Web Science/Part2: Emerging Web Properties/Modeling the Web as a graph

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Web Science/Part2: Emerging Web Properties

Web Science/Part2: Emerging Web Properties/Modeling the Web as a graph

Web Science/Part2: Emerging Web Properties/MoocIndex

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Modeling the Web as a graph

Learning goals

Associated units

Further reading

Discussion

Learning goals

Associated units

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Reviewing terms from graph theory

1. Be familiar with a set theoretic way of denoting a graph
2. Know at least 4 different types of graphs
3. Have practiced your abilities in reading and writing mathematical formulas

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The standard web graph model

Be able to model web pages as a graph

Know that the authorship graph is bipartite

Know what kind of graph the graph of web pages is

(as always) be aware of the fact that modeling is done by making choices

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Descriptive statistics of the web graph

Know terms like Size and (unique) volume

Be able to count the in and out degree of web pages

Have an idea what kind of law (in & out) degree distributions follow

Know that degree is not distributed in a fair way

Know that the Gini coefficient can be used to measure fairness

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Topology of the web graph

Understand the notion of a path in a (directed) graph

Know that shortest paths between nodes need not be unique

Understand the notion of a strongly connected component

Know about the diameter of a graph

Be aware of the bow tie structure of the Web

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Modelling-graphs-with-linear-algebra

Be able to read and build an adjacency matrix of a graph

Know some basic matrix vector multiplications to generate some statistics out of the adjacency matrix

Understand what is encoded in the components of the k-th power of the Adjacency matrix of a graph

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Further reading

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Discussion

Navigation

1. How big is the World Wide Web
   1. Problems with the question about the size of the Web
   2. 3 ways to study the Web
   3. A simplistic descriptive model
   4. An unrealistic, simplistic generative model
   5. Summary, further reading, homework
2. Simple statistical descriptive Models for the Web
   1. Counting Words And Documents
   2. Typical length of a document
   3. How to formulate a research hypothesis
   4. Number of words needed to understand most of Wikipedia
   5. Linguists way of checking simplicity of text
3. Advanced statistical descriptive models for the Web
   1. The Zipf law for text
   2. Visually straight lines on log log plots
   3. Fitting a curve on a log log plot
   4. Zipf law powerlaw or pareto law.webm
4. Modelling Similarity of Text
   1. Similarity Measures and their Applications
   2. Jaccard Similarity for Sets
   3. Cosine Similarity For Vectorspaces
   4. Probabilistic Similarity Measures Kullback Leibler Divergence
   5. Comparing Results of Similarity Merasures
5. Generative Models for the Web
   1. Introduction to generative modelling.webm
   2. Sampling from a probability distribution
   3. Evaluating a generative model
   4. Pittfalls when increasing the number of model parameters
6. Modeling the Web as a graph
   1. Reviewing terms from graph theory
   2. The standard web graph model
   3. Descriptive statistics of the web graph
   4. Topology of the web graph
   5. Modelling-graphs-with-linear-algebra