In this paper, we propose a new Social Network Analysis based approach to providing a multi-dimensional picture of the research scenarios of a set of countries of interest and to detecting possible “research hubs” operating therein. This knowledge allows innovation managers to understand the impact of different socio-economic conditions on the research level of a country. Furthermore, it may help the design of policies for supporting the accumulation of scientific and technological capabilities. In the last part of this paper, we apply our approach to four North African countries (i.e., Algeria, Egypt, Morocco and Tunisia) in such a way as to show its potential.
In the last years, scientometrics and bibliometrics received a growing interest
both in research literature and as objective ways for evaluating the performances
of researchers, universities, institutions, etc. [
This paper aims at providing a contribution in this setting. Indeed, it
proposes a new Social Network Analysis based approach to extracting knowledge
about research scenarios and spillovers [
This paper is organized as follows. In Section 2, we illustrate our approach. In Section 3, we apply it to the four North African countries mentioned above. Finally, in Section 4, we draw our conclusions and overview some possible future developments. 2
Our approach operates on a set P ub of publications at our disposal and on a set C of countries to investigate. It will be described in the next subsections. 2.1
In this section, we aim at defining a method for detecting both hubs and their features in a set of countries. For this purpose, we preliminarily introduce a first support data structure. It is a social network: G = ⟨N; E⟩. N is the set of the nodes of G. A node ni ∈ N corresponds to exactly one institution registered in our database. Since there is a biunivocal correspondence between a node of N and the corresponding institution, in the following, we will use the symbol ni to indicate both of them. Each node of N is labeled with an element of C depending on the country of the corresponding institution. We indicate by li the label of ni. E is the set of the edges of G. There exists an edge eij = (ni; nj; wij) ∈ E if there exists at least one publication involving one author of ni and one author of nj. wij is the weight of eij; it denotes the number of publications having at least one researcher of ni and one researcher of nj among their authors. If a paper has more than one author of the same institution ni, then there is a self-edge linking ni with itself.
Now, we are able to introduce the concept of hub. With regard to this fact, we point out that we do not aim at proposing a new concept, characterized by a mathematical foundation supporting it. Instead, we would like to introduce an informal and empirical, yet reasonable, concept, which can support innovation managers to make their decisions. In carrying out this activity, we strongly benefited from the observations, suggestions and experience of innovation management researchers, who guided us in its formulation. Taking this purpose into account, we can say that, in order to be a hub, an institution must satisfy the following conditions: (i) C1: it should have published a very high number of papers; (ii) C2: it should have published a high number of papers in cooperation with institutions different from the ones of its country; (iii) C3: it should have published many papers in cooperation with institutions of its country.
To “quantify” conditions C1, C2 and C3, we use three metrics, namely M1, M2
and M3, respectively. M1 coincides with the classical weighted degree centrality,
M2 coincides with the normalized weighted degree centrality and M3 is analogous
to the E-I index [
As theoretically conjectured in the past literature, and as verified for the countries composing our case study, M1, M2 and M3 follow a power law distribution. Taking all these considerations into account, the set HX of hubs for the countries into consideration can be defined as the set of those institutions simultaneously belonging to the top X% of the institutions with the highest values of M1, M2 and M3 (we call I1X , I2X and I3X these three sets, when considered separately). In this definition, X is a threshold allowing the selection of the institutions having the highest values of M1, M2 and M3. The choice to use X as a threshold parameter derives from the power law distributions characterizing all the three metrics. Reasonable values of X could be 10, 15 and 20. After several experiments, we decided to consider a default value of X equal to 20. As a consequence, in the following, when X is not specified, we intend that it is equal to 20. Below, we use the symbol HkX to indicate the hubs of a given country k. 2.2
In this section, we aim at analyzing the research scenarios of the countries into examination. Initially, we can introduce three indicators that could give us some knowledge about the research scenarios of the countries into consideration. The first one, RQ, is an indicator of the overall research quality in the countries of interest. In fact, it measures how many institutions of I1 belong to these countries. The second one, F C, indicates how many institutions, among the top ones of the countries of interest, publish many papers with foreign institutions. The third one, T P , indicates how many institutions that publish very much with foreign institutions belong to the top institutions of the countries of interest.
In the investigation of the research scenario of a country k and of the role of its hubs, it appears very interesting to analyze its paper distribution. For this purpose, we introduce the average number AvgP ubkH of the publications of its hubs. Another interesting issue to investigate is to verify if a hub of k publishes more with institutions of k (we call “internal” the corresponding publications) than with foreign ones (we call “external” the corresponding publications) or alone. To carry out this investigation, we introduce: (i) the average number AvgHubP ubIk of publications performed by the hubs of k with institutions of k; (ii) the average number AvgHubP ubkF of publications performed by the hubs of k with foreign institutions; (iii) the average number AvgHubP ubkA of publications performed alone by the hubs of k (we call them “alone publications” in the following).
A further interesting analysis is devoted to understand if, in their cooperation with foreign institutions, the hubs of a given country k privilege one or few countries. For this purpose, we specialize to our research context the Herfindahl Index. This index is very used in economics. It is defined as the sum of the squares of the market shares of the firms within the industry, where market shares are expressed as fractions. It can range from 0.0 to 1.0, moving from a huge number of very small firms to a single monopolistic producer. In our case, we extend the Herfindahl index to our context and define the Herfindahl Index HIk associated with the papers published by the hubs of k to verify if these hubs published in cooperation with institutions of few (implying high values of HIk) or many (implying low values of HIk) countries. 2.3
In this section, we aim at investigating the cooperation levels of the hubs of a given country k. For this purpose, we preliminarily define a support data structure called clique social network. In particular, let G be the social network defined in Section 2.1 and let Gk be its “projection” on the country k. Let Ck be the set of cliques of Gk and let Hk be the set of the hubs of k. A clique social network CGk has a node for each hub of Hk belonging to at least one clique of Ck. Each node ni of CGk has associated a weight wi denoting the number of cliques of Ck which it belongs to. An edge (ni; nj ) of CGk denotes that ni and nj together belong to at least one clique of Ck.
Some measures capable of quantitatively representing the differences that characterize the cooperation among hubs are the following: (i) the number of cliques |Ck|; (ii) the absolute dimension dCk of the largest clique in Ck; (iii) the relative dimension dCk of the largest clique in Ck; (iv) the fraction fCHk of hubs |Hk| belonging to at least one clique of Ck. In order to avoid that results are biased by the number of publications (which can be very different in the different countries of interest), we defined a normalized version CdGk of CGk. Finally, we searched for some measures to compare clique social networks. After several experiments, we found that the most significant ones were: (i) the number of nodes; (ii) the number of edges; (iii) density4. 2.4
All indicators introduced above are based only on the number of publications. Actually, it would be important to take also their quality into account. One way to do this consists in taking their impact factor into consideration; another way consists in considering the number of citations received by papers. Impact factors are measured only for journal papers. As a consequence, if we want to exploit this measure, we must define a new support data structure. This structure, that we indicate by G′, is, once again, a social network. It is defined as G′ = ⟨N ′; E′⟩. 4 Actually, this last measure can be derived from the two other ones. However, it is very expressing and, consequently, we decided to explicitly consider it. There is a node ni ∈ N ′ for each institution having at least one author, who published at least one journal paper. An edge e′ij = (n′i; n′j; wi′j) has a semantics similar to the one of eij except that the weight wi′j = ∑p∈(P ubij∩JP ub) IFp considers both the number of publications performed by ni and nj simultaneously and the corresponding impact factors. Paper citations are valid both for conference proceedings and for journal papers. However, in order to make our analyses about the quality of publications homogeneous, we chose to investigate only journal papers. In this case, we used the same support social network as the one exploited for impact factors, but the edge weights wi′j was computed as: wi′j = ∑p∈(P ubij∩JP ub) CitNp, where CitNp is the number of citations of p. 2.5
A first parameter useful to characterize hub neighbors is the average number AvgP ub of publications of the hub neighborhoods. A second parameter regards their average dimension AvgDim. Even in this case, we disaggregate data per country, and we call AvgDimk the corresponding parameter for the country k.
A next analysis regards the cooperation level among the institutions belonging to hub neighborhoods. To perform this task, we define a new support social network. We call it nbh social network and we represent it by means of the symbol N bhGi. Given a neighborhood nbhi, the corresponding nbh social network is defined as follows: nbhGi = ⟨nbhi; nbhEi⟩. There is a node in N bhGi for each node of nbhi; there is an edge (ni; nj) ∈ nbhEi if there exists at least one publication between an author of ni and an author of nj.
After having introduced this social network, we define a first parameter on it. This parameter is called AvgCF rac and corresponds to the average fraction of the real number of cliques existing in hub neighborhoods against their possible number. It is an indicator of the cooperation level among hubs. As usual, we call AvgCF rack the “projection” of AvgCF rac on the country k. A second parameter about intra-neighborhood cooperation regards the average fraction AvgCN bh of the number of cliques existing in hub neighborhoods against the number of neighborhood nodes. Again, we call AvgCN bhk the “projection” of AvgCN bh on the country k. A final parameter measuring the cooperation level among hub neighbors is the average density AvgDens of the nbh social network. As usual, we call AvgDensk the “projection” of AvgDens on the country k. 3
As pointed out in the introduction, we applied our approach to four North African countries, namely Algeria, Egypt, Morocco and Tunisia. As a consequence, in our case study, the set C of the countries to investigate (see Section 2) consisted of the following elements: C = {‘A’, ‘E’, ‘M’, ‘T’, ‘O’}, where ‘A’ (resp., ‘E’, ‘M’, ‘T’, ‘O’) stands for ‘Algeria’ (resp., ‘Egypt’, ‘Morocco’, ‘Tunisia’, ‘Others’). Clearly, ‘O’ indicates all the countries different from the four into examination. We chose these four countries because we had the possibility to access the corresponding data thanks to an academic partner that was carrying out a project aiming at investigating their research and innovation scenarios. Our dataset was stored in a MongoDB database. To give an idea of it, we report some of its features: (i) dimension = 10.27 GB; (ii) number of institutions = 278,696 ; (iii) number of authorships = 89,008,846; (iv) number of publications = 6,599,104; (v) number of research areas = 6; (vi) number of research fields = 251. Due to space limitations we can present only a very limited number of the results that we obtained.
In Figure 1, we report the variation of the number of hubs for each country. From the analysis of this figure, we can see that the country with the highest number of hubs is Tunisia. This result was unexpected also because both the extension and the number of citizens of Tunisia were smaller than the ones of the other three countries.
In Figure 2, we report the Herfindahl index HIk for the four countries. From the analysis of this figure we can observe that Tunisia and Algeria have a high Herfindahl index, which implies that their hubs cooperate mostly with one or few countries. In particular, after some investigations, we have seen that Tunisia and Algeria cooperate mostly with France, which is reasonable if we consider that they are French past colonies. By contrast, Egypt has a very low Herfindahl index, i.e., its hubs cooperate with many countries. An interesting trend is the one of Morocco; in fact, it initially has a behavior like the ones of Tunisia and Algeria, whereas, in the last years, it shows a behavior like the one of Egypt.
To determine the cooperation levels among hubs for the four North African countries into consideration, for each country k, we performed the following tasks: (i) we considered the two time intervals [2003; 2009] and [2007; 2013]; (ii) we computed the clique social networks CG1k (resp., CG2k), corresponding to the first and the second time intervals, respectively; (iii) we measured the four parameters introduced in Section 2.2 for quantitatively evaluating clique social networks. Obtained results for the first time interval are reported in Table 1. From the analysis of this table we can draw the following conclusions: (i) Egypt has the largest clique; this clique is much larger than the maximum cliques of the other countries; (ii) in Egypt almost all hubs belong to at least one clique. These results indicate that Egyptian hubs are more prone to cooperation than the hubs of the other countries.
In Figure 3, we report the graphs CG2k for all the four countries; in these graphs the dimension of nodes is proportional to the corresponding weight, i.e., to the number of cliques they belong to. The analysis of this figure confirms the previous conjecture; in fact, the number of edges in the Egyptian graph is much higher than in the other graphs. This fact, along with the presence of many not very large nodes, allows us to derive another important knowledge pattern, i.e., that research activities in Egypt are more “distributed” among hubs. 4
In this paper, we have proposed a new Social Network Analysis based approach to investigating the research scenarios of a set of countries of interest and to detecting possible hubs operating in these countries. Extracted knowledge allows the evaluation of the impact of different socio-economic conditions on research and favors the design of policies for supporting innovation in the countries of interest. We applied our approach to four North African countries. In the future, we plan to exploit techniques for analyzing information diffusion in social networks to understand how the possible mobility of top researchers from one institution to another can impact on the quality of both of them. Moreover, we plan to investigate the possible application of classification techniques to derive hub profiles in different countries. Furthermore, it is necessary to consider that a network changes over time. As a consequence, hubs could also change over time. The evolution of an institution’s capability of becoming hub, remaining hub or no longer being a hub is a challenging task that we plan to investigate. Finally, we plan to analyze the possible application of prediction techniques to understand what kind of financial investment must be performed for maximizing the increase of both the number and the quality of hubs and publications in the countries of interest.