Social Network of Faculties Accordıng to Student Preferences in Transition to Higher Education

Social network analysis has a wide and diversified application area. For this area which showed fast development recently, necessary basic theories and models are being used; however, development of new models and theories also continues. Another field which began to develop in late 1990s and early 2000s is the value of the links between nodes of social networks. In most studies the adjacency matrix for social networks is composed of 0 and 1 values. However, this situation does not completely reflect the systems encountered in real life. For this reason studies conducted on weighted links increases on a daily basis. In addition, although network sciences deals with the characteristics of the links between nodes unlike statistics, one must not neglect the fact that characteristic of the node also has a role in the formation of a link between two nodes. In this paper, emphasis has been put on the fact that due to the structures of some social mechanisms, weights of the used links do not sufficiently reflect the reality. In order to use in this type of social structures, characteristics of nodes were given more place in evaluations and a new weighting method was proposed, which was also shown with an application.


Introduction
While working on social networks, most models assume that the links between nodes are equal.An adjacency matrix consists of values 0 and 1.However, in real life, links are not equal in most social, biological, ecological and economic systems.[11], [4] Girvan and Newman [5] repeated their weighted network study conducted with 16 apes in 2004 taking into consideration whether apes groomed each other or not.In a non-weighted social network adjacency matrix, attention was paid only to whether apes groomed each other or not, and only the values of 0 and 1 were included in the matrix.In a weighted social network matrix, on the other hand, information on how many times the apes groomed each other during the observation period was also included.In addition, in the tree diagram formed with a non-weighted adjacency matrix, no societal structure was observed for apes.Conversely, clear structures appeared in the tree diagram created with a weighted adjacency matrix.It can be seen that female and male apes were assigned to different groups in terms of their grooming behaviour [7], [1].In social networks, the weights of links can be the frequencies of connections between the nodes; in road or air transport network, it can be the distance between the nodes or the time spent on travelling from one node to the other in the distance between the two nodes [8], [10], [6].In addition, as in the application of Cai et al. [2], correlation or distance matrixes between nodes can also be used as the weights of links.
In this study, the data obtained during transition to higher education in Turkey have been used.In Turkey, students graduating from high school take the exams organized by the Measurement, Selection and Placement Center (Ölçme, Seçme ve Yerleştirme Merkezi, ÖSYM) and aim to be placed in one of the universities with their exam scores.The minimum scores of departments are determined by the students who were placed in that department in the previous year.In the current year, students take into consideration these scores and apply to ÖSYM by adding the universities/departments they want to be placed to their preference lists.Each student has the right to make 30 choices.In this application, these preference lists were utilized.Here departments in universities combine to form faculties.In each faculty, which represents natural clusters, there is a different number of departments.
In this paper, while evaluating the weights of the links between clusters (faculties), emphasis will be put on the fact that the frequency of being seen together in preference lists did not reflect the real link weights completely due to the difference in node numbers within clusters; therefore, a different weight calculation method is recommended.In natural clusters formed within systems, it can be clearly seen in the study of Wang et al. [9] on multi-weighted links that the evaluation of the links and weights both between and within clusters is essential.

Higher education preference network model
In the study, the preference lists of 1000 students who took the exams necessary for transition to higher education in 2010 and were placed in one of the undergraduate programs were examined.Faculties in the preference lists were divided into 7 geographical regions so as to allow for classification and make a better evaluation of the networks which would be drawn.In this paper, the analysis made for the Mediterranean Region is used and comparisons are made.From the preference lists, data belonging to 68 different faculties in the Mediterranean Region were obtained.
In the study, a non-weighted social network is being established with the adjacency matrix which shows whether two faculties are included in the same preference list or not. ( Non-weighted adjacency matrix (2) However, the weighted social network matrix which will be created with information on the frequency of two faculties appearing together in the preference lists will provide more detailed information. ( The network which was structured based on the information on coexistence in preference lists of nodes only for the Mediterranean Region is given in Figure 1.The figure shows that the link between some of the nodes is drawn with thicker lines, compared to others.The thickness of the links seen in the figure is proportional to the coexistence in the preference lists.Some sample node couples with a strong link have been examined.a ij is the existence or absence of a link between two nodes (faculties).If there is a link between two nodes, a ij =1; otherwise, a ij =0.This information shows whether two faculties coexist in the same preference list.Figure 1 is drawn according to the calculated a w ij values.a w ij values show whether two faculties coexist in the same preference list; however, they also consist of information on the number of preference lists in which they coexist.a w ij not only shows whether there is a link between two faculties but also displays the level of the existing link value.The bigger the link value, the thicker the link line.When the node couples given in Table 1 are examined, it can be seen that a faculty of education has the most frequent coexistence with other faculties of education, and a faculty of economic and administrative sciences has the most frequent coexistence with other faculties of economic and administrative sciences.It is not surprising that such faculties with several departments and a variety of minimum scores frequently appear in preference lists together.
However, when examined in terms of the strength of their coexistence, more information is needed related to nodes.Everybody knows that it is natural that faculties of medicine, dentistry, and pharmacy which have only one department that can be preferred and which have very close areas of profession are preferred together.Therefore, strong links between these and similar faculties should not be neglected.
At this stage, it was believed that the distance matrixes used in clustering analysis could be utilized.It was planned to use the adjacency matrix obtained from different characteristics of faculties other than appearing together in preference lists in calculating link weights.
One of the widely-used distance measures developed for quantitative data is Euclidean distance.Euclidean distance is found by taking the square root of the squares of differences between i and j objects in each dimension.The Euclidean distance between two points in a p dimension space, and , is calculated as follows: [3] (5) The distance obtained by taking the square root of Euclidean distance is called squared Euclidean distance.
Some of the reasons that could explain the preference for faculties were determined, and an adjacency matrix squared Euclidean distance was calculated and formed between faculties based on these characteristics.The variables used in the calculation of the adjacency matrix and their descriptive statistics are given in Table 2. Due to the differences in the mean and standard deviation, the data were standardized between 0 and 1 before the adjacency matrix was calculated.Starting from here, the adjacency matrix is formed as follows: The values in A d ij matrix formed with the calculation of the distance between two faculties by using the variables which are given in Table 2 show the distance between the i th and the j th faculty.The smaller the a d ij value, the closer the two faculties in terms of the relevant variables.
When both matrixes were calculated, the adjacency matrix weighted by frequency was treated with a weighting procedure again with the adjacency matrix calculated by using the characteristics of nodes.The matrix recommended for the weighted adjacency matrix to be used with the networks that have interbedded social structures is as follows: Adjacency matrix weighted with Euclidean distance (7) Each cell of the adjacency matrix obtained from the characteristics of faculties was multiplied by the same cell in the adjacency matrix of coexistence frequencies of faculties, and a new adjacency matrix was formed.The network drawn with this new matrix can be seen in Figure 2.
The network drawing of the matrix weighted with the adjacency matrix obtained by using different characteristics of nodes can be seen in Figure 2. First of all, the comparison between the two figures shows that no change occurred in the structure of the network after reweighting.The only difference that occurred between the networks was in the link weights between the nodes.Some node couples with a strong link in the network obtained with a reweighted matrix are given in Table 3.

Figure 2. Network reweighted with Euclidean distance for the Mediterranean Region
As can be seen in Table 3, strong links occurred between different faculties in the network that were obtained with a reweighted matrix.Here the link between the faculties with no variety in department and minimum score such as medicine, dentistry and pharmacy appeared to be stronger.In this reweighted network, the strength of the links in the faculties of economic and administrative sciences became somewhat weaker but still remained strong.However, it is clear that the strong link between such faculties as medicine, dentistry and pharmacy, which are well-known for their coexistence in the preference lists of students, could not be revealed with the adjacency matrix which was obtained with the number of coexistence in preference lists.The strength of the link between the nodes in the social network that occurred in the course of the analysis of the adjacency matrix weighted with frequency and the strength of the link between the nodes in the social network that occurred with the adjacency matrix reweighted with Euclidean distance appeared to be different.When this dissimilarity was evaluated, it became clear that the links between two nodes obtained with the adjacency matrix weighted with frequency were less strong than those obtained with the adjacency matrix reweighted with Euclidean distance.At this point, the relation between the faculties which appeared to have a strong link due to the multitude of departments was subject to a "correction" operation using node characteristics.Thus, it was ensured that faculties with a single department but strong links occur.When the ranks of the nodes of two matrixes are examined for the Mediterranean Region, it can be seen that they both comply with the laws of force.Therefore, it can be said that they are appropriate for the model irrespective of the scale.The fact that no significant change occurred in rank distribution makes it clear that reweighting was concentrated in correlation weights only.

Conclusions
The strength of the link between nodes in social networks is an issue which is as important as the existence of that link.The more information these network weights between nodes include, the more realistic the evaluations and the resulting strong and weak links will be.When social networks are examined, it can be seen that the strong links

Figure 1 .
Figure 1.Network weighted with frequency for the Mediterranean Region

Figure 3 .
Figure 3. Ranks of the nodes of two weighted matrixes for the Mediterranean Region

Table 1 .
Node couples with a strong link in a frequency-weighted adjacency matrix for the Mediterranean Region

Table 2 .
Descriptive statistics of node characteristics

Table 3 .
Node couples with a strong link in the adjacency matrix reweighted with Euclidean distance for the Mediterranean Region