分形網(wǎng)絡(luò)結(jié)構(gòu)性質(zhì)、建模與動(dòng)力學(xué)ppt課件

1、章 忠 志復(fù)旦大學(xué)計(jì)算機(jī)科學(xué)技術(shù)學(xué)院: Homepage: /zhangzz/Blog: group.sciencenet/home.php?mod=space&uid=311410網(wǎng)絡(luò)結(jié)構(gòu)分析和拓?fù)渥R(shí)別學(xué)術(shù)研討會(huì)網(wǎng)絡(luò)結(jié)構(gòu)分析和拓?fù)渥R(shí)別學(xué)術(shù)研討會(huì)復(fù)旦大學(xué)復(fù)旦大學(xué) Main Contents Introduction to Fractal Networks1Structural Properites of Fractal Networks 2 Modelling of Fractal Networks3Impact of

2、 Fractality on Dynamics4Conclusion and outlook5復(fù)旦大學(xué)復(fù)旦大學(xué)u Small-world EffectRemarkable properties of networksu Scale-free PropertyORu Fractal Behavior Small world seemingly contradicts fractality!復(fù)旦大學(xué)復(fù)旦大學(xué)Many real networks are fractal( ) BdBBBNll4BN 3BN 2BN -dBlog(lB)log(NB)fractalNon-fractalBd u Pro

3、tein interaction networku Hollywood film actor networku Metabolic networku World Wide WebBox-covering method Song, Havlin, and Makse, Nature (2019) 復(fù)旦大學(xué)復(fù)旦大學(xué)Fractal biological networksMetabolicProtein interactionSong, Havlin, Makse, Nature (2019)( ) BdBBN ll2.3Bd 3.5Bd Three domains of life: archaea,

4、 bacteria, eukariaE. coli, H. sapiens, yeast 43 organisms - all scale復(fù)旦大學(xué)復(fù)旦大學(xué)Fractal information and social networks World Wide Web( ) BdBBN ll6.25Bd 4.15Bd domainHollywood film actors 212,000 actors300,000 web-pagesOther bio networks: Khang and Bremen groups Internet is not fractal!復(fù)旦大學(xué)復(fù)旦大學(xué)M

5、ost efficient box-covering method4 boxes5 boxes10012p Mapping to graph colouring problemp Greedy algorithm to find minimum boxesJ. Stat. Mech. (2019) P03006復(fù)旦大學(xué)復(fù)旦大學(xué)Invariant of scaling under renormalizationk=2renormalizations=1/4k=8factor1Gallos et al. PNAS (2019)( ) kdBBs llandfollow the same distr

6、ibution.: exponent of the boxes復(fù)旦大學(xué)復(fù)旦大學(xué)Renormalization of WWW with 復(fù)旦大學(xué)復(fù)旦大學(xué)Degree distribution of WWW 2022-4-2復(fù)旦大學(xué)復(fù)旦大學(xué)Scaling relationsNew scaling relationNumboer of boxesBox sizeDegree of boxBox exponent( ) kdBBs ll復(fù)旦大學(xué)復(fù)旦大學(xué)Structural properties of fractal networks v Fractal networks are disassortat

7、ive Fractal networks are disassortativev Betweennees distribution Betweennees distribution v The number of spanning trees in The number of spanning trees in fractal networks is larger than that in fractal networks is larger than that in non-fractal networksnon-fractal networks2022-4-2復(fù)旦大學(xué)復(fù)旦大學(xué)2022-4-

8、2Brief introduction to spanning treesNumber of spanning trees:EPL (Europhysics Letters), 2019, 90:68002.Entropy of spanning trees:The larger the entropy, the larger the number of spanning trees.復(fù)旦大學(xué)復(fù)旦大學(xué)2022-4-2Spanning trees in a non-fractal scale-free webThe entropy for spanning trees in square lat

9、tice is 1.16624A counterintuitive conclusion that a network with more spanning trees may be relatively unreliable.EPL, 2019, 90:68002復(fù)旦大學(xué)復(fù)旦大學(xué)2022-4-2Spanning trees in a fractal scale-free networkPhysical Review E, 2019, 83:016116Fractality can significantly increase the number of spanning trees in f

10、ractal scale-free networks.復(fù)旦大學(xué)復(fù)旦大學(xué)A model of fractal scale-free network2022-4-2European Physical Journal B, 2019, 56:259-27.large-worlddisassortative復(fù)旦大學(xué)復(fù)旦大學(xué)2022-4-2Model: from fractal to non-fractal SF treesEPJ B, 2019, 64:277-283復(fù)旦大學(xué)復(fù)旦大學(xué)2022-4-2A model for fractal and nonfractal scale-free networ

11、ks with identical degree sequencesPhysical Review E, 2021, 79: 031110.Advantages： without crossing edges always connectedAs q drops from 1 to 0, it undergoes transitions from large to small world and from fractal to non-fractal.復(fù)旦大學(xué)復(fù)旦大學(xué)Impact of fractality on dynamics2022-4-2p Robustness (Reliabilit

12、y)p Percolationp Disease spreadingp Random walksp Synchronizationp Gamep 復(fù)旦大學(xué)復(fù)旦大學(xué)Fractal networks are more robust under intentional attack2022-4-2Nature Physics, 2019, 2:275-281.European Physical Journal B, 2019, 56:259-27.Relative size of the largest cluster, S, and the average size of the remainin

13、g isolated clusters, as a function of t h e r e m o v a l fraction f of the largest hubs.復(fù)旦大學(xué)復(fù)旦大學(xué)Bond percolation: nonzero thresholds 2022-4-2It is in contrast to the conventional wisdom that null percolation threshold is an intrinsic nature of scale-free networks.PRE, 2021, 79: 031110復(fù)旦大學(xué)復(fù)旦大學(xué)Fracta

14、lity can resist disease spread2022-4-2SI model:J. Phys. A, 2019, 43:065001SIR model: nonzero epidemic thresholdsJ. Stat. Mech. (2019) P09008復(fù)旦大學(xué)復(fù)旦大學(xué)2022-4-2Trapping problem: Random walks on graphs with an immobile trapvTrapping time (TT) for node i denoted by vAverage trapping time (ATT) Research go

15、al: obtain the dependence of average trapping time on the system size N.復(fù)旦大學(xué)復(fù)旦大學(xué)2022-4-2Previous work:ATT on Sierpinski gasket and complete graphPRE, 2019, 65: 021105. New J. Phys. 7, 26 (2019)復(fù)旦大學(xué)復(fù)旦大學(xué)2022-4-2Walks on nonfractal scale-free nets PRE, 2021, 79: 021127.New finding: ATT scales sublinear

16、ly with network size.EPL, 2021, 86: 10006.復(fù)旦大學(xué)復(fù)旦大學(xué)2022-4-2Walks on a fractal scale-free treeEPL, 2021, 88: 10001.Conclusion: fractality can induce a general slowing down of diffusion.復(fù)旦大學(xué)復(fù)旦大學(xué)2022-4-2Trapping time in fractal and non-fractal scale-free networks with identical degree sequencesPhysical

17、Review E, 2021, 80: 06111127復(fù)旦大學(xué)復(fù)旦大學(xué)2022-4-2Significant impact of trap position on ATT in non-fractal scale-free treesJournal of Mathematical Physics, 2021, 50: 033514.Journal of Physics A, 2019, 44: 075102復(fù)旦大學(xué)復(fù)旦大學(xué)2022-4-2No essential impact of trap position on MTT in fractal scale-free treesJournal

18、 of Physics A, 2019, 44: 075102.The networks seem homogeneous in this sense. Fractality plays a dominant role in determining the ATT in fractal scale-free networks.復(fù)旦大學(xué)復(fù)旦大學(xué)2022-4-2No qualitative effect of trap location on MFPT in extended T-graphsPhysical Review E, 2019, 82: 031140.New Journal of Physics, 2021, 11: 103043.復(fù)旦大學(xué)復(fù)旦大學(xué)Impact of fractality on synchronization and game2022-4-2 Fractality suppresses the synchoronizability in scale-free networks. Fractality is unfavouble for emergence of cooperation in scale-free networks. Fractality may ha