Graph Theoretical Analysis for Small Components of Complex Network : A Survey

Recently,complex networks are hot topics among many research area, such as in the domain of bioinformatics, there are many such as protein networks, gene networks, neuro networks.Some other examples are ecological network, social network and world wide web. Because they play some certain functional role, their topological structures are different from each other for distinct networks, for instance, the degrees of some networks behave differently, some subgraph occurs frequently etc. So using the topological structure discovery methodology, say graph theory approach, to study the complex networks could be effective and significant useful way to discover the feature of the network. The papers surveys many important but not all literatures and results of studies of complex network by graph theory.

[1]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[2]  Bruce A. Reed,et al.  A Critical Point for Random Graphs with a Given Degree Sequence , 1995, Random Struct. Algorithms.

[3]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[4]  Uri Alon,et al.  Uniform generation of random graphs with arbitrary degree sequences , 2003 .

[5]  Vojtech Rödl,et al.  A Fast Approximation Algorithm for Computing the Frequencies of Subgraphs in a Given Graph , 1995, SIAM J. Comput..

[6]  Martin E. Dyer,et al.  Approximately counting Hamilton cycles in dense graphs , 1994, SODA '94.

[7]  Donald E. Knuth,et al.  The Art of Computer Programming, Volume I: Fundamental Algorithms, 2nd Edition , 1997 .

[8]  Martin E. Dyer,et al.  A Random Polynomial Time Algorithm for Approximating the Volume of Convex Bodies , 1989, STOC.

[9]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[10]  Uri Alon,et al.  Efficient sampling algorithm for estimating subgraph concentrations and detecting network motifs , 2004, Bioinform..

[11]  S. Mangan,et al.  Structure and function of the feed-forward loop network motif , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[12]  B. Monien How to Find Long Paths Efficiently , 1985 .

[13]  Rajeev Motwani,et al.  Random sampling for histogram construction: how much is enough? , 1998, SIGMOD '98.

[14]  Noga Alon,et al.  Finding and counting given length cycles , 1997, Algorithmica.

[15]  S. Shen-Orr,et al.  Network motifs in the transcriptional regulation network of Escherichia coli , 2002, Nature Genetics.

[16]  R. Milo,et al.  Subgraphs in random networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Russ Bubley,et al.  Randomized algorithms , 1995, CSUR.