The Topology and Dynamics of Complex Networks

Doctoral Dissertation

Abstract

We start with a brief introduction about the topological properties of real networks. Most real networks are scale-free, being characterized by a power-law degree distribution. The scale-free nature of real networks leads to unexpected properties such as the vanishing epidemic threshold. Traditional methods aiming to reduce the spreading rate of viruses cannot succeed on eradicating the epidemic on a scale-free network. We demonstrate that policies that discriminate between the nodes, curing mostly the highly connected nodes, can restore a finite epidemic threshold and potentially eradicate the virus. We find that the more biased a policy is towards the hubs, the more chance it has to bring the epidemic threshold above the virus’ spreading rate.

We continue by studying a large Web portal as a model system for a rapidly evolving network. We find that the visitation pattern of a news document decays as a power law, in contrast with the exponential prediction provided by simple models of site visitation. This is rooted in the inhomogeneous nature of the browsing pattern characterizing individual users: the time interval between consecutive visits by the same user to the site follows a power law distribution, in contrast with the exponential expected for Poisson processes. We show that the exponent characterizing the individual user’s browsing patterns determines the power-law decay in a document’s visitation.

Finally, we turn our attention to biological networks and demonstrate quantitatively that protein complexes in the yeast, Saccharomyces cerevisiae, are comprised of a core in which subunits are highly coexpressed, display the same deletion phenotype (essential or non-essential) and share identical functional classification and cellular localization. The results allow us to define the deletion phenotype and cellular task of most known complexes, and to identify with high confidence the biochemical role of hundreds of proteins with yet unassigned functionality.

Attributes

Attribute NameValues
URN
  • etd-08312005-210328

Author Zoltan Dezso
Advisor Michael Gekhtman
Contributor Jones, Gerald, Committee Member
Contributor Barabási, Albert-László, Committee Member
Contributor Kolda, Christopher, Committee Member
Contributor Newman, Kathie, Committee Member
Contributor Michael Gekhtman, Committee Chair
Degree Level Doctoral Dissertation
Degree Discipline Physics
Degree Name PhD
Defense Date
  • 2005-08-25

Submission Date 2005-08-31
Country
  • United States of America

Subject
  • virus spreading

  • information acces

  • protein complexes

  • complex networks

Publisher
  • University of Notre Dame

Language
  • English

Record Visibility Public
Content License
  • All rights reserved

Departments and Units

Files

Please Note: You may encounter a delay before a download begins. Large or infrequently accessed files can take several minutes to retrieve from our archival storage system.