Static and Dynamic Models of Network Interaction
in Secondary Education
M. I. Razumovskaya
1a
and O. L. Kondratyeva
2
1
Department of Economics and Commerce, Far Eastern State Transport University, Serysheva str, 47,
Khabarovsk, Russia
2
School administration, Secondary school № 44, Trekhgornaya str, 80A, Khabarovsk, Russia
Keywords: Services of Secondary Education, Network Integration, Provision of Service, Network’s Member, Models of
Economic Relations.
Abstract: This article shows the outcomes of modelling of areas of network integration regarding the provision of
services of secondary education. We have developed static and dynamic models focused on the conditions of
network’s functioning on the base of a regional experimental area of the Municipal Budget Educational
Institution “Secondary school № 44” (in the city of Khabarovsk). Both models belong to the category of the
system’s structure. Their characteristics reflect the content of the following processes within the network’s
members’ interaction: production, organization, and regulation. The results of this modelling let us to make
an assessment of the recourses essential for network’s members for the implementation of an educational
trajectory as a student’s personal choice, on the one hand; and an educational program as a public choice, on
the another. In this research we have used universal scientific methods, statistical analysis’ techniques,
economically social research, and vector-network assessment.
1 INTRODUCTION
In Russia, unification of funding of secondary
education costs with regional and municipal budgets
contributes to the following principal contradiction of
secondary education: to provide the implementation
of educational trajectory from the point of individual
choice, on the one hand; and fulfilment of educational
program as a public choice - on the other. The
integration lets us to alleviate this contradiction. At
market, sector, and sequenced value creation level, in
J. Kommons’ opinion (Uni, 2017), it should set the
procedure of economic interaction of its initiator and
his partners, facilitating mitigation of the conflict, and
realizing mutual benefits. We shall agree with it, as
well as with the following point: regarding the
integration, J. Kommons emphasizes the importance
of private nature of the interaction’s settlement, based
on a mutual agreement up-on personal opportunities
and interests (Uni, 2017). Several analysts point to the
fact that we can observe a decreasing tendency to the
depth of integration, that is a concentration level of
decision making at a unified company, joint
a
https://orcid.org/ 0000-0003-3269-0264
administrative body of integrated organizations.
Which means the future increasing popularity of
network structures in organizations and open markets.
(Mintzberg et all., 2000).
2 METHODOLOGY OF
RESEARCH
Initiators of a network can become the schools
implementing two following models of economic
relations: “market model of education aimed at free
market” (paid educational services), “market model
of education aimed at public market” (budget funding
upon the number of students). Apart from the above,
among the participants of network interaction, we can
also find public schools with a “non-market model of
education”. For both models of secondary education,
their success or failures can be explained from the
point of view of the following current scientifically
economical approaches: the school of intellectual
capital (Kamoche and Mueller, 1998), (Kogut and
662
Razumovskaya, M. and Kondratyeva, O.
Static and Dynamic Models of Network Interaction in Secondary Education.
DOI: 10.5220/0010595606620668
In Proceedings of the International Scientific and Practical Conference on Sustainable Development of Regional Infrastructure (ISSDRI 2021), pages 662-668
ISBN: 978-989-758-519-7
Copyright
c
 2021 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

Zander, 2003), (Foss, 2006), (Spender, 2013);
approach based on knowledge (Forcadell, 2004),
(Barney, 2006), (Winter, 2003), (Priem and Butler,
2001); network and evolutionary economy
(Dangayach and Deshmukh, 2001). Their supporters
focus on a conscious creation of the demand, aiming
at implementation of the unique benefit of the
service’ executor (provider). And basing on this, we
decide what educational programs to offer in the
markets. We recall that the researches by B.
Vernelfelt (Young et al., 2018) and R. Rumelt (Knott
et all., 2018) based on the J.A. Shumpeter and E.
Penrose’ (Shumpeter,1934), (Penrose, 1959) ideas
have contributed to the establishment of the
approaches mentioned above.
The network’s participants must analyze the
following critical factors and processes
(Razumovskaya, 2019): 1) the system of elements
and resources (people and their specific features,
capital, technology, and information) involved into
production processes and providing fulfilment of the
actual demand of external environment; 2)
arrangement of monetization of value (goods or
services) created mutually upon a request of external
environment (consumer); 3) regulation of mutual
requirements linked by common tasks aimed at the
achievement of the desired outcome or a goal within
limited time and with required resources.
The assets specificity (resources and
competences) used in an educational process, as well
as an economically feasible frequency of enrollment
into educational programs should be considered as the
primary characteristics of secondary education
services. Substantially, these are the characteristics
offered by О. Williamson for classification of
transactions (Williamson,1996). Non-specific assets
are applied upon an implementation of a generally-
pedagogical method aimed at standard programs of
secondary education. While specific assets are used
in a private pedagogical technology implementing
remedial or gymnasium educational programs,
featuring low reproducibility and narrow area of
distribution. Both methods contain procedural,
numerical, and theoretical components; however, the
generally-pedagogical technology shows stable
results and absence of various “if” (conditions -
Translator's Note) (if the teacher is talented, if the
children are smart, if the parents are caring, etc.)
In general, the amount of finance disposed by an
institution of secondary education de-pends on the
gap between the income (enrollment) and outcome
(graduation or transfer) of students in an academic
year. The flow of financing provides the
interconnection of organizational-economic
operations aimed, on the demand of external
environment, at the achievement of re-producible and
repeatable result stipulated by the technology of
educational program implementation, in a certain
time fame.
This approach follows the opinions of R. Coase.,
O. Williamson and their successors on sustainable
frames of business partnership that depend not only
on technology, but also on dynamic of costs financing
and benefits of various organizational alternative
options (Nicita, 2014), (Baggio and Sheresheva,
2014).
3 RESULTS OF THE STUDY
FINDINGS
To model an integrated educational process, we
developed a three-dimensional paradigm:
“capabilities, skills – integration – technologies”
(Razumovskaya, 2019). Upon this paradigm, the
fulfilment of actual demands of external environment
is characterized in three spheres: subject, quasi-
organizational, and institutional. The research of the
mentioned spheres led to the development of static
and dynamic models of the areas of network
integration in a territorially localized market of the
services of secondary education (Razumovskaya,
2019). The development of static models is based on
the research of general conditions, so each child
(adolescent) could succeed in the solution of his/her
personal educational tasks, develop a sense of self-
worth, and realize what his/her social role is and what
his/her truthful beliefs are. The development of
dynamic models is based on the re-search of
implementation of transactional costs of subject-
object relations’ coordination in pro-grams of
secondary education, to provide the solution of
common tasks to satisfy the demands of external
environment.
Both models of network structure (static and
dynamic) aim at “unsuccessful” students when
pedagogical technologies are supplemented with
network interactions with external environment. For
the regional experimental area of the Municipal
Budget Educational Institution “Secondary school №
44” (in the city of Khabarovsk) this environment is
performed by social and medical services, law
enforcement authorities, institutions of prevention of
social orphan-hood, business structures, public
organizations, and private individuals. Their
resources were used not only as a factor of production
of an educational service, but primarily as a system of
Static and Dynamic Models of Network Interaction in Secondary Education
663

interrelationships built around every single student
for the modification of negative perception of
education being essential for the future achievement
of socially relevant results. The reason for this is well
known: the budget does not stipulate any funding of
acquisition of specific assets in different fields of
activity of children and adolescents at risk groups.
The designation of these assets is a positive influence
on lifestyle of “unsuccessful” students because it
defines the system of notional relations (motives and
goals) to the actions in educational process, and
situations and their results regarding provision of
services.
The static structural model has been developed
basing on two following methods of re-search of
secondary education services aimed at
“unsuccessful” students. The first demonstrates a
self-development of a network. We have modeled
several situations of 2015-2018 when the members’
interaction was having no exposure to any
supervising impact (Figure 1). The second shows a
mode of coordination (Figure 2).
Figure 1: Static model of network structure of 2015-2018
(assessment).
Figure 2: Static model of network structure of 2018-2020
(forecast).
An expert assessment of the coordinational
impacts of the previous period of 2019-2020 was
preceded by the detention of network’s members and
their target values of interaction. The estimation was
based on an expected growth of a unit cost created
within a network. For both methods we have
calculated the values of density and the network’s
general centrality, as well as the centrality of each
member of the network.
4 DISCUSSION OF THE
RESULTS
Regarding the representation in detail of the evolution
of initial indices of the number of interactions among
the members, we have developed a dynamic model of
network structure. It shows a transition of states of all
considered variables to determine the positions of
network’s members and characteristics of the links.
As a usual practice, the base of an empirical research
of a model of this category is an economically social
approach. In alignment with it, initial indices of the
number of linkages are estimated in a range of [– 1;
1]. Upon the further movement forward with the step
equal to 0.2, we have determined the qualitative
interpretation of activity in a network interaction. The
dynamic of network’s self-development is shown by
the Table 1, and the Table 2 demonstrates the mode
of coordination. In order to learn the resulting values
of network’s interaction upon the mode of
coordination, we have used the following formula:
𝑥(𝑡)=(IN+ A+ A1 +…..At )𝑥(0)+(IN+ A+ A1+ …..
At-1)𝐵𝑈(0) (1)
where 𝑥(𝑡) is a vector column of the resulting
values that were determined after the launch of the
mode of coordination (size1×𝑛);
𝑁 is a number of network’s members;
𝐴 is a transposed matrix of interference, namely
matrix of contiguity (size 𝑛×𝑛);
𝐼𝑁 is a singular matrix (size 𝑛×𝑛);
𝑥(0) is a vector of initial tendencies of factors (size
1×𝑛);
𝑈(0) is a vector of coordination,
𝑈(0)=(𝑢1(0),…,𝑢𝑝(0)), where 𝑢1(0) is an impulsive
coordinating cooperation with the value within the
interval equal to [0;1] supplied at the moment of time
𝑡=0 for the variable factor 𝑥1;
B - (0,1) is a matrix measured 𝑝×𝑛, whose non-
zero elements identify the numbers of adjustable
coordinates of the initial statement 𝑥(0).
The expert assessment of a coordination impact
on the previous period has been preceded by the
ШК
УЗ
1
УЗ2
УЗ3
УЗ4
СЗ
КДН
ИЗП
ЦН
ОП
УО
3
УО4
УО5
УО6
УО7
ГНК
РГ
ГИБДД
ЦЗ
ОПП
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composition of the network’s members and
determination of target values of their interactions.
The assessment was based on an expected unit cost
created in the network. It should approach to the
standard of funding per student at a school for the
children and adolescents with special educational
needs. We have learned that the target values of
expected indices had reached the prevised level or
were approaching to it, regarding the following
partners: “The department of social support to the
population of Kirovsky and Krasnoflotsky districts of
the city of Khabarovsk”; Regional State Budget
Institution “Khabarovsk Regional Centre of
Psychological and Pedagogical Rehabilitation and
Correction”; Regional State Budget Institution of
Healthcare “Children Clinical Centre of Medical
Reabilitation” “Amursky”. However, among the
institutions unable to achieve the target indices stated
by the experts are the following: Regional State
Budget Institution “Regional Youth Social Medical
Pedagogical Centre “Contact”; Regional State-
Owned Institution “Khabarovsk Social Rehabilitation
Centre for Juvenile”; and the working group of
Krasnoflotsky district in Khabarovsk.
Table 1: The assessment of indices of static and dynamic network structure providing the secondary education services for
the students at a risk group on the base of the regional experimental area of the Municipal Budget Educational Institution
“Secondary school № 44” (the city of Khabarovsk) in a mode of self-organization of network processes (productional,
organizational, regulatory)
Characteristics of indices of static model of the structure
Characteristics of indices of dynamic model
of the structure
Network in a mode of self-organization (assessment)
Network’s characteristics 2015–2018
2008 2018 Modification, +/-
Network density, (L) 0,491
Standard coefficient of centralization, (CD) 0,032
Standard centralization of network’s members, (CD (ni)), including
УЗ1 – Regional State Budget Institution of Healthcare
“Children Clinical Hospital №3” in Khabarovsk
0,611 0,333 0,611
0,278 (low
increase)
УЗ2 – Regional State Budget Institution of Healthcare
“Children Clinical Centre of Medical Reabilitation
“Amursky”
0,389 0,555 0,389
–0,166 (slight
decrease)
УЗ3 – women's clinic of Krasnoflotsky district №3,
Regional State Budget Institution of Healthcare
“Maternity hospital №1”
in Khabarovsk
0,500 0 0,500
0,500 (moderate
increase)
УЗ4 – Regional State Budget Institution of Healthcare
“City Clinical Hospital № 10” in Khabarovsk
0,555 0 0,555
0,555 (moderate
increase)
СЗ – The department of social support to the
population of Kirovsky and
Krasnoflotsky districts in Khabarovsk
0,500 0,666 0,500
–0,166 (slight
decrease)
КДНиЗП – Commission for Protection of Minors and
their Rights of Krasnoflotsky district of urban district
“
The city of Khabarovsk
”
0,889 0,555 0,889
0,334 (low
increase)
УО1 – International Association of Universities
“Centre of Development of
Education”
- 0,222 - Left the network
УО2 – Regional State Budget Educational Institution
“Khabarovsk Regional Institution of the Development
of Education”
- 0,222 - Left the network
УО3 – Education Management of the Khabarovsk City
Administration
0,333 0 0,333
0,333 (low
increase)
УО4 – Regional State Budget Institution “Regional
Youth Social Medical Pedagogical Centre “Contact”
0,167 0 0,167
0,167 (low
increase)
Static and Dynamic Models of Network Interaction in Secondary Education
665

УО5 – Regional State-Owned Institution “Khabarovsk
Social Rehabilitation Centre for Juvenile”,
0,167 0 0,167
0,167 (low
increase
)
УО6 – Regional State Government-financed
Institution “Khabarovsk Regional Centre of
Psychological and Pedagogical Rehabilitation and
0,500 0 0,500
0,500 (moderate
increase)
ОП – The department of guardianship and trusteeship
in Khabarovsk
0,778 0,444 0,778
0,334 (low
increase)
ГНК – Regional Administration of the Federal Service
of the Russian Federation for drug trafficking control
in Khabarovsk
y
Krai and the cit
y
of Khabarovsk
0,389 0 0,389
0,389 (slight
increase)
РГ – The working group of Krasnoflotsky district of
the cit
y
of Khabarovs
k
0,333 0,333 0,333 0 (unchangeable)
ГИБДД – The department of work with schools of the
State Inspectorate for Road Traffic Safety of the
Ministry of the Interior of Russia in Khabarovsk
0,222 0 0,222
0,222 (low
increase)
ЦЗ – Regional State-Owned Institution “Employment
center” in Khabarovsky Krai and the city of
Khabarovsk
0,333 0 0,333
0,333 (low
increase)
ОПП - The department of guardianship and trusteeship
in the city of Khabarovsk
0,611 0,555 0,611
0,560 (slight
increase)
ЦН – The Centre for Detention of Minor Offenders in
the cit
y
of Khabarovsk
0,333 0 0,333
0,333 (low
increase
)
ОУ7 – The schools of Krasnoflotsky district in
Khabarovsk (Municipal Budget Educational
Institution “Gymnasium №7”, Municipal Autonomous
Educational Institution “Economic Gymnasium”,
Municipal Autonomous Educational Institution
“Secondary school “Success”, Municipal Autonomous
Educational Institution “Secondary Education School
№ 51”)
0,722 0 0,722
0,722 (significant
increase)
ШК – Municipal Budget Educational Institution
“Secondary school № 44”
1,000 1,000 1,000 0 (unchangeable)
Table 2: The assessment of indices of static and dynamic network structure providing the secondary education services for
the students at a risk group on the base of the regional experimental area of Municipal Autonomous Educational Institution
Secondary Education School № 44 (the city of Khabarovsk) in a mode of coordination of implementation of network
processes (production, organizational, regulatory)
Characteristics of indices of static model of the structure
Characteristics of indices of dynamic model
of the structure
Network in a mode of coordination (forecast)
Network’s characteristics 2019–2020
гг. 20018 2020 Modification, +/-
Network density, (L)
0,692
Standard coefficient of centralization, (CD)
0,024
Standard centralization of network’s members, (CD (ni)), including
УЗ1 – Regional State Budget Institution of Healthcare
“Children Clinical Hospital №3” in Khabarovsk
0,666 0,611 0,666
0,055 (slight
increase)
УЗ2 – Regional State Budget Institution of Healthcare
“Children Clinical Centre of Medical Reabilitation
“Amursky”
0,800 0,389 0,700
0,311 (low
increase)
УЗ3 – women's clinic of Krasnoflotsky district №3,
Regional State Budget Institution of Healthcare
“Maternity hospital №1”
in Khabarovs
k
- 0,500 - Left the network
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УЗ4 – Regional State Budget Institution of Healthcare
“City Clinical Hospital № 10” in Khabarovsk
0,600 0,555 0,600
–0,005 (slight
decrease)
СЗ – The department of social support to the
population of Kirovsky and
Krasnoflotsky districts in Khabarovsk
0,800 0,500 0,800
0,300 (low
increase)
КДНиЗП – Commission for Protection of Minors and
their Rights of Krasnoflotsky district of urban district
“The city of Khabarovsk”
1,000 0,889 1,00
0,111
(незначительное
увеличение)
УО1 – International Association of Universities
“Centre of Development of
- - -
Left the network
b
efore 2018
УО2 – Regional State Budget Educational Institution
“Khabarovsk Regional Institution of the Development
- - -
Left the network
b
efore 2018
УО3 – Education Management of the Khabarovsk City
Administration
- 0,333 - Left the network
УО4 – Regional State Budget Institution “Regional
Youth Social Medical Pedagogical Centre “Contact”
0,600 0,167 0,600
0,433 (slight
increase)
УО5 – Regional State-Owned Institution “Khabarovsk
Social Rehabilitation Centre for Juvenile”
0,600 0,167 0,600
0,433 (slight
increase)
УО6 – Regional State Government-financed
Institution “Khabarovsk Regional Centre of
Psychological and Pedagogical Rehabilitation and
Correction
”
0,733 0,500 0,700
0,200 (slight
increase)
ОП – The department of guardianship and trusteeship
in Khabarovsk
0,933 0,778 0,933
0,155 (slight
increase)
ГНК – Regional Administration of the Federal Service
of the Russian Federation for drug trafficking control
in Khabarovsky Krai and the city of Khabarovsk
0,667 0,389 0,667
0,278 (low
increase)
РГ – The working group of Krasnoflotsky district of
the city of Khabarovsk
0,467 0,333 0,467
0,134 (low
increase)
ГИБДД – The department of work with schools of the
State Inspectorate for Road Traffic Safety of the
Ministr
y
of the Interior of Russia in Khabarovs
k
- 0,222 - Left the network
ЦЗ – Regional State-Owned Institution “Employment
center” in Khabarovsky Krai and the city of
Khabarovsk
0,333 0,333 0,333 0 (unchangeable)
ОПП - The department of guardianship and trusteeship
in the city of Khabarovsk
0,600 0,611 0,600
–0,011 (slight
decrease)
ЦН – The Centre for Detention of Minor Offenders in
the city of Khabarovsk
0,467 0,333 0,467
0,134 (slight
increase)
ОУ7 – The schools of Krasnoflotsky district in
Khabarovsk (Municipal Budget Educational
Institution “Gymnasium №7”, Municipal Autonomous
Educational Institution “Economic Gymnasium”,
Municipal Autonomous Educational Institution
“Secondary school “Success”, Municipal Autonomous
Educational Institution “Secondary Education School
№ 51”)
0,800 0,722 0,800
0,078 (slight
increase)
ШК – Municipal Budget Educational Institution
“Secondary school № 44”
1,000 1,000 1,00 0 (unchangeable)
Static and Dynamic Models of Network Interaction in Secondary Education
667

5 CONCLUSIONS
A network is modeled as an organizational system of
open type. Within the network we plan to achieve
standard (reproducible) outcomes of the programs of
secondary education, whose organization continually
repeats within the time frame upon the modification
of resources’ condition impacted by the external
environment. An existence of any network starts with
self-organization (“organized disorganization”) of its
members and lasts while the actual demands of
external environment are being fulfilled upon the use
of external recourses.
Given that the network’s opportunities are
followed by the transactional costs of coordination of
subject-object relations in programs of secondary
education, a focus on an increase of the amount of
finance and material resources within a network may
become a guarantee of successful fulfillment of actual
parameters of external environment. And thus, it can
decrease an outflow of students at the levels of
primary and secondary education.
The network’s research regarding three
dimensions of modification of attracted resources
(subject, quasi organizational, and institutional)
contributes to the solution of related tasks of
synchronization of main processes (production,
organization, regulation) and coordination of re-
courses and competences of a school and its social
partners.
And therefore, we provide an implementation of
an educational trajectory from the perspective of
private personal choice, on the one hand, and
implementation of an educational program as a public
choice, on the another.
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