Journal of KIISE:Computer Systems and Theory (한국정보과학회논문지:시스템및이론)

Korean Institute of Information Scientists and Engineers (한국정보과학회)
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A Graph Layout Algorithm for Scale-free Network

척도 없는 네트워크를 위한 그래프 레이아웃 알고리즘

  • 조용만 (강릉대학교 컴퓨터공학과) ;
  • 강태원 (강릉대학교 컴퓨터공학과)
  • Published : 2007.06.15
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Abstract

A network is an important model widely used in natural and social science as well as engineering. To analyze these networks easily it is necessary that we should layout the features of networks visually. These Graph-Layout researches have been performed recently according to the development of the computer technology. Among them, the Scale-free Network that stands out in these days is widely used in analyzing and understanding the complicated situations in various fields. The Scale-free Network is featured in two points. The first, the number of link(Degree) shows the Power-function distribution. The second, the network has the hub that has multiple links. Consequently, it is important for us to represent the hub visually in Scale-free Network but the existing Graph-layout algorithms only represent clusters for the present. Therefor in this thesis we suggest Graph-layout algorithm that effectively presents the Scale-free network. The Hubity(hub+ity) repulsive force between hubs in suggested algorithm in this thesis is in inverse proportion to the distance, and if the degree of hubs increases in a times the Hubity repulsive force between hubs is ${\alpha}^{\gamma}$ times (${\gamma}$??is a connection line index). Also, if the algorithm has the counter that controls the force in proportion to the total node number and the total link number, The Hubity repulsive force is independent of the scale of a network. The proposed algorithm is compared with Graph-layout algorithm through an experiment. The experimental process is as follows: First of all, make out the hub that exists in the network or not. Check out the connection line index to recognize the existence of hub, and then if the value of connection line index is between 2 and 3, then conclude the Scale-free network that has a hub. And then use the suggested algorithm. In result, We validated that the proposed Graph-layout algorithm showed the Scale-free network more effectively than the existing cluster-centered algorithms[Noack, etc.].

네트워크는 공학이나 자연과학은 물론이고 사회과학의 여러 분야를 연구하는데 중요하게 사용되는 모델이다. 이런 네트워크를 좀 더 쉽게 분석하기 위해서는 시각적으로 네트워크의 특징을 잘 나타내는 것이 필요하다. 이러한 그래프 레이아웃 연구는 컴퓨터 기술이 발달함에 따라 많이 연구되고 있다. 그 중에서 요즘 새롭게 부각되고 있는 척도 없는(Scale-free) 네트워크는 다양한 분야에서 복잡한 현상들을 분석하고 이해하는데 유용하게 쓰이고 있다. 이 네트워크의 특징은 링크의 수(Degree)가 멱함수(power law) 분포를 보이고, 다수의 링크를 가지는 허브가 존재함이 알려졌다. 따라서 척도 없는 네트워크에서는 허브를 시각적으로 잘 표현하는 것이 중요하지만 기존의 그래프 레이아웃 알고리즘은 클러스터를 잘 표현하는 정도이다. 그래서 본 논문에서는 척도 없는 네트워크를 잘 표현하는 그래프 레이아웃 알고리즘을 제안한다. 본 논문에서 제안한 알고리즘에서 허브들 간에 작용하는 허브성 척력이 거리에 반비례하고, 허브들의 degree가 a배 증가하면, 허브사이에 작용하는 척력의 크기는 ${\alpha}^{\gamma}({\gamma}$는 연결선 지수)배가 된다. 또한, 전체 노드수와 전체 링크수에 따라 적용되는 힘의 크기를 조정하는 계수를 두어서 네트워크의 규모에 관계없이 허브성 척력이 적용되는 특성이 있다. 제안한 알고리즘이 허브를 잘 표현하는 그래프 레이아웃 알고리즘인지를 기존의 방식과 실험을 통해서 비교하였다. 실험의 절차는 먼저 네트워크에 허브가 존재하는지를 식별한다. 허브의 존재를 식별하기 위한 방법은 연결선 지수를 확인하고, 연결선 지수의 값이 2와 3사이에 있으면 허브가 존재하는 척도 없는 네트워크로 판단한다. 다음은 이 네트워크의 레이아웃 작성에 제안한 알고리즘을 사용한다. 그 결과, 제안한 그래프 레이아웃 알고리즘이 기존의 Noack등의 클러스터중심의 알고리즘에 비해서 척도 없는 네트워크의 허브를 확실히 잘 보여주고 있음을 확인할 수 있었다.

Keywords

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