Crawling on Simple Models of Web Graphs

We consider the problem of searching a randomly growing graph by a random walk. In particular we consider two simple models of "web-graphs." Thus at each time step a new vertex is added and it is connected to the current graph by randomly chosen edges. At the same time a "spider" S makes a number of steps of a random walk on the current graph. The parameter we consider is the expected proportion of vertices that have been visited by S up to time t.

[1]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[2]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[3]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[4]  Deryk Osthus,et al.  Popularity based random graph models leading to a scale-free degree sequence , 2004, Discret. Math..

[5]  Marc Najork,et al.  Measuring Index Quality Using Random Walks on the Web , 1999, Comput. Networks.

[6]  Eli Upfal,et al.  The Web as a graph , 2000, PODS.

[7]  Amos Fiat,et al.  Web search via hub synthesis , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[8]  Micah Adler,et al.  Towards compressing Web graphs , 2001, Proceedings DCC 2001. Data Compression Conference.

[9]  Eli Upfal,et al.  Stochastic models for the Web graph , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[10]  W. Hoeffding.  Probability Inequalities for sums of Bounded Random Variables , 1963 .

[11]  Anna R. Karlin,et al.  Random walks with `back buttons' , 2001, STOC 2000.

[12]  Mark Jerrum,et al.  Approximate Counting, Uniform Generation and Rapidly Mixing Markov Chains , 1987, WG.

[13]  Jie Wu,et al.  Small Worlds: The Dynamics of Networks between Order and Randomness , 2003 .

[14]  Fan Chung Graham,et al.  Random evolution in massive graphs , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[15]  Andrei Z. Broder,et al.  Graph structure in the Web , 2000, Comput. Networks.

[16]  Béla Bollobás,et al.  The Diameter of a Scale-Free Random Graph , 2004, Comb..

[17]  Linyuan Lu,et al.  The diameter of random massive graphs , 2001, SODA '01.

[18]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[19]  Mihaela Enachescu,et al.  Variations on Random Graph Models for the Web , 2001 .

[20]  Sergey Brin,et al.  The Anatomy of a Large-Scale Hypertextual Web Search Engine , 1998, Comput. Networks.

[21]  F. Chung,et al.  The average distances in random graphs with given expected degrees , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[22]  Fan Chung Graham,et al.  A Random Graph Model for Power Law Graphs , 2001, Exp. Math..

[23]  Béla Bollobás,et al.  Robustness and Vulnerability of Scale-Free Random Graphs , 2004, Internet Math..

[24]  Béla Bollobás,et al.  The degree sequence of a scale‐free random graph process , 2001, Random Struct. Algorithms.

[25]  Alan M. Frieze,et al.  A general model of web graphs , 2003, Random Struct. Algorithms.

[26]  A. Barabasi,et al.  Scale-free characteristics of random networks: the topology of the world-wide web , 2000 .