1. Social Networking: Large scale Networks
Contents:
Random Networks Vs. Scale Free Networks
Preferential Attachments.
Scale Free Networks: Formal Definitions.
Scale Free Networks: Other Definitions
Strength and Weakness of Scale Free Networks.
Scale Free Networks: Examples
Degree of Separation
Small World Networks: Stanely Milgram’s Experiment.
Small World Networks.

2. Random Networks Vs. Scale Free Networks
Scale-free networks follow a power law distribution.
The scale free model describes networks as having many nodes with only a few links and a few nodes with many links.

3. Scale Free Networks: Preferential Attachment

4. Scale Free Networks: Formal Definition

5. Scale Free Networks: Other Definition

6. The Strength and Weakness of Scale Free Networks

7. Scale Free Network: Examples

8. Degree of Separation

9. Small World Networks

10. Small World Networks

11. Small World Networks

12. Test your understanding
Q1. Suppose you have two graphs (a) Social Networking site’s graph, where all members are represented as nodes and connections between them are represented as undirected edges, (b) Road network, where cities are represented as node of graph and if there exist road-path between any two cities then, it is represented as undirected edge of graph. It is possible to categorize both networks (i.e. whether scale-free of random network). If yes then what will be the merits and demerits of both networks. Q2. Can you represent the author citation network as small-world network ? Q3. Is it possible to develop scale-free networks without using preferential attachments ? Q4.Can you use the characteristics of scale-free networks for network security ? (describe)

13. References
Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286 (1999)
Barabási, A.L., Oltvai, Z.N.: Network biology: understanding the cell's functional organization. Nat Rev Genet 5 (2004)
Bollobas, B.: Random graphs. Cambridge University Press, Cambridge (2001), ISBN:
Barabási, A-L.; Albert, R.; and Jeong, H. "Mean-Field Theory for Scale-Free Random Networks." Physica A 272, , 1999.
Milgram, Stanley (1967). "The Small World Problem". Psychology Today 1 (1): 60–67.
Buchanan, Mark (2003). Nexus: Small Worlds and the Groundbreaking Theory of Networks. Norton, W. W. & Company, Inc. ISBN