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The validity of the network load distribution in more realistic situation

The validity of the network load distribution in more realistic situation. Seung-Woo Son, Dong-Hee Kim, and Hawoong Jeong Complex System and Statistical Physics Lab., Dept. Physics, KAIST, Taejeon 305-701, Korea. Next One?. 0. 6. 2. 1. 4. 3. 5. Introduction : Scale-free network.

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The validity of the network load distribution in more realistic situation

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  1. The validity of the network load distribution in more realistic situation Seung-Woo Son, Dong-Hee Kim, and Hawoong Jeong Complex System and Statistical Physics Lab., Dept. Physics, KAIST, Taejeon 305-701, Korea

  2. Next One? 0 6 2 1 4 3 5 Introduction : Scale-free network • What is the Scale Free Network? • SF network is the network with the power-law degree distribution. Ex) BA modelgrowth and preferential attachmentA.-L.Barabási and R. Albert, Emergence of scaling in random networks, Science, 286, 509 (1999) • Ex) Empirical Results of Real NetworksWorld-Wide Web, Internet, Movie actor collaboration network, Science collaboration graph, Cellular network, etc.R. Albert, H. Jeong, and A.-L.Barabási, Nature(London), 406, 378 (2000) • SF network shows error and attack tolerance.

  3. start D B A G E C F Introduction : Load & Classification of networks • What is the “Load” ? • When every pair of nodes in a network exchanges data packets along the shortest path, load, or “betweenness centrality,” of node is the total number of data packets passing through that node. Ex) Internet traffic jam, Influential people in social network, etc. δ is universal value ! • “It is found that the load distribution follows a power-law with the exponent δ~2.2(1)”K.-I. Goh, B. Kahng, and D. Kim, Universal Behavior of Load Distribution in Scale-Free Networks, PRL, 87, 27 (2001) • The exponent of load is robust without network model dependency. It can be used to classify the networks. • Kwang-Il Goh, et al., Classification of scale-free networks, PNAS, 99, 20 (2002)

  4. 1 1 1 1 6 4 2 3 2 2 2 3 5 3 7 6 4 3 3 3 3 3 5 5 4 5 4 3 SHT Introduction : Local Path Finding Strategies • Why we should study Local Path Finding Strategy (LPFS) ? • The shortest path finding strategy requires the global network information which is not accessible to each node in real network. • When the only local network information is available, the actual path can be longer than the shortest path.B. J. Kim, C. N. Yoon, S. K. Han, and H. Jeong, Path finding strategies in scale-free networks, PRE, 65, 027103 (2002) • What kinds of Local Path Finding Strategies (LPFSs) ? • Traveling to the neighbor node with the largest degree first Schematic view !! MAX & MMX BMX PMX & DMX

  5. Fitting line of SHT BA model - Degree & load distributions • load of LPFSs > load of SHT • The load distributions of PMX & DMX exhibit similar power-law distribution like SHT with some different exponents. • MAX, MMX, & BMX show that the heavily loaded nodes exist. • The accessibility of MAX is 60% in BA model. ( m=2 )

  6. BA model - Correlation between strategies • The larger degree, the larger load with SHT, MAX, DMX, & PMX. ( not with BMX, MMX ) • SHT and MAX are weakly correlated. • (MMX,BMX), (MAX,DMX), (PMX,SHT) pairs have reasonable correlation of load distribution. • MAX & DMX can be substituted for SHT to calculate the load of network.

  7. BA Tree - More simple case • BA tree(m=1) shows similar degree and load distribution to BA model. • The accessibility of MAX is 3.1% with 1.3% standard deviation. Because of tree structure, accessibility has small value. It cause small load with MAX strategy. ( BA model with m=3 case, 71% accessibility ) • The load of MAX has positive correlation with that of SHT as before.

  8. Real network : Internet • Real Internet networks appear power-law degree distribution with exponent γ = 2.2 in 1997 & 1999 data. • The exponent of SHT load distribution is δ = 2.0 • The exponents of LPFSs are smaller than that of SHT. The accessibility is 36%. • The result of Internet network shows that Internet has a tree-like structure.

  9. Real network : Internet • The result of Internet in 1999 is almost identical with that of 1997’s. Though the number of nodes are increase, its structure & characteristics are invariant. • Not only in the BA model but also in real Internet data, there exist correlation between load of SHT and that of MAX. • The accessibility about 30% is not bad and reliable to the result of Internet search engines. It also shows Internet has less loop structure that BA model(m=2).

  10. Real network : WWW & Protain network

  11. Result table of real networks

  12. Conclusions & Future works • Conclusions • We study the similarity of load distribution using the shortest path method and the local path finding strategies, traveling to the neighbor node with the largest degree. • With various model, we study the load distributions with SHT and LPFSs. They all show power-law distribution. The calculated exponents with LPFS are smaller than with SHT. • For real networks and BA model, we measure the exponents and study the network structure. • Future works • The relation between network structure and the exponents of LPFSs. • Classification of networks with load distribution exponents using SHT and LPFSs.

  13. Conclusions

  14. Summary

  15. Acknowledgments • ^^

  16. Simulations

  17. Introduction : Classification of scale-free networks

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