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What does the Web look like? How can we find patterns, communities,
outliers, in a social network? Which are the most central nodes in
a network? These are the questions that motivate this work.
Networks and graphs appear in many diverse settings, for example in
social networks, computer-communication networks (intrusion
detection, traffic management), protein-protein interaction
networks in biology, document-text bipartite graphs in text
retrieval, person-account graphs in financial fraud detection, and
others. In this work, first we list several surprising patterns
that real graphs tend to follow. Then we give a detailed list of
generators that try to mirror these patterns. Generators are
important, because they can help with "what if" scenarios,
extrapolations, and anonymization. Then we provide a list of
powerful tools for graph analysis, and specifically spectral
methods (Singular Value Decomposition (SVD)), tensors, and case
studies like the famous "pageRank" algorithm and the "HITS"
algorithm for ranking web search results. Finally, we conclude with
a survey of tools and observations from related fields like
sociology, which provide complementary viewpoints. Table of
Contents: Introduction / Patterns in Static Graphs / Patterns in
Evolving Graphs / Patterns in Weighted Graphs / Discussion: The
Structure of Specific Graphs / Discussion: Power Laws and
Deviations / Summary of Patterns / Graph Generators / Preferential
Attachment and Variants / Incorporating Geographical Information /
The RMat / Graph Generation by Kronecker Multiplication / Summary
and Practitioner's Guide / SVD, Random Walks, and Tensors / Tensors
/ Community Detection / Influence/Virus Propagation and
Immunization / Case Studies / Social Networks / Other Related Work
/ Conclusions
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