2.1 Database surveyed

The journal selected for the systematic review was the RBEE maintained by the Brazilian Association of Researchers in Special Education (Associação Brasileira de Pesquisadores em Educação Especial - ABPEE). A national journal that disseminates knowledge and the interchange among researchers in the field of Special Education and related areas, through publications of research papers, review papers, essays and book reviews. It was founded in 1992 and, until the end of 2017, had 23 volumes with a quarterly publication (^{ABPEE, 2018}).

The choice of the journal is justified for the following reasons: it is a reference in the area of ​​research in Special Education and inclusion in Brazil; it is classified in relation to Qualis issued by the Capes as A2 in the area of ​​education and A1 in the area of ​​Teaching and has been incorporated into the Scientific Electronic Library Online (SciELO), where the most recent editions of the journal are available. The access took place on two websites: ABPEE official website, which provides journals from 1992 to 2006, and SciELO website, from 2005 until today. The studies included in the research had to: (1) be published in the RBEE; (2) contain the keywords and have a summary - for this criterion, data were collected from 1999 to 2017, as only from 1999 onwards the keywords were systematically included in the papers; and (3) have an empirical research design. In refining the search, the following were excluded: (1) papers published in the RBEE since January/2018 and (2) type of paper with essay design, literature and bibliographic review, book review and experience report.

2.2 Procedure

In this subsection, we discuss how data collection took place; then, on the definition of search terms and keyword treatment; and, finally, on the instruments used in data analysis.

3.1 Density, clustering and other metrics

In Table 1 below, it is possible to identify the structural characteristics of the KW network. The 615 KWs found, after the standardization process, were reduced to 527. 2,374 combinations of KW pairs (referred to as adjacent KWs) were identified, 899 of which were duplicated, with an average of 3.94 KWs per paper. The network density index is low, since it has a value equal to 0.012 and the density result varies from a range between 0 and 1, indicating how the vertices are interconnected in the network. The density of the graph is calculated by dividing the number of total connections by the maximum number of possible connections, the more connections existing, the denser the network (^{Hanneman & Riddle, 2005}).

The low density of the network, verified in the value of 0.012 (Table 1) and pointed out in the graph (Figure 1), indicates that there is a smaller number of vertices connected to all the others and a diversity of different clusters. Thus, the less dense network has a high rate of clustering. The score reached was high (0.84), which shows that the network is not connected at a global level, but has a high number of clusters, in which internally its elements (KWs) are densely connected, which is expressed in the topology of Figure 1. By observing these two data (density and clustering) in a complementary way, the low density of the KW network can be considered positive, as it reveals a diversity of variables being investigated in national surveys regarding the Special Education area; and the high index of clustering indicates this diversity, pointing to the fact that the number of researchers developing unprecedented and innovative research in this area is growing, showing how dynamic this subarea is. This aspect also indicates that the Special Education area is formed by subareas that are able to develop more intense communication, clusters in which the transit of knowledge in the network is intercommunicated in a better way.

In the network graph shown below (Figure 1), resulting from the association between the KWs, it is possible to verify the existence of seven components. A component of a network is the isolated subnet in which the nodes are connected to each other, but are not connected to any other subnet within the total network (^{Hanneman & Riddle, 2005}). In other words, within a component, all nodes are accessible to each other, but are disconnected from the other components of the network (^{Wasserman & Faust, 1994}); therefore, it appears that the knowledge network present in the RBEE is composed of seven groups of knowledge that do not trace any type of relationship. The number of components informs about the intercommunication of concepts within a given field or, conversely, the existence of theoretical, conceptual and/or methodological barriers. Subsequently, the fields or communities of knowledge involved in these components will be discussed.

Figure 1 Communities of subgraphs produced from the RBEE network. 

The diameter, represented by the maximum geodesic distance, presents the linear size of the network and provides the notion of the distance between the information or ideas that circulate in it. The maximum distance between two KWs in the network had a value of 5. The network obtained in the research has a small world pattern, that is, it has a high coefficient of clustering and a small average distance. The heuristic for determining a small world network according to ^{Watts and Strogatz (1998)} is that the average Clustering Coefficient (CCij) is greater than the density of the graph (CCrg). In this network, CCij = 0.84> CCrg = 0.012 were obtained. The network also fulfills the small world requirement since, in the network of size N (number of keywords) with an average path length of L, it fulfills the distance requirement for a small world network if L <1 + log100 N (^{Yi & Choi, 2012}). In this case, “L” fulfills the requirement of a small world: 2.28 <2.36. This also implies a high probability that two words linked to one another are, themselves, linked together.

In another sense, the structuring of the knowledge network present in the RBEE has a profile of free scale (^{Barabási & Albert, 1999}). Figure 2 below shows the dispersion graph of the degree centrality (G) of the vertices, that is, the number of connections that one KW has with the others. The linear relationship presented here implies that the KWs follow a degree distribution of the power law in which the probability that a keyword has x connections is proportional to x - γ (^{Barabási & Albert, 1999}). This data is congruent to the work of ^{Yi and Choi (2012)} for the information technology area, in which, in such networks, most KWs have a small number of connections, but certain KWs are associated with a large number of KWs.

The curve formed in Figure 2 is different from a Gaussian curve; thus, the association between KWs does not appear to be random, but rather characteristic of a preferred connection. Networks with this profile have vertices with degrees of connectivity based on a power law in which most vertices have low connectivity (^{Barabási & Albert, 1999}). In systems of this type, the vertex connectivity distribution tends to follow a preferential connectivity principle, since the greater the number of connections of a KW, the greater the probability that other KWs will preferentially connect to it. This pattern has been evidenced in biological, neural, linguistic and internet networks and tends to form more robust networks (^{Albert & Barabási, 2002}; Barabási & Bonabeau, 2003; Barabási, 2009). We will return to this question later, presenting the characteristics of KWs in terms of networks.

Figure 2 Degree of distribution of KW networks present in the main component of the RBEE network. 

Being a network with a free scale profile, does it also have a hierarchical pattern or not? Many complex systems have an almost decomposable hierarchical structure (modular architecture) - the architecture in modules allows for understanding of the systems and their parts (^{Simon, 1962}). In order to identify the presence of hierarchy, it is necessary to consider the correlation between the G of each keyword and its local grouping coefficient, which demonstrates a measure of the degree of the hierarchical structure. Figure 3 below shows the correlation between the degree of each keyword and the clustering coefficient on a base 100 logarithmic scale. On the one hand, in hierarchical networks, the correlation between the local clustering coefficient (connection density at a given vertex) and degree (the number of connections) exhibits scale behavior; on the other hand, in non-hierarchical networks (such as an electrical network), they usually exhibit constant grouping (^{Ravasz & Barabási, 2003}; ^{Ravasz, Somera, Mongru, Oltvai & Barabási, 2002}). The results found in the RBEE network show a linear correlation, that is, it demonstrates that KW networks have a hierarchical structure (^{Ravasz et al., 2002}).

Figure 3 Correlation between the clustering coefficient and Degree centrality. 

As conceived by ^{Yi and Choi (2012)}, this structural characteristic provides clues about the generative mechanism underlying the organization and evolution of scientific knowledge. First of all, small groups of concepts are organized hierarchically in increasingly larger groups, which results in two fundamental characteristics of the network: a high degree of grouping and a topology without scale, as proposed by Ravasz and ^{Barabási (2003)}. The modular structure found is indicative of sub-specialties that can be decomposed, but as they participate in the same cluster, they can be integrated into a more complex network.

3.2 Communities of concepts

Due to the characteristic of the network with a free scale standard, there are obviously KWs more connected to each other than to other KWs, thus constituting clusters with greater internal than external connections, which in Social Network Analysis (SNA) is called communities, here, analogously, these are communities of concepts. A community is understood as a group of vertices that have common properties, and/or perform a similar function within a network (^{Justel, Maia, Nobre, & Oliveira, 2014}). The mathematical formulation for determining communities in a network is called graph clustering. In complex networks, communities, also called modules or clusters, are groups of vertices that probably share common properties and/or follow similar rules within the network (^{Fortunato, 2010}).

The problem of community detection lies in the better division of the network into partitions of the set of densely connected vertices. The algorithm used here was a “greedy” algorithm, as it has an agglomerative profile, unites nodes/communities recursively. The CNM algorithm (^{Clauset, Newman, & Moore, 2004}) seeks to partition the graph in communities in such a way that modularity is maximized. Modularity is a property of a network and a proposal to divide that network into communities, it measures when the division is good, in the sense that there are many edges within the communities and only a few between them.

Figure 1 presented above represents the clusters generated by the CNM algorithm in the RBEE network. The resulting clusters of the algorithm are in different quadrants and colors, the vertices of the clusters belonging to the same (main) component are presented in a sphere shape and the rest in a square shape. The total number of vertices in each cluster is represented in the lower right corner of each quadrant. The thickness of the edges indicates the frequency that pairs of KWs are repeatedly encountered. The connection between the clusters is represented by the gray lines and the greater the thickness of the line, the greater the frequency of connection between them. The sizes of the vertices are related to the value of their centrality of intermediation (CI), which reveals how much a vertex is in the path of others, representing the importance of KW in establishing bridges between other subsets of KWs.

It is noteworthy that, in a network perspective, a KW is configured as a vertex and its popularity is measured by the network variable centrality of intermediation, a metric that assesses the importance of a KW to establish “bridges” between KWs or clusters of KWs. For example, a KW that is between two different research topics (that is, groups of closely related KWs) will have a high intermediation centrality index, based on the analysis made through the Graph Theory. As can be seen in Figure 1, 18 clusters were found. It should be noted that part of these clusters make up the seven components found in the network, so that, of the 18 clusters, 12 form a single component (because there is a connection between these clusters, represented by the gray outline in the graph) and the other 6 form subgroups without any type of communication (edges) with the others (positioned close to the lower right corner). It appears that this large component covers a total of 95% of the network’s KWs. Clusters reveal the communities of concepts within a network of keywords, the presence of clusters in that network expresses evidence of a close relationship between the keywords of the various research published in the journal, evidence of a theoretically pertinent articulation.

3.3 KW analysis

In the previous sections, global structural aspects of the network were discussed. In this section, properties at the vertex level (keywords) are discussed. Table 2 below describes the degree centrality (number of links that a keyword has with other KWs in the network) and the centrality of intermediation of the 21 highest KW values found.

As can be seen, the keyword Special Education is the main hub in the investigated knowledge network, as it has the highest IC score. It is understood that intermediation represents a more precise measure in terms of the power of a KW in a knowledge network. Considering the values ​​of the 21 largest IC, it appears that the main disabilities that mediate the knowledge network are: mental disability, Down Syndrome, deafness, hearing impairment, vision disorder and cerebral palsy. Aside from the disabilities, categories of KWs that move around teaching and education are highlighted: special education, inclusive education, regular education, gifted students, students with disabilities, elementary school, special classes and curriculum; and of concepts, fundamental rights and contexts involved: inclusion, people with disabilities, special needs, work and families.

With regard to the fields or communities of knowledge identified in the 12 main clusters, from the different papers that were part of this review (Figure 1 and Table 2), it was found that the cluster with the largest number of KWs is 1, but the keyword Special Education centralizes this field of knowledge, which makes most peripheral vertices of little importance in terms of intermediation - there is a much greater asymmetry here when compared to other clusters. Centralized profile networks tend to have a high degree of dependence on the intermediary vertex, since it controls the flow of intermediation in the network. In another sense, Cluster 2 has a smaller number of KWs, however it has a higher density, better distribution of IC, it has in its list six of the KWs with a higher IC and, comparatively, has a higher frequency of KWs with ICs above 0.001. Such networks with a more distributed profile tend to be more resistant due to the diversity of existing integration paths, as they are more distributed, have greater transitivity and, therefore, are more dynamic, since they allow more innovative articulations. However, this is an assessment only regarding the structural character of the network. The Table 3 below summarizes the main KWs of each cluster according to their IC.

The Table 3 shows that, in many of the clusters, there are underlying main themes. Particularly in the cluster with greater dynamics (2), there is an integration of aspects, variables, methods, concepts, disabilities, which are related to the issue of school inclusion in regular education (KWs with higher IC in the group). This is the area of ​​greatest challenge at the same time and it is not surprising for its dynamics of intercrossing issues in the knowledge network. As an example, the papers published in the RBEE and their respective citation in Google Academic until March/2019 stand out in this line: “School inclusion, teacher training and consultancy based on educational social skills” (^{Rosin-Pinola & Del Prette, 2014} - cited 39 times), “Assisted assessment for children with special educational needs: an auxiliary resource for school inclusion” (^{Enumo, 2005} - cited 81 times) and “Pedagogical action and special education: the resource room as a priority in the provision of specialized services” (^{Baptista, 2011} - cited 107 times), which discuss the challenges imposed to the implementation of strategies in the school environment, from the provision of educational services and resources to the actions of educators for the effective inclusion of students with different types of disabilities, with a view of breaking with the traditional teaching model.

In another perspective, it is possible to verify some pairs of KWs more frequently associated with the knowledge network (Figure 4 below). The recurrence informs about the tradition of association between the themes involved. As it is possible to verify by the high value of IC of the keyword Special Education, many associations between themes are intermediated through this keyword. However, it is possible to verify that, in addition to the intermediation power exercised by the keyword Special Education, there are other interchanges independent of this that are carried out between the KWs Assistive Technology, Cerebral Palsy, Inclusive Education, Deafness and Brazilian Sign Language; and between Down Syndrome, Families and Inclusion.

Figure 4 Pairs of keywords repeated over 4 times in the knowledge network. 

In Figure 4, it can be seen that the KWs have different sizes - in this case, the larger the size of the vertex, the greater its intermediation power. This type of centrality indicates the vertices located in a position of intermediation to other vertices. In the investigated network, the degree of participation of the most important KWs is presented, with the function of establishing links with other KWs or subgroups, acting as important elements in this structure.

The recurrence of association between KWs indicates specific niches of the publication knowledge network in the RBEE; the line thickness indicates more intense recurrences of association of KW pairs, which, in this case, are more outstanding with the keyword Special Education (Inclusion; Deafness; Inclusive Education; Intellectual Disability; Cerebral Palsy; Vision Disorders; School Inclusion and People with disabilities). As can be seen, half of the major recurrences refer to disabilities. These are the most intersected thematic fields. The striking association between these keywords creates semantic fields with a greater tradition of research.