 1,15 -
C3_8FLQ 5,49 0,11 0,81 -
C4_8FLQ 5,01 0,14 0,99 -
C5_8FLQ 4,37 0,17 1,22 -
C6_8FLQ 4,55 0,17 1,18 -
E1_8FLQ 5,14 0,15 1,05 -
E2_8FLQ 4,06 0,19 1,34 -
E3_8FLQ 4,70 0,15 1,09 -
E4_8FLQ 4,51 0,16 1,16 -
E5_8FLQ 4,95 0,15 1,04 -
E6_8FLQ 5,16 0,16 1,14 -
A1_8FLQ 4,34 0,15 1,06 -
A2_8FLQ 4,94 0,20 1,41 -
A3_8FLQ 5,00 0,10 0,71 -
A4_8FLQ 4,36 0,16 1,16 -
A5_8FLQ 4,80 0,17 1,24 -
A6_8FLQ 4,53 0,13 0,93 -
N1_8FLQ 4,63 0,17 1,21 -
N2_8FLQ 4,18 0,16 1,18 -
N3_8FLQ 3,81 0,19 1,38 -
N4_8FLQ 4,23 0,17 1,23 -
N5_8FLQ 3,61 0,21 1,49 -
N6_8FLQ 3,22 0,16 1,11 -
MO_8FLQ 3,75 0,08 0,57 F06
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Table 2
The average values of these leadership styles
Standard error Average deviation Factors for visual
Scale ID Average (M)
(m) (ϭ) analysis
LL_8FLQ 3,09 0,12 0,87 F07
TA_8FLQ 4,95 0,12 0,83 F08
TF_8FLQ 5,13 0,09 0,67 F09
LL_NE_8FLQ 2,90 0,13 0,93 F10
LL_RU_8FLQ 3,35 0,17 1,18 F11
TA_PU_8FLQ 4,67 0,16 1,13 F12
TA_SV_8FLQ 5,23 0,11 0,82 F13
TF_VM_8FLQ 4,98 0,15 1,06 F14
TF_IP_8FLQ 5,50 0,10 0,69 F15
TF_IS_8FLQ 4,97 0,14 0,96 F16
TF_IV_8FLQ 5,10 0,11 0,78 F17
TF_LV_8FLQ 4,67 0,15 1,08 F18
TF_PV_8FLQ 5,54 0,11 0,76 F19
Indicators on the Limited Leadership (3.09), Passive Management-by-Exception (3.35) and
Laissez-Faire (2.90) scales fall within the range of medium and low values. This means that subjects
are less likely to resort to these leadership styles than to transactional and transformational ones.
Rarely does their behavior show aloofness from communication with followers, unwillingness and
lack of desire to understand the needs of followers, as well as a lack of assistance to satisfy them. The
subjects are not inclined to use a system of penalties and sanctions against followers. Indicators on the
scales Transactional Leadership (4.95), Proactive Management-by-Exception (4.67) are in the range
of average values, it can be concluded that the subjects tend to control the performance of tasks by
their followers, as well as take proactive actions when problems arise, another indicator of
transactional Leadership, Contingent Reward (5.23), Scale scores are in the high range, which means
that subjects tend to reward followers for successful tasks and other expected results. Most often,
subjects use styles related to Transformational Leadership (5,13), among them, an Individualized
Consideration (5.50), Idealized Influence (5.10) and in particular Behavioral Influence (5.54), this
means that the behavior of the subjects, characterized by a trusting attitude towards followers,
understanding of their intellectual needs and the ability to satisfy them, purposefulness, perseverance,
is a reference and arouses respect from followers. Inspirational Motivation (4.98), Intellectual
Stimulation (4.97), and Idealized Influence (attributed) (4.67) are somewhat less common, however,
the indicators of these factors border on high. This means that the subjects are able to predict the
future of joint activities with followers from a positive side, as well as effectively broadcast this point
of view. It should be noted that the results of the 8FLQ Eight-Factor Leadership Questionnaire are
similar to the results on the Multifactor Leadership Questionnaire in that subjects rarely resort to
hands-off and tend to resort to transactional leadership styles more often when communicating with
followers. As a result of the correlation analysis of the data, relationships were found between the
personality traits of the Big Five NEO-PI-R and the leadership qualities of the eight-factor leadership
questionnaire, the personality characteristics of the Big Five and the leadership styles of the eight-
276
factor leadership questionnaire. The variables were tested for normal distribution, since a number of
variables had a distribution that differed from the normal one; later, a nonparametric method of
statistical analysis, the Spearman method, was chosen. So, Figure 1 shows a table with the results of
the correlation analysis of the Big Five data of the NEO-PI-R questionnaire and the leadership
qualities of the eight-factor leadership questionnaire. Negative correlations are indicated in red,
positive correlations are in green. The cells contain Spearman's correlation coefficient and the
significance level below the coefficient. The sign * marks the presence of the significance of
correlation (bilateral) at the level of 0.05, and ** - at the level of 0.01.
Figure 1: Correlations between the Big Five NEO-PI-R and the leadership qualities of the eight-factor
leadership questionnaire
The complete correlation matrix in this study is a 198x198 array, a fragment of which is shown in
Figure 2. It is clear that in such a presentation, it is poorly suitable for visualization or presentation by
any other alternative means. On the other hand, it seems possible to transform it into an adjacency
matrix by transforming it according to a simple rule - if there is a significant relationship between
elements in the direction from “row” to “column”, the presence of such a relationship can be
displayed as “1”, and the absence - as “0".
An adjacency matrix can serve as a basis for constructing a directed graph for subsequent analysis.
As known, a system that combines sets of some entities, for example
S{s1, s2, …, sm}, (1)
which are vertices of an oriented graph connected by oriented arcs
G{g1, g2, …, gr}, (2)
can be displayed using the adjacency matrix
[сij]S = [i, j], (3)
each line of which shows the connections of one vertex with other vertices of the graph [32]. The
element сij = 1, then it reflects the arc between the vertices Si and Sj. If сij = 0, then the arc directly
between the vertices of the graph i and j is absent.
For the analysis of such structures use the adjacency matrix, which has specific properties [32]. In
the case of successive reduction of the adjacency matrix in the degree n = 2, 3 ... the elements of the
n-th degree (сij)n show the path containing n arcs between the i-th and j-th vertices of the graph.
To formalize the adjacency matrix obtained by the method described above, it is proposed to use
the Microsoft Excel [17] software, in particular, so that other actions can be performed in the same
277
computing environment to simulate the behavior of the system under study. In particular, due to the
fact that this software in its basic functionality supports the necessary set of operations with matrices.
For further visualization and presentation in the form of a graph, it is proposed to use the yEd [18]
software.
Figure 2: Complete correlation matrix for the data of the conducted study on all scales (fragment)
Correlations between the selected factors F01-F19, noted in Tables 1 and 2, based on a sample of
the relevant data from the full correlation matrix (Figure 2), using the above rules, can be represented
as the following adjacency matrix (Figure 3).
An adjacency matrix can serve as the basis for constructing a directed graph for subsequent
analysis. For further visual analysis of the resulting graph, it is proposed to use such well-known and
open-source software as yEd, which allows modeling various kinds of complex structures, in
particular, using a wide range of different graph representations. Figure 4 shows the structure of a
graph created in the yEd environment using the standard Shape Nodes template of structural
Figure 3: Formation of a first-order adjacency matrix for F01-F19 elements (screenshot fragment)
278
e
Figure 4: Directed graph for FL01-FL19 subsystem model implemented in yEd (screenshot fragment)
As you can see from the presented figure 4, yEd allows you to visualize the links (edges) between
the elements of the model (the vertices of the graph), including the direction of these links. Nodes FL
in this graph correspond to the elements F from adjacency matrix for F01-F19 elements
Unfortunately, such a basic view does not allow making any analytical conclusions. It is worth
using other representations to analyze the graph. In particular, the simplest next step can also be a
"circular representation", but with the visualization of the weights of the vertices based on the number
of their connections with other vertices of the graph, as shown in Figure 5 (normalized with respect to
the element FL02 with the maximum number of connections).
As can be seen in the presented figure 5, yEd allows visualizing the weights of vertices (model
elements) based on information about the number of edges (links), which makes such a representation
much more information-rich than the primary representation of the model in the form of a graph
presented in Figure 4. Nevertheless, such a representation, although it already allows you to form
some hypothesis based on the visualization of the parameters of the system of links, in particular, to
allow ranking the vertices by the number of links, but any spreadsheet editor in which you can sum up
values in rows and columns of the original adjacency matrix (Figure 3) or primary corellation matrix
(Figure 2). In graph analysis, one of the key concepts is centrality. Accordingly, visualization of
representations of such a parameter as "centrality" will be of undoubted interest. At the same time,
"centrality" can be considered both "structural" and "weighted". In particular, thanks to such a
representation as "Weighted Centrality" (Figure 6), it is possible to assess the importance for the
entire structure as a whole, for FL02 element. This representation allows one to form a number of
hypotheses regarding the role of elements FL01 and F04 presented in the "far orbit" in the system
under consideration, in addition to other assumptions that can be formed on the basis of the
visualization presented in Figure 5. In any case , it is obvious that the information content of such a
representation is much higher than that of Figure 4 or Figure 5. The visualization capabilities allow
you to assess "centrality" directly from a structural point of view as shown in Figure 7. In particular,
such a representation allows us to develop the previous hypothesis - the absence of significant
relationships of the FL01 element in the structure of the fragment under consideration is visible,
which suggests the possibility of excluding this element from consideration (accordingly, to further
optimize the set of scales for further use of the already initially optimized method). Moreover, judging
by the visual representation of the links of the FL04 element, such an exception for this element may
not be worth making.
279
Figure 5: Directed graph for FL01-FL19 subsystem model, implemented in yEd (Circular Layout -
Single Cycle representation)
Figure 6: Visualization of some structural indicators (fragment) for a directed graph for FL01-FL19
subsystem model in the yEd environment in the Radial Layout view for Weighted Centrality
(Distance From Center)
5. Discussion
The approach proposed in the article significantly expands the previously described [33] approach
to the analysis of the properties of structural models. Nevertheless, the visual representation of the
280
"centrality" properties, from our point of view, significantly expands the possibilities of understanding
the features of the systems under study. As can be seen from the views in Figures 6 and 7, they are
fundamentally different from the “descriptive” view in Fig. 4. Although they are still representations
of the same system.
Figure 7: Visualization of some structural indicators (fragment) for a directed graph for FL01-FL19
subsystem model in the yEd environment in the Radial Layout view for Centrality (Distance From
Center)
In our opinion, the use of such powerful tools for versatile visualization of the graphs of the
studied models allows us to look somewhat differently at the systems under study than only through
the prism of analytical indicators presented in a matrix (tabular) form. Based on the information
presented graphically, it becomes possible not only to propose new hypotheses regarding the
structural relationships of the systems under study, but also to “quickly test” them by visual means.
The presented visualizations certainly provide a lot of information, at least for the formation of
hypotheses. it is obvious that some of these hypotheses, in principle, could not have appeared without
visualization, similar to the one shown in the screenshots of the model views made in the yEd
environment. It is of interest to consider other possible representations that are possible for
visualization in the yEd environment. In particular, when calculating the weight characteristics, taking
into account not only the presence of the number of links, but also their structure, as suggested by the
Page Rank method [34], we can conclude about another element that is very significant for the system
as a whole - FL03 (Figure 8).
6. Conclusion
The presented approach to the use of graphical representations, according to the authors, can be
used in the analysis of any other complex systems, where a sufficiently large number of mutually
influencing elements can be identified. In order for the analysis of such systems to be as effective as
possible, it is necessary to use the appropriate systems that automate the work on the primary
processing and visual presentation of information. Such an effective tool for an analyst's work can be
software with functionality similar to the example of using the yEd product presented in the article.
Perhaps this approach will allow a more “instrumental” approach to assessing the importance of
individual elements, incl. by modeling situations such as “excluding” a number of nodes or edges
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(elements of the studied systems or connections between them), and “adding” (predicting the need for
a real but previously unidentified element or a connection between identified elements), which will
allow a more professional and objectively approach the assessment of complex systems.
Figure 8: Visualization of some structural indicators (fragment) for a directed graph for FL01-FL19
subsystem model in the yEd environment in the Radial Layout view for Centrality (Page Rank)
7. Acknowledgment
I would like to express my gratitude to the developers of the yEd software, thanks to which today
any computer user has the opportunity to perform a visual analysis of complex systems, which can be
converted into a graph form. I would also like to express my gratitude to prof. V.D. Gogunsky
(ONPU), thanks to whom the topic of using methods of graph theory appeared in the works of the
authors.
8. References
[1]. IPMA, 2019 URL: https://www.ipma.world/
[2]. PMI, 2020 URL: https://www.pmi.org/
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