Complex networks usually exhibit small diameter, high clustering and power-law degree distribution. Define these three properties, in particular explain what is meant by ?small? and ?high.?

Consider an epidemic disease spreading in a regular graph with degree d. An infected node can infect a susceptible neighbour with probability p.
How do you define the basic reproductive number and how does it affect the disease?s evolution?

In class we studied an algorithm that uses a random walk to estimate the number of nodes in a network. Along similar lines, devise an algorithm to estimate the number of nodes with degree greater than a fixed number, say 10. Hint: Assume that the number of links in the network is known.

What is the Bulk Synchronous Process (BSP) model? What are pros and cons? 

Imagine you work for a library which data are in a triple store. The RDF graphs it contains are following a fictitious schema having for namespace and URL http://lib-int.org/voc# typically associated to the prefix ``lint.''
This schema contains:
- a class lint:Book representing the different books in the Library,
- a class lint:Author representing the different Authors known in the Library,
- a class lint:Editor representing the Editors known in the Library,
- a class lint:Article representing the different articles in the Library,
- a property lint:workedOn indicating that an Author or an Editor (domain) worked on an Article or a Book (range).
Write a SPARQL query extracting all the pairs of nodes of the graph that represent an Author that worked on an Article.

Explain why Twitter users belonging to the same strongly connected component (SCC) were grouped together in order to identify the highways of information propagation of Twitter? What are the properties of SCCs in terms of information propagation.