### I. Introduction

### II. Methods

### 1. Data

### 2. Matrix

### 3. Centralization, Centrality

*eg*, centrality, cohesion, brokerage) among others, as well as hypothesis testing can be performed. Pajek is a program, for Windows, for analysis and visualization of large networks and is freely available, for noncommercial use at web site [6]. Also, NetDraw ver. 2.090 (Analytic Technologies, Lexington, KY, USA) were used to draw sociogram. NetDraw is social network visualization software with which graphic representation of networks including relations and attributes can be drawn. We analyzed four centralization indices (degree centrality, closeness centrality, betweenness centrality) and Eigenventor centrality index as suggested by Freeman [7]. The network measurement methods were applied to, one for individual node (vertex) and one for entire network.

### 4. Key Player Analysis

### 5. Structural Equivalence

### 6. Multidimensional Scaling

*X*(

*i,j*) will draw i and j close together on the MDS map. If dissimilarities exit, large values will push

*i*and

*j*apart on the map.

### III. Results

### 1. Centralization According to Period

### 2. Centralization According to Subcategories

### 3. Centrality Changes According to Period

#### 1) Degree centrality

#### 2) Betweenness centrality

#### 3) Eigenvector centrality

#### 4) Sociogram

### 4. Key Players Analysis

### 5. Structural Equivalence

^{2}=0.240). The analysis produced eight groups and the medical schools in a group may be regarded as a 'Clique.' Group A was 'Gacheon,' 'Dankook,' 'Chosun,' 'Konyang,' 'Chung-Ang,' 'Eulji,' and 'Chungbuk.' Group B was 'Pochon CHA,' 'Chonnam,' 'Soonchunhyang,' 'Inha,' and 'Chonbuk.' Group C was 'Kangwon,' 'Inje,' 'Wonkwang,' 'Cheju,' 'Hallym,' and 'Kwandong.' Group D was 'Konkuk,' 'Hanyang,' 'Kyung Hee,' 'Catholic Univ. of Korea,' 'Yeungnam,' 'Ulsan,' 'Ehwa,' 'Ajou,' 'Korea,' 'Seoul National,' 'Yonsei,' and 'Sungkyunkwan.' Group E was 'Chungnam,' and 'Kyungpook.' Group F was 'Keimyung' and 'Dongguk.' Group G was 'Gyeongsang,' and 'Seonam.' Group H was 'Pusan,' 'Catholic Univ. of Daegu,' 'Dong-A,' and 'Kosin.'

### 6. Multidimensional Scaling

### IV. Discussion

### 1. Centralization According to Period

#### 1) Degree centrality

#### 2) Closeness centrality

#### 3) Betweenness centrality

#### 4) Eigenvector centrality

### 2. Centralization According to Subcategories

#### 1) Degree centrality

#### 2) Betweenness centrality

#### 3) Eigenvector centrality

### 3. Key Player

*"Given a social network (represented as an undirected graph), and a set of k nodes (called a kp-set of order k) such that, 1. (KPP-Neg) Removing the kp-set would result in a residual network with the least possible cohesion, 2. (KPP-Pos) The kp-set is maximally connected to all other nodes."*The program KeyPlayer ver. 1.44 is developed by Borgatti himself to find a solution of key players problem. We used distance weighted reach criterion method (KPP-NEG) with the goal consists of identifying those k-players that, if removed, will disrupt or fragment the network. As shown above, the degree of centralization was relieved through the period. However, the number of key players has been shrunk through the period. The four medical schools, SNU, Yonsei, Sungkyunkwan, and Ulsan University were 'key player' 54 subcategories (90%). In earliest period (1997-2000), the number of medical schools as 'key player' was 15, but it changed to 12 and 10 in period 2001-2004 and 2005-2008, respectively. Also, the occupation by those four medical schools was increase from 40 subcategories in earliest period to 46 subcategories in latest period. Thus even though centralization degree is relieved and the 'key players' are changing dynamically, the significance of those four medical schools is still going profound inside the scientific network of medical schools of Korea.