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Subway networks in two cities 장기호 1 , H. Oshima 2 , 윤성민 3 , 김경식 3 1. 기상청 기상연구소 원격탐사연구실

Subway networks in two cities 장기호 1 , H. Oshima 2 , 윤성민 3 , 김경식 3 1. 기상청 기상연구소 원격탐사연구실 2. 큐슈대 물리학과 3. 부경대 물리학과. Contents. I. Introduction II. General formalism for the network III. Application to the subway networks IV. Results and discussion. I. Introduction.

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Subway networks in two cities 장기호 1 , H. Oshima 2 , 윤성민 3 , 김경식 3 1. 기상청 기상연구소 원격탐사연구실

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  1. Subway networks in two cities 장기호1, H. Oshima 2, 윤성민3, 김경식3 1. 기상청 기상연구소 원격탐사연구실 2. 큐슈대 물리학과 3. 부경대 물리학과

  2. Contents I. Introduction II. General formalism for the network III. Application to the subway networks IV. Results and discussion

  3. I. Introduction ◎ Watts and Storogatz (Nature, 1998): Small world => applications to a lot of network problems : www, internet, social network, biochemical networks, subways,… ◎ Commonly used analysis tool for the network : Characteristic length, Clustering Coeff., Pi(ki), .. ◎ Latora and Marchiori (PRL, 2001) => “LM” hereafter : suggests a new tool (global and local efficiency) for the network analysis ◎ This work : the previous analysis method and LM’s method are compared. : the optimized network analysis method is suggested and applied to the city-subway networks.

  4. II. General Formalism (1): Basic Definitions A network consists of a set of N nodes and a set of L links connecting the nodes. A graph “G”consists of a set of N vertices and L edges A graph “Gid” is an ideal graph having all the N(N-1)/2 possible edges G Gid Adjacency Matrix A {aij}: aij=1 if i and j are linked, 0 otherwise

  5. II. General Formalism (2): Clustering Coeff. • Ci(ki) : Characterizes the tendency of node vi to form clusters or groups • ki: degree of node vi • ni: number of edges between neighbors of vi ki=4 ni=0 ⇒ Ci(ki)=0 ni=3 ⇒ Ci(ki)=0.5 ni=6 ⇒ Ci(ki)=1

  6. II. General Formalism (3): Measure Previous measures LM(Latora &. Marchiori, PRL, 2001) : the subgraph of the neighbors : the shortest path length bet’n i and j vertices : the path length bet’n i and j vertices when they are directly connected - WS has the following limitations: 1. Connected 2. Sparce [ K << N(N-1)/2 ] 3. Unweighted (edges all equal) Overcomes, but the concept of network length?

  7. II. General Formalism (4): Unweighted Ex. Previous LM

  8. II. General Formalism (5): Weighted Ex. 1 1 1 1 5 1 1 1 1 1 LM Previous

  9. III. Applications to the subway (a) Seoul (c) Boston LEGEND subway line with a station exchange with other lines (b) Tokyo (e) Sample (d) Beijing

  10. IV. Results and Discussion Assume the unweighted to simultaneously compare with the networks * Calculated in Latora & Machiori (PRL,2001) ◎ Boston: very low Eloc <= very low # of triangular geometries Beijing &. Sample: Eloc =0 <= No triangular geometries ◎ Eglob: Beijing>Tokyo>Sample>Boston>Seoul ~ 1/L=> LM’s suggestion is verified ◎ Clustering Analysis: Eloc seems better than C (Eloc depends on path length) but Ci is still meaningful when concerning a clustering for i-edge ◎ LM’s is free from the limitations (connectedness, sparceness, unweightness) but L is still useful for its concept of physical distance

  11. THE END THANKS

  12. 광고: 기상청(기상연구소) 관측 자료 개괄 - Temperature - Pressure - Wind - Reflectivity(Radar) 과학자 여러분의 많은 연구참여 기대함.

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