Networks with High Clustering Coefficients Based on BA Model

doi:10.3969/j.issn.1007-2985.2012.01.009

Abstract

Abstract: The authors discuss briefly some properties of the BA model and point out that such model is insufficient to describe real networks for its relatively small clustering coefficient.Based on the BA model,and introducing edge addition into network evolution,the authors propose a modified network model.Numerical simulation results indicate that in the modified model,the networks are scale-free,just as the networks in the BA model.In addition,the networks in such model are highly clustered.It is shown that the clustering coefficient C of network increases with the increase of edge-addition probability p in the modified model.In particular,when p=1,C is found to be 100 times higher in the modified model than that in the BA model with the same network-size.

Key words: complex networks, clustering, edge addition, scale-free

WANG Xiao-Yun, DENG Ke. Networks with High Clustering Coefficients Based on BA Model[J]. journal6, 2012, 33(1): 32-35.

References

[1] WATTS D J,STROGATZ S H.Collective Dynamics of‘Small-World’ Networks [J].Nature,1998,393(6):440-442.

[2] STROGATZ S H.Exploring Complex Networks [J].Nature,2001,410(6 825):268-276.

[3] ALBERT R,BARABASI A L.Statistical Mechanics of Complex Networks [J].Rev. Mod. Phys.,2002,74(1):47-97.

[4] DOROGOVTSEV S N,MENDES J F F.Evolution of Networks [J].Adv. Phys.,2002,51(4):1 079-1 181.

[5] NEWMAN M E J.The Structure and Function of Complex Networks [J].SIAM Review,2003,45〖CX1〗〖CX〗(2):167-256.

[6] BARABASI A L,ALBERT R.Emergence of Scaling In Random Networks [J].Science,1999,286(5 439):509-512.

[7] BARABASI A L,ALBERT R.Jeong H.Mean-Field Theory for Scale-Free Random Networks [J].Physica A,1999,272(1):173-187.

[8] ERDOS P,RLENYI A.On Random Graphs [J].Publ. Math. Debrecen,1959,6(1):90-297.

[9] AMARAL L A N,SCALA A,BARTHELEMY M,STANLEY H E.Classes of Small-World Networks [J].Proc. Natl. Acad. Sci. U S A,2000,97(21):11 149-11 152.〖

[10] CAMACHO J,GUIMERA R,AMARAL L A N.Robust Patterns in Food Web Structure [J].Phys. Rev. Lett.,2002,88(22):2 281 021-2 281 024.

[11] BARABASI A L,BONABEAU E.Scale-Free Networks [J].Science American,2003,1(5):50-59.

[12] ALBERT R,JEONG H,BARABASI A L.Attack and Error Tolerance of Complex Networks [J].Nature,2000,406(7):378-382.

[13] PASTOR-SATORRAS R,VESPIGNANI A.Epidemic Spreading In Scale-Free Networks [J].Phys. Rev. Lett.,2001,86(14):3 200-3 203.

[14] BOGUNA M,SATORRAS R P,VESPIGNANI A.Absence of Epidemic Threshold In Scale-Free Networks with Degree Correlations [J].Phys. Rev. Lett.,2003,90(2):0 287 011-0 287 014.

[15] KRAPIVSKY P L,REDNER S,LEYVRAZ F.Connectivity of Growing Random Networks [J].Phys. Rev. Lett.,2001,85(21):4 629-4 632.

[16] DOROGOVTSEV S N,MENDES J F F,SAMUKHIN A N.Structure of Growing Networks with Preferential Linking [J].Phys Rev Lett,2000,85(21):4 633-4 636.

[17] DOROGOVTSEV S N,MENDES J F F,SAMUKHIN A N.〖CX1〗〖CX〗Size-Dependent Degree Distribution of A Scale-Free Growing Network [J].Phys. Rev. E,63(6):0 621 011- 0 621 014.

[18] KLEMM K,EGUILUZ V M.Highly Clustered Scale-Free Networks [J].Phy. Rev. E,2002,65(3):0 361 231-0 361 235.