Analysis and Application of Semantic Networks in Education

Arnold E. Kiv

1,3 a

, Vladimir N. Soloviev

2 b

, Elena Yu. Tarasova

2 c

, Tetyana I. Koycheva

3 d

and

Katrina V. Kolesnykova

3 e

Ben-Gurion University of the Negev, P.O.B. 653, Beer Sheva, 8410501, Israel

Kryvyi Rih State Pedagogical University, 54 Gagarin Ave., Kryvyi Rih, 50086, Ukraine

South Ukrainian National Pedagogical University named after K. D. Ushinsky, 26 Staroportofrankivska Str., Odessa,

65020, Ukraine

Keywords:

Semantic Knowledge Network, Course Concept, Topic Adjacency Matrix, Gephi.

Abstract:

The basis of any discipline is a set of didactic units. The task of the educational process management apparatus

is to ensure compliance with the requirements for the order of the didactic units and their full implementation

within the framework of the formation of the curriculum while minimizing its duration. A signiﬁcant difﬁculty

is the logical linking of didactic units with each other, since it is impossible to break the logic of presentation of

materials of one discipline and there is a relationship between didactic units of different disciplines. The paper

compares the topological characteristics of the concept graphs related to various disciplines. We develop the

algorithm to implement the subject area model in the form of a semantic knowledge network. 125 concepts are

analyzed that provide optimal mastering disciplines and establish the connection between them. A survey of

the dynamics of the popularity of the term “network science” from 2004 to 2020 using Google Trends showed

a steady trend of user interest. On average, 80 requests are executed (calculated in arbitrary units), with the

largest volume of requests being 100.

1 INTRODUCTION

Education is the foundation of sustainable develop-

ment and the main tool for creating a humane, equal

and attentive society to human problems, in which

each individual should have his or her human dignity.

Obviously, the main reason for the emergence of ed-

ucation for sustainable development is the awareness

of the need for changes in the educational paradigm

in order to further sustainable development of soci-

ety, the economy and preservation of the environment.

Sustainable development education involves a transi-

tion to an economically and socially oriented learning

model. This model should be based on broad interdis-

ciplinary knowledge, which is based on an integrated

approach to the development of society, and allows

making and implementing decisions at the local and

global levels. All these steps are aimed at improving

the quality of life and do not threaten the ability of

https://orcid.org/0000-0002-0991-2343

https://orcid.org/0000-0002-4945-202X

https://orcid.org/0000-0002-6001-5672

https://orcid.org/0000-0002-5518-4260

https://orcid.org/0000-0002-4818-5580

future generations to meet their needs.

Many researchers consider the problems of edu-

cation modernization in the framework of sustainable

development. In recent years, the interest in research

concerning Education for Sustainable Development

(ESD) has grown considerably. In research (Grosseck

et al., 2019) using a bibliometric approach, analyzed

1813 papers on the subject, indexed by the Web of

Science, between 1992 and 2018. The number of pub-

lications, authors, and journals has increased, proving

that ESD has gained momentum over the period ex-

amined in the study. In study (Grosseck et al., 2019)

illustrates two main research directions for the entire

time span: integration of education into sustainable

development and of sustainable development into ed-

ucation. In study (Holfelder, 2019) is to show that

education must be thought of as something other than

just training: considering education predominantly as

subjectiﬁcation holds the possibility for open and al-

ternative futures. that education is more than train-

ing. The main message – education is more than

training. Evaluation case studies in (Eilks, 2015)

show that thoroughly combining the ESD framework

with science teaching that follows a socio-scientiﬁc

416

Kiv, A., Soloviev, V., Tarasova, E., Koycheva, T. and Kolesnykova, K.

Analysis and Application of Semantic Networks in Education.

DOI: 10.5220/0010924800003364

In Proceedings of the 1st Symposium on Advances in Educational Technology (AET 2020) - Volume 1, pages 416-431

ISBN: 978-989-758-558-6

issues-based approach to education has great poten-

tial for helping students develop many general educa-

tional skills. In articles (Byrch et al., 2015; Morioka

et al., 2006) has laid out the initiatives to contribute

to global sustainability through reform and streamlin-

ing of the current technological paradigm and busi-

ness. This reform is based on a future-oriented and

global approach. In this initiative, industry and busi-

ness plays a critical role as a link between technol-

ogy, business and society. Leicht et al. (Leicht et al.,

2018) presents an overview of ESD and highlights

key issues related to ESD policy and practice. Topics

include key ESD competencies and themes, policy,

changes in the learning environment, teacher training,

youth as lead actors, scaling-up action, and the moni-

toring of progress.

The epidemics, the destruction of the natural en-

vironment and climate change, the depletion of ma-

terial and energy resources, the population explosion

and lack of food, as well as the civilization crisis as

a whole, are complex interdisciplinary problems of

the humankind. New directions of science appear for

their solution. The convergence of methods and inter-

disciplinary approaches is the main characteristic of

these advanced scientiﬁc communities.

Supra-sectorial technologies (information, cogni-

tive, nano-, bio-, social technologies) are currently

actively developing. Thanks to them, new branches

of science appear and serve as a new methodologi-

cal basis for studying nature (Arshinov et al., 2011;

Ahromeeva et al., 2013; Kovalchuk, 2011). Such in-

terdisciplinary scientiﬁc ﬁelds lead to new directions

in science such as risk management, sustainable de-

velopment, new nature management, etc.

The quality of professional training of students in

the modern sense determines their readiness and abil-

ity to use the acquired professional competencies to

solve not only professional tasks, but also multidisci-

plinary tasks. Solving such problems contributes to

sustainable development at the level of the country,

region and the world as a whole. This implies updat-

ing the content and methods of professional training

of specialists at a modern university taking into ac-

count the requirements of interdisciplinary integration

and the implementation of sustainable development

ideas (Shults and Tsyiganov, 2010; Solodova and Ma-

linetskiy, 2013).

The work (Chekmarev, 2014) emphasizes that the

competitive professional competence of university

graduates in the labor market in the light of inter-

national requirements can be achieved subject to sig-

niﬁcant changes in the system of higher professional

school. The articles (Sirenko, 2014, 2013) presents

the ways of enriching the content of the academic dis-

cipline “Fundamentals of Information Technologies”

with interdisciplinary components. The diffuse prin-

ciple of penetration of general scientiﬁc and philo-

sophical knowledge into the content of the academic

discipline is substantiated. The characteristics of gen-

eralized tasks as a means of interdisciplinary integra-

tion are given. The results of experimental work on

checking the effectiveness of the method of using gen-

eralized problems are analyzed.

Interdisciplinary integration in higher education

institutions has to be an important component of

introducing sustainable development ideas into the

training of modern specialists. The problems of sus-

tainable development itself are multidisciplinary.

Such integration will solve the signiﬁcant contra-

dictions of education, namely the contradiction be-

tween the vast knowledge and limited human possi-

bilities. The optimal combination of computer sci-

ence and other academic disciplines within the same

topic will provide conditions for a signiﬁcant increase

of the level of the educational process.

Jurgena and Cedere (Jurgena and Cedere, 2018)

concluded that students have a large non-used po-

tential to understand more deeply the nature of sci-

ence and acquire the knowledge important for their

future lives and work. Recently, a lot of talk has

been going on about the transition to a knowledge-

based society. Knowledge management systems are

evolving and knowledge management professionals

are employed in large corporations. Unfortunately,

in the discussions of this topic higher education is

not considered (Kumar and Agrawal, 2011; Boca and

Mukaj, 2016). This is unacceptable, because knowl-

edge is created, systematized and accumulated in uni-

versities, and then passed on to the next generation of

people.

The learning process is the management of the

process of student’s knowledge accumulation and sys-

tematization. Only a few researchers focus their at-

tention on this fact (Martins et al., 2019; Fazey et al.,

2013; Sanguankaew and Ractham, 2019; Vlasenko

et al., 2021). An automated learning environment

based on semantic knowledge networks is largely ca-

pable of solving a wide range of knowledge manage-

ment tasks at the university. A feature of the mod-

ern stage in the development of educational systems is

the necessity of expending the use of formal methods

for presenting knowledge and organizing the learning

process. The achievements of cybernetic, synergetic

and the theory of artiﬁcial intelligence are the basis of

these scientiﬁc directions. Many objects of cognitive

research are networks. Alternatively, you can imagine

them like that.

In the 1940s, scientists who study the human brain

Analysis and Application of Semantic Networks in Education

417

hypothesized that its unique properties are due not

to the characteristics of individual nerve cells, but to

the structure of the connections between them (Se-

merikov et al., 2018). To date, research on networks

of a very different nature – biological, physical, social

and economic – has been collectively called network

science, or the science of networks.

Over the past two decades, many studies have

focused on the network science methodology as an

extensive scientiﬁc ﬁeld of studying complex sys-

tems (for example, (Malineckiy, 2013; Barrat, 2008;

Soloviev et al., 2016; Liu et al., 2010)). Complex

systems contain several components that interact with

each other, producing complex behaviour.

The human brain and the cognitive processes oc-

curring in it are an example of a complex system.

These processes provide memory and language (for

example, (Sporns, 2011; Baronchelli et al., 2013;

Beckage and Colunga, 2015; Jones, 2016; Sol

e et al.,

2010; Wulff et al., 2019; Boccaletti et al., 2006;

Borge-Holthoefer and Arenas, 2010)). The founda-

tion of network science is mathematical graph theory.

It is contains powerful quantitative methods for study-

ing systems such as networks (for example, (Carring-

ton et al., 2015)).

At this stage in the development of the educa-

tion system, the priority is to ﬁnd ways to improve

the learning process, its content and structure. Re-

ceiving a fundamental and holistic education can be

only as result of the learning process at the level of

new quality. In this case, the content of various disci-

plines should reﬂect the logic and structure of knowl-

edge ties between disciplines. In the absence of inter-

subjective communications, the knowledge will be

fragmentary, unsystematic. Cognitive networks are

not only a tool for cognition, but can also a basis for

controlling student’s knowledge.

In different historical periods, many variants of

semantic knowledge networks that take into account

the speciﬁcs of intellectual activity have been cre-

ated. In the “precomputer era” the prototype of se-

mantic knowledge networks was used to formalize

logical reasoning. At the beginning of the twentieth

century, in psychology, graphs were ﬁrst used to rep-

resent hierarchies of concepts and inherit properties,

model human memory and intellectual activity. In the

early 60-s the ﬁrst machine implementations of se-

mantic networks were made. One of the ﬁrst systems

of practical importance (Masterman, 1961) contained

100 primitive types of concepts for solving the prob-

lem of automatic translation. Dictionary of 15 000

concepts was deﬁned.

At present, semantic knowledge networks are

widely used in solving many different problems, in

particular when building knowledge bases, in prob-

lems of machine translation and processing of text in

a natural language. Due to the wide range of use of

such graphs, there is a need for their reﬁnement – an

increase in the number of nodes and an increase in the

connectivity between them.

Actual modern studies are devoted to the use of se-

mantic networks in the ﬁeld of education. For exam-

ple, in the work (Xie et al., 2015) the interdisciplinary

of applied mathematics is quantitatively analyzed by

using statistical and network methods on the corpus

PNAS 1999–2013. Czerkawski (Czerkawski, 2014)

discusses the potential Semantic Web for teacher ed-

ucation.

Dunn (Dunn, 2013) presents a theoretical method

for the integration of semantic knowledge network

utilization into the classroom. This paper will also in-

troduce insights from Cognitive Linguistics as to how

the brain best learns vocabulary. The method of Dunn

(Dunn, 2013) springs from the ﬁelds of psychology

and neuroscience as well as inspiration from educa-

tors who are building new teaching styles. The pur-

pose of the method detailed in this paper is to inspire

other educators to incorporate cognitive linguistic in-

sights into their classes as well as further the discourse

on integrating this ﬁeld into the teaching of English as

a second or foreign language.

Teng et al. (Teng et al., 2012) formulate recipe

recommendations using ingredient networks. Re-

searchers have shown how information about cooking

can be used to glean insights about regional prefer-

ence sand modiﬁability of individual ingredients, and

also how it can be used to construct two kinds of net-

works, one of ingredient complements, the other of

ingredient substitutes. These networks test which in-

gredients work well with each other and which ones

are better to replace. Allows you to predict which of

a pair of related recipes will work best for the user.

Traditionally, researchers formed networks of se-

mantic knowledge manually. This is labour intensive.

Such networks contain a small number of nodes, but

they have an important advantage - they are checked

manually. An alternative approach is the automatic

construction of a semantic network based on an exter-

nal source generated by Internet users (Zesch et al.,

2008). A striking example of such a source is the

Wiktionary (Wiktionary Statistics, 2020).

In (Kiv et al., 2014) a new stylistic-mathematical

approach (SMA) for analysis of translation works was

introduced. It was postulated that the important re-

quirement to translation is its compliance with the

language in which the translation was done from the

point of view of Zipf’s laws and information charac-

teristics. According to SMA any translation should

AET 2020 - Symposium on Advances in Educational Technology

418

satisfy at least to the following requirements:

• The sense of the translation version must exactly

reﬂect the intention of the author of original text.

• It is necessary to ﬁnd the equivalent constructions

in the translation version for idioms and other spe-

ciﬁc expressions in the original text.

• The translator should reach the appropriate differ-

ence between Zipf’s constants for the original text

and for the translation.

A computer program for application of Zipf’s

Laws was developed for analysis of English and Rus-

sian literary texts. This program uses the algorithms

of texts data processing from the Microsoft products,

such as Microsoft C#, Microsoft SQL 2008. The Mi-

crosoft SQL 2008 was chosen because it is enough

powerful full-text modules, realized on more than

10 languages, The algorithm realized in the devel-

oped program allows processing any texts in order to

present them as tables of database with necessary pa-

rameters. As a result of uniting capabilities of these

products, the client-server structure of the program,

where the program is a client and Microsoft SQL2008

is a server was obtained. The user enables to specify

a set of search criteria. The program gets the answers

and outputs from the server in the comfortable to user

form.

This program was applied to compare different

translations of the famous play of William Shake-

speare “Hamlet. Prince of Denmark” (Shakespeare,

1985). Various characteristics of this work given by

critics were accounted. They analyzed these trans-

lations from the point of view of the exact reﬂec-

tion of Shakespeare’s ideas, preservations of original

thoughts, and the quality of the translation language.

Then Zipf’s constants were estimated for the original

text and translations taken from (Shakespeare, 1985)

(Edition of 1828). In table 1 one can see the obtained

results.

We see that table 1 Zipf’s constants are varied

from 0.0954 (that is close to English language) to

0.0684 (that is close to Russian language). On the ba-

sis of these results and semantic analysis performed

by other researchers it was come to conclusion that

the translation of Pasternak satisﬁed the conditions of

the high level translation described above. His trans-

lation is the most closely to the native Russian lan-

guage. At the same time in this translation Pasternak

reproduced the music and the spirit of Shakespeare’s

masterpiece (Shakespeare, 1985). The opposite trans-

lation approach we see in the Radlova’s translation.

She tried do not omit any word in the original text.

As a result she did not reproduce in Russian version

the sense of Shakespeare’s work and her text is closer

to the structure of English language.

Thus, all of these works are devoted to the in-

tegration of semantic knowledge networks in teach-

ing. The increasing information volumes of the edu-

cational material of the disciplines dictate the need to

use cognitive modelling to solve complex problems of

training and teaching.

2 MATERIALS AND METHODS

There are various ways of representing knowledge, in

particular, such visual methods for describing knowl-

edge in the subject ﬁeld: semantic networks, graphs

of conceptual dependencies, scripts, frames, concep-

tual graphics and ontology.

Ontologies are an effective means of representing

and organizing knowledge. For the formal speciﬁ-

cation of concepts and relationships, researchers use

ontologies. Ontologies characterize a speciﬁc subject

area. Ontology consists of terms (concepts), their def-

initions and attributes, as well as associated axioms

and inference rules.

Formally, ontology is a relation:

O =< T, R,F >,

where T – concepts (terms) of the subject area de-

scribed by the ontology O, R – relationship between

terms of the subject area, F – functions of interpreta-

tion, given on terms and relations of the ontology.

Let us determine the deﬁnitions that are important

for this work: “semantic knowledge network”, “se-

mantic network”, “network model”, “cognitive map”,

“cognitive network”, “cognitive scheme”. Figure 1

shows a diagram of the types of cognitive schema.

Figure 1: Cognitive scheme type chart.

Cognitive maps are a concept of cognitive psy-

chology pioneered by Tolman (Tolman, 1948). A cog-

nitive map is an active, information-seeking structure.

Analysis and Application of Semantic Networks in Education

419

Table 1: Zipf’s constants for different translations of “Hamlet. Prince of Denmark”.

Author and translators Year Zipf’s constant Comments

Shakespeare 1603 0.1191 Original

Pasternak 1940 0.0684 Translation

Romanov 1899 0.0882 Translation

Averkiev 1895 0.0827 Translation

Kroneberg 1925 0.0837 Translation

Lozinski 1933 0.0877 Translation

Radlova 1937 0.0954 Translation

In our work, the concepts of “semantic knowledge

network” and “semantic network” are identical.

In cognitive science, the network is one of the

most common types of information models. Typi-

cally, a network consists of two components – nodes

as network elements and edges, reﬂecting the interac-

tion between the elements. Using these simple com-

ponents, you can describe a wide range of objects of

different nature and complexity. The network concept

is the foundation of network models. In such mod-

els, all relationships are clearly distinguished. These

relations constitute the framework of knowledge of

the subject area, the model of which must be cre-

ated. This class of models includes semantic net-

works, functional networks, and frames (frame rep-

resentation).

Although the terminology and structure are differ-

ent, there are similarities inherent in almost all seman-

tic networks:

• Different nodes of one concept belong to different

values, if not it is marked that they relate to one

concept.

• Edges of semantic networks create relationships

between concept nodes (marks above arcs indicate

the type of relationship).

• Relations between concepts can be linguistic

cases, such as “agent”, “object”, “recipient” and

“instrument” (others mean temporal, spatial, logi-

cal relations).

• The concepts are organized by level in accordance

with the degree of generalization.

An associative approach to knowledge represen-

tation deﬁnes an object value in terms of its connec-

tions (associations) with other objects. Thus, when a

person perceives an object and discusses it. At this

time, the brain maps the object of perception into a

certain concept (ﬁgure 2 (Babkin et al., 2006)). This

concept is part of general knowledge about the world.

Therefore, it is associated with various associations

with other concepts. Associations deﬁne properties

and behaviour of the perceived object.

Figure 2: The relationship of the concept, subject and word

denoting this subject (Babkin et al., 2006).

Scientists have developed semantic networks

within a scientiﬁc ﬁeld that relates to the represen-

tation of knowledge to model human thinking. This

area of research has arisen within the general prob-

lem of artiﬁcial intelligence. It focuses on the devel-

opment of specialized languages and graphical tools

for representing declarative or static domain knowl-

edge. The results of research in the ﬁeld of semantic

networks have been reﬁned and successfully used in

the construction of conceptual models and relational

database schemes.

Semantic networks are the most powerful math-

ematical model for representing knowledge about a

subject area, one of the most important areas of arti-

ﬁcial intelligence. Currently, the scientiﬁc literature

describes many alternative representations of seman-

tic network models. Researchers use them to solve a

variety of problems in a variety of software.

In general, a semantic network is an expression:

S = (O,R

,... ,R

where O is a set of objects of a speciﬁc subject area,

|i = 1 .. .n is a set of relationships between objects,

i is the type of relationship.

In the general case, a semantic network is under-

stood as a certain graph G

= (V

), in which the

set of vertices V

and the set of edges Es are divided

into separate types that have special semantics char-

acteristic of a particular subject area. In this situa-

tion, the set of vertices can correspond to objects or

entities of the considered domain and have the cor-

responding explicit names of these entities instead of

the vertex numbers. Such names should allow unam-

biguous identiﬁcation of the corresponding objects,

AET 2020 - Symposium on Advances in Educational Technology

420

Figure 3: The relationship of various concepts in the human

mind (Babkin et al., 2006).

while there are no general formal rules for recording

names. There are also different types of edge sets that

correspond to different types of relationships between

entities in the area in question.

Many real-world phenomena can be modelling

with the help of a graph. For example, we can think

of various web pages as nodes and hyperlinks as di-

rected edges to represent the World Wide Web as a

graph. For instance, we can view various web-pages

as nodes and hyperlinks as directed edges to represent

the World Wide Web as a graph. Such a modelling

can help perform various graph computations on the

web. For instance, PageRank algorithm is a popular

graph algorithm, which is used to rank the web-pages.

Alternatively, the web-graph can be used to ﬁnd clus-

ters of web-pages, which link one another. This can

help in categorizing the web-pages into various topics

(Cheramangalath et al., 2020).

Graphs are best suited for explicitly expressing as-

sociations between different concepts. Thus, in the

form of a semantic network, knowledge of the world

is expressed. A semantic knowledge network is a

marked graph in which nodes correspond to certain

facts or general concepts, and edges mean relation-

ships or associations between different facts or con-

cepts (ﬁgure 3 (Babkin et al., 2006)).

In each academic discipline (in every science) the

number of concepts reﬂecting the knowledge of this

discipline (this science) is ﬁnite. There are a number

of words that need to be conveyed to the audience.

The number of these words is not inﬁnite, because

time for their transfer is limited. Textbooks establish

linear links between concepts.

A normalized description of knowledge networks

can be formulated as follows. The body of knowledge

of the studied discipline is a system (S). The elemen-

tary component that is part of S is a word that reﬂects

a certain concept. With the help of words, all the con-

cepts that make up the S system are recorded. Links

between the concepts are established using the gram-

matical rules of a particular language. With respect

to each concept from S, there is a primary sentence

that contains its deﬁnition. The totality of such deﬁ-

nitions forms an invariant kernel S, which ensures the

unambiguity of the perception of knowledge within a

particular academic discipline. The invariant core of

the discipline uses words from other areas of knowl-

edge to determine its concepts. All concepts from S

are divided into main and auxiliary. The basic con-

cepts include speciﬁc concepts of this particular disci-

pline, which are the subject of its deﬁnition and study.

Supporting concepts include concepts borrowed from

other areas of knowledge that are not studied in this

discipline, but are used to determine the content of ba-

sic concepts. Many of the basic concepts of a particu-

lar discipline, together with the internal relationships

between them, form a hierarchically ordered network

of knowledge, the nodes of which are the identiﬁers

of the basic concepts.

Thus, the knowledge system can be represented in

the form of a hierarchical directed graph – a semantic

knowledge network.

The semantic knowledge network building algo-

rithm involves several steps:

(1) Writing all the basic terms of the subject area and

formulate their deﬁnitions (composing the the-

saurus of the subject area).

(2) Selecting the terms from the list that appear in the

deﬁnition of the other terms listed in step 1.

(3) At the lower (I) level, arranging the terms in the

deﬁnition of which the terms from the list are not

used.

(4) At the next (II) level, arranging the terms in the

deﬁnition of which the terms of level I are used.

(5) At the III level – terms in the deﬁnition of which

the terms of I and II levels are used, etc.

(6) At the last level, arranging terms that are not used

in the deﬁnition of other terms.

(7) Connecting the concepts.

Visualization of data in a structural network model

is the ﬁrst step, but the strength of the method lies in

the ability to extract important knowledge about the

system through a statistical analysis of the network

topology. It seems that topology bears an evolution-

ary imprint and functional (Barab

asi, 2012). A de-

tailed analysis of the available metrics can be found,

for example, in (Barab

asi, 2016). Consider just a few

metrics often used in cognitive model research.

Let us consider in detail the network structure. A

network consists of nodes and links between them,

edges. Nodes are more or less stable entities that do

not change over time.

Edges represent relationships, interactions, trans-

actions, or any other temporary connections that oc-

cur between nodes over a certain period of the time.

Analysis and Application of Semantic Networks in Education

421

Edges represent connections between them: friend-

ships, proximity, transactions, exchanges and any

other temporary connections between stable objects

that occur with a certain frequency.

Edges are important to network analysis because

they represent the connectivity basis that will be using

to get insights about the complexity network. In a

graph database, the relationships between the data are

just as important as the data itself.

Giant component is an important notion in net-

work analysis. It’s an interconnected constellation

that includes most of the nodes in a network.

Clusters are the constellations of nodes that are

more densely connected together than with the rest

of the nodes in the network. Clusters represent differ-

ent sub networks within a network and can be used to

identify various subcategories that are present within.

In modern network theory, the number of node

connections (in the theory of graphs, nodes and nodes

are edges and vertices of a graph, respectively) is

called a degree. A node’s degree indicates how many

connections it has to the other nodes in the network.

The more degree a node has, the more “connected”

it is, which indicates its relative inﬂuence in the net-

work.

The concept of degree is a local characteristic of

a graph. A nonlocal, integral network structure is de-

ﬁned by two concepts – a path and a loop or cycle.

A path is a sequential sequence of adjacent nodes and

the links between these nodes when the nodes do not

repeat. A loop or cycle is a path when the start and

end nodes coincide. Networks without loops are trees.

The number of nodes (N) (network size) and the num-

ber of links (L) are related as N = L − 1 (Soloviev

et al., 2016).

Identifying the nodes with the highest degree (also

called “hubs”) is an important part of network analy-

sis as it helps identify the most crucial parts of the net-

work. This knowledge can then later be used both to

improve network’s connectivity (by linking the hubs

together) and disrupt it (by removing the nodes).

Betweenness centrality is another important mea-

sure of the node’s inﬂuence within the whole network.

While degree simply shows the number of connec-

tions the node has, betweenness centrality shows how

often the node appears on the shortest path between

any two randomly chosen nodes in a network. Thus,

betweenness centrality is a much better measure of

inﬂuence because it takes the whole network into ac-

count, not only the local connectivity that the node

belongs to.

A node may have high degree but low between-

ness centrality. This indicates that it’s well-connected

within the cluster that it belongs to, but not so well

connected to the rest of the nodes that belong to the

other clusters within the network. Such nodes may

have high local inﬂuence, but not globally over the

whole network.

Alternatively, other nodes may have low degree

but high betweenness centrality. Such nodes may

have fewer connections, but the connections they

do have are linking different groups and clusters

together, making such nodes inﬂuential across the

whole network.

In network visualization, we often range the node

sizes by their degree or betweenness centrality to in-

dicate the most inﬂuential nodes.

Network topology is an important element of net-

work analysis. If we analyse networks on the struc-

tural basis we will discover many differences among

them. A tool for studying complex networks based on

graph theory is topological analysis.

When performing network analysis and visualiza-

tion it is important to classify the topology of the

network (Gephi, 2020a). This can be done through

quantitative analysis of degree distribution among the

nodes and/or through qualitative analysis using vari-

ous visual graph layouts.

Degree distribution can be a good indicator of the

network’s topology. If most of the nodes in the net-

work have exactly the same degree, the network is

more of a regular one (it may also indicate the pres-

ence of tree-like hierarchical system within the net-

work). If most of the nodes have an average num-

ber of connections that is the same and then some of

the nodes have more and some of the nodes have less

(normal bell-curve distribution of degree), we’re deal-

ing with a randomized network. Finally, if there’s a

small, but signiﬁcant number of nodes with a high

degree and then degree distribution follows a long

tail towards a gradual decline (scale-free distribution),

this is a small-world network, where there’s a signif-

icant amount of well-connected hubs, which are sur-

rounded by less connected satellites, which form clus-

ters. Those clusters are connected to one another via

the hubs and the nodes that belong to several commu-

nities at once.

Graph layout a qualitative measure for identifying

topology of a network. A very useful type of layout

is Force Atlas, where the most connected nodes with

the highest degree are pushed apart from each other,

while the nodes that are connected to them but have

lower degree are grouped around those hubs. After

several iterations this sort of layout produces a very

readable representation of a network, which can be

used to better understand its structural properties and

identify the most inﬂuential groups, differences be-

tween them, and structural gaps within networks.

AET 2020 - Symposium on Advances in Educational Technology

422

Network motifs are the different types of constel-

lations that emerge within network graphs. They can

provide a lot of useful information about the structural

nature of networks.

For example, some networks may be comprised of

diads or pairs of nodes (which indicates that the level

of overall connectivity is quite low). Some other net-

works can have a high proportion of triads, which usu-

ally indicate the presence of feedback loops, which

makes the resulting network formations much more

stable. More complex formations include groups of

four nodes that can be connected as a sequence or

between each other, forming interconnected clusters

that can encode certain levels of complexity that go

beyond simple triad feedback constellations.

It is important to take notice of the network motifs

that emerge within a network because it will provide

a very good indication of the level of complexity and

thus the capacity of the network.

Modularity is a quantitative measure that indicates

the presence of distinct communities within a net-

work. If the network’s modularity is high, it means

it has a pronounced community structure, which, in

turn, means that there’s a space for plurality and di-

versity inside. If the modularity is too high, how-

ever, it might also indicate that the network consists of

many disconnected communities, which are not glob-

ally connected, making it much less efﬁcient than an

interconnected one.

Modularity works through an iterative algorithm,

which identiﬁes the nodes that are more densely con-

nected to each other than to the rest of the nodes

in the network. It will then calculate the measure

of modularity for the network at large. The higher

this measure is, the more distinct those communities

of densely connected nodes are. If the modularity

measure is 0.4 or above it means that, the commu-

nity structure in the network is quite pronounced. If

it’s less it means that there are no big differences be-

tween the different clusters and most of the nodes are

equally densely connected to each other across the

whole network.

So far we’ve looked at the different measures of

connectivity that exist within networks and that help

us identify the most inﬂuential nodes, clusters, and

deduce some basic functional properties of the net-

works we study.

However, one of the most important aspects of

network graphs is that they also let you see the gaps,

empty blank spaces, between the islands. Those gaps

are usually referred to as “structural gaps” and it has

been shown that bridging those gaps can spur innova-

tion, create most interesting collaborations, and give

rise to new, unexpected ideas.

In other words, “structural gaps” is where creativ-

ity and potential is hidden within the network. There-

fore, when visualizing a network it is important to

identify those structural gaps and to devise differ-

ent actions that could help bridge different nodes and

clusters across those empty spaces within the graph in

order to spur creativity and innovation.

3 RESULTS AND DISCUSSION

A study of the dynamics of the popularity of the term

“network science” from 2004 to 2020 using Google

Trends (Google, 2021), carried out at the time of writ-

ing this manuscript, showed a steady trend (ﬁgure 4).

Of queries, which hold an average of about 80 con-

ventional units, while the mark 100 corresponds to

the largest volume of requests.

As an example of modeling semantic knowledge

networks, we analyze the relationship between the

concepts of academic disciplines. As you know, that

discipline mastering is closely connected with the as-

similation and comprehension of the course concept

thesaurus. To assimilate further concepts within the

framework of this discipline, it is necessary to under-

stand the already learned, often in the framework of

the already studied disciplines. Therefore, an actual

task is to study the dependencies between concepts

and to model them, using cognitive networks (Gephi,

2020a).

The ﬁgure 5 shows a fragment of the construction

of a semantic knowledge network.

To implement the subject area model in the form

of a semantic knowledge network, we propose the fol-

lowing algorithm:

(1) Classiﬁcation of all concepts of the subject

area into macro concepts (class of concepts),

meta-concepts (generalized concepts) and micro-

concepts (elementary concepts).

(2) The allocation of common properties, characteris-

tics inherent in each level of concepts.

(3) Highlighting the hallmarks of each level of con-

cepts.

(4) Establishing links between concepts related to the

same level.

(5) The allocation of inter-level ties.

We have analysed 125 concepts that are necessary

for the “Economic Cybernetics” discipline mastering

and the relationship between them (communication

means the need for one concept to master another).

We conducted a similar study for 125 concepts of the

Analysis and Application of Semantic Networks in Education

423

Figure 4: Dynamics of the popularity of the query “network science” in Google Trends (Google, 2021).

“Algorithmization and Programming” and 125 con-

cepts of the “Mathematical Analysis” discipline.

There are many systems used by analysts (mainly

researchers), both for visualizing network structures

and for performing computations. At the time of

this writing on Wikipedia (Wikipedia, 2021), we have

counted 89 links to various programs for analyzing

complex networks. To select the most popular pro-

grams, we turned to the analysis of software tools that

are used by the world’s leading universities (Gephi,

2020b; iGraph, 2021; NetworkX, 2021; SNAP, 2021).

These can be ready-made products with a user inter-

face and a set of implemented functions, as well as

libraries of computational methods. Some systems

developed for scientiﬁc research are brieﬂy described

in the table. All considered systems, except Gephi,

do not have a user interface and are simply libraries

of computational functions for analyzing and visual-

izing graphs (table 2).

After a comparative analysis, the results of which

are presented in the table, the obtained graphs were

visualized using the Gephi software product (Yevin,

2010). Gephi is free open-source, leading visualiza-

tion and exploration software for all kinds of networks

and runs on Windows, macOS, and Linux. It is highly

interactive and user can easily edit the node/edge

shapes and colors to reveal hidden patterns. The aim

of the Gephi is to assist user in pattern discovery and

AET 2020 - Symposium on Advances in Educational Technology

424

Figure 5: The semantic knowledge network diagram.

hypothesis making through efﬁcient dynamic ﬁltering

and iterative visualization routines.

Gephi allows to calculate the topological charac-

teristics of the graph, as:

• Nodes and edges (what networks are made of).

• Clusters (groups of nodes that are connected).

• Degree (the number of connections that the node

has).

• Centrality between (how inﬂuential a node is).

• Modularity (community structure).

Gephi comes with a very fast rendering engine and

sophisticated data structures for object handling, thus

making it one of the most suitable tools for large-scale

network visualization. It offers very highly appealing

visualizations and, in a typical computer, it can eas-

ily render networks up to 300 000 nodes and 1 000

000 edges. Compared to other tools, it comes with a

very efﬁcient multithreading scheme, and thus users

can perform multiple analyses simultaneously with-

out suffering from panel “freezing” issues.

In large-scale network analysis, fast layout is a

bottleneck as most sophisticated layout algorithms

become CPU and memory greedy by requiring long

running time to be completed. While Gephi comes

with a great variety of layout algorithms, OpenOrd

(Martin et al., 2011) and Yifan-Hu (Hu, 2005) force-

directed algorithms are mostly recommended for

large-scale network visualization. OpenOrd, for ex-

ample, can scale up to over a million nodes in less

than half an hour while Yifan-Hu is an ideal option

to apply after the OpenOrd layout. Notably, Yifan-

Hu layout can give aesthetically comparable views to

the ones produced by the widely used but conserva-

tive and time-consuming (Fruchterman and Reingold,

1991). Other algorithms offered by Gephi are the cir-

cular, contraction, dual circle, random, MDS, Geo,

Isometric, GraphViz, and Force atlas layouts. While

most of them can run in an affordable running time,

the combination of OpenOrd and Yifan-Hu seems to

give the most appealing visualizations. Descent vi-

sualization is also offered by OpenOrd layout algo-

rithm if a user stops the process when 50–60% of

the progress has been completed. Of course, efﬁcient

parameterization of any chosen layout algorithm will

affect both the running time and the visual result.

The constructed graphs (ﬁgures 6–8) can be used

to identify the most important concepts that have the

highest degree of apex, as well as concepts that are in

the way of studying other important course concepts.

In ﬁgures 6, 7 and 8 the size of the nodes-concepts

of semantic knowledge networks characterizes the de-

gree of importance and fundamentality of the corre-

sponding terms of the academic discipline.

The table 3 shows various metrics and methods for

calculating them. For the obtained graphs, their topo-

logical characteristics were calculated and analysed.

The results of the study are shown in table 4.

Let us analyse the found values of measures (ta-

ble 4). The Network Density measure is a measure

of the density of edges, calculated as the ratio of the

number of edges of a graph to the corresponding num-

ber of vertices and determines the maximum number

of edges in a given graph. Thus, the values 0.17 – for

the graph of discipline “Economic cybernetics” and

0.2 – for the “Mathematical Analysis” means that the

edges are ﬁlled with about 17.3% and 19.5% of the

maximum possible respectively. The density of the

Analysis and Application of Semantic Networks in Education

425

Table 2: Comparative characteristics of systems for analyzing network structures.

Gephi Igraph NetworkX SNAP

Website gephi.org igraph.sourceforge.net networkx.lanl.gov snap.stanford.edu

Users Scientiﬁc, Educational Organizations

Data Vol-

umes

Up to 1 million

nodes and edges

Up to several million nodes and edges

Data Col-

lection

None

Data

Sources

None

Analysis

Mode

Retrospective Analysis

Methods Visual Analysis,

Basic Statistical

Methods, Basic

Methods of Graph

Theory

A wide range of graph theory methods

Objects

Considered

Network structure (nodes, directional and non-directional links)

Distribution

Terms

OpenSource

(CDDL 1.0, GPL

3.0)

OpenSource

(GPL 2.0+)

OpenSource (BSD License)

Language

support

English

Developer Gephi Consortium

(more than 10 or-

ganizations). USA,

France, Germany,

etc.

abor Cs

ardi (Har-

vard University,

USA), Tam

Nepusz (E

otv

University, Hun-

gary)

AricHagberg, Dan

Schult, Pieter Swart

and others

Stanford University

Clients Used in research

projects, data vi-

sualization and

educational pro-

grams.

Used in research

projects

Scientiﬁc organiza-

tions

Used in research

projects, in partic-

ular by Stanford

University

graph of concepts of the discipline “Programming” is

less: 11%, which can be explained by a smaller num-

ber of connections between concepts on average in the

graph.

The maximum degree of 121 vertices was demon-

strated by the concept graph in the “Programming”.

The maximum value of the degree of the vertex in

the column “Economic cybernetics” – 111. The mini-

mum degree of vertices in the graphs “Economic Cy-

bernetics” and “Programming” are 3 and 1, respec-

tively, which are almost the same. For “Mathematical

Analysis”, the number of weakly connected nodes is

higher – 7, and strongly connected – 113, which is

less than in “Programming”, but more than in “Cy-

bernetics”.

It also conﬁrms a greater connection between the

concepts of the “Economic cybernetics” and “Pro-

gramming” than the concepts of the “Mathematical

Analysis”.

Mean average node degree for the “Economic Cy-

bernetics” graph is 21.45, and for the “Programming”

graph – it is 13.66 and for the “Mathematical Anal-

ysis” – 24.18. This is conﬁrms the presence of more

connections in the last graph.

The global clustering coefﬁcient (clustering) for

a graph is the ratio of the number of vertically con-

nected triples of vertices to the number of triangles

(cyclically connected triples of vertices). For the

“Economic Cybernetics” graph, the clustering coefﬁ-

cient is 0.4, for the “Programming” graph – it is 0.33,

and for the “Mathematical Analysis” – 0.59. This

means that the concepts of the “Mathematical Anal-

ysis” course are more often on the path to mastering

other important concepts.

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426

Figure 6: The semantic knowledge network of the course concepts “Economic Cybernetics”.

Figure 7: The semantic knowledge network of the course concepts “Algorithmization and Programming”.

As for the diameters of the graphs – for the “Eco-

nomic Cybernetics” concept graph the diameter value

is 5, for the “Programming” graph – 9 and for “Mathe-

matical Analysis” – 3. The same relationships are ob-

served for average shortest path-lengths. Which may

mean the existence of longer paths in the connections

between the “Programming” discipline concepts.

The modularity index is less than 0.4, which

means that the structure of communities in all three

networks is not sufﬁciently expressed.

In the ﬁeld of education, there is always a problem

of the contradiction between increasing the amount of

scientiﬁc information and limiting the time allotted

for its assimilation. Teaching academic disciplines

in higher education requires constant work on edu-

cational information in order to move from extensive

to intensive teaching methods. One of the ways to

intensify the educational process can be the optimal

“packaging” of educational information.

The solution to this problem is the construction

of a semantic network. An important condition for

the successful mastering of educational material is the

ability of the teacher to highlight the key issues of the

program. Nodal issues of the program are the basis

for studying the whole topic. Their signiﬁcance can

be determined using a graph or adjacency matrix.

For example, let a topic contain 6 questions and

the logical connections between them are presented

Analysis and Application of Semantic Networks in Education

427

Table 3: Metrics used for network analysis in Gephi.

Metric How calculated

Nodes Nodes contain discipline concepts. Sim-

ple count.

Weakly

Con-

nected

Number of maximally sized clusters in

which each node is reachable from every

other node along undirected edges.

Strongly

Con-

nected

Number of maximally sized clusters in

which each node is reachable from every

other node along directed edges.

Diameter Longest ﬁnite optimal path between

nodes using undirected edges.

Average

Short-

est Path

Length

Average Shortest Path Length (along

undirected edges) between all connected

nodes.

Network

Density

Fraction of all possible undirected edges

present.

Average

Degree

Average number of undirected, un-

weighted edges per node.

ModularityCalculated using Gephi algorithm.

Clustering

Coefﬁ-

cient

A node’s clustering coefﬁcient is the ra-

tio of the number of actual connections

between the node’s neighbours, to the

number of the maximum potential con-

nections between those neighbours. The

network’s clustering coefﬁcient is the

average of the clustering coefﬁcients for

all the nodes.

Table 4: Comparison topological characteristics of the

graphs of the relationship between the concepts of the disci-

plines: “Economic Cybernetics” (E), “Algorithmization and

Programming” (P) and “Mathematical Analysis” (M).

Parameters E P M

Nodes 125 125 125

Weakly Connected 3 1 7

Strongly Connected 111 121 113

Diameter 5 9 3

Average Shortest Path

Length 2.21 3.416 1.806

Network Density 0.17 0.11 0.20

Average Degree 21.45 13.66 24.18

Modularity 0.25 0.30 0.23

Clustering Coefﬁcient 0.40 0.33 0.59

in the form of an adjacency matrix (table 5).

The signiﬁcance of the question can be character-

ized by the weight coefﬁcient determined by the for-

mula:

= S

/k,

where S

is the number of references to the i-th ques-

tion when studying the others contained in this topic,

k is the total number of questions in this section.

Table 5: Example topic adjacency matrix.

0 1 1 0 0 1 3/6

0 0 1 1 1 1 4/6

0 0 0 1 1 0 2/6

0 0 0 0 1 0 1/6

0 0 0 0 0 0 0

0 0 0 1 0 0 1/6

The larger the coefﬁcient leads to the greater the

signiﬁcance of the issue. Thus, it is possible to deter-

mine the importance of the discipline (section) in the

study of all disciplines of the curriculum. A similar

technique can be used in the formation of the content

of academic subjects on the basis of discipline stan-

dards, in the development of curricula and tests, in the

selection and organization of educational information

for training.

4 CONCLUSIONS

Algorithms for the formation of a semantic knowl-

edge network are developed. The knowledge network

is the basic concept of knowledge management. In

fact we introduce a new discipline that implements

the principles of sustainable development of educa-

tion. The method of constructing a semantic knowl-

edge network of terms allows forming a so called ad-

jacency matrix that reﬂects the correlation of terms

from a terminological dictionary. This matrix allows

to evaluate the quality of the terminology in the par-

ticular discipline, as well as to determine quantify the

semantic connectivity of the whole tutorial. Accord-

ing to obtained results, we can conclude that the con-

cept system in the “Economic Cybernetics” is con-

nected and complex. This means that in this case

when studying any concepts, it is necessary to re-

peat the meaning of those already studied. The con-

cept system in the “Programming” contains fewer de-

pendencies and less connectivity in comparison with

graphs. However, the experience of studying these

disciplines indicates that also the “Programming” is

not easy to learn. Further the problem of planning

the learning process based on semantic networks of

knowledge will be studied. Namely, the distribution

of lectures, practical and laboratory exercises will be

determined to achieve successfully the learning ob-

jectives.

We can continue to analyse the network structure

of the curriculum. The curriculum is a complex sys-

tem with nodes representing courses and links be-

tween nodes, course prerequisites. The latter is easy

to obtain from the course catalogue. The resulting

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428

Figure 8: The semantic knowledge network of the course concepts “Mathematical Analysis”.

network of curriculum prerequisites is in the form of

a directed acyclic graph. This graph has certain ana-

lytical characteristics. In future work, we will to cal-

culate spectral characteristics of graphs for the studied

disciplines, as it was done in (Soloviev et al., 2020).

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