1. Identity and Search in Social Networks
Alireza Abbasi
Industrial Information Technology
Technical Paper Presentation
Information Technology Policy Program
Seoul National University

2. Bibliographic Details
Title: Identity and search in social networks
Authors:
Duncan J. Watts (Department of Sociology, Columbia University),
Peter Sheridan Dodds (Columbia Earth Institute, Columbia University),
M. E. J. Newman (Santa Fe Institute)
Journal: Science
Vol.: 262
No.: 5571
Pp.:
Month: April
Year: 2002

3. Context Small-World Experiment Searchability of Networks
Proposed Model
Six Contentions about Social Networks
Research Objective
Results
Conclusion

4. Small-World Experiment
Travers & Milgram’s famous Small-World experiment (1960s):
Choose a random person in Nebraska, Bob
Ask Bob to deliver a letter to a random person in Massachusetts, Lashawn (Target Person)
Tell Bob target’s name, address, and occupation
Instruct Bob to only send letter to people he knows on a first-name basis

5. Small-World Experiment
Bernard, David’s cousin who went to college with
David, mayor of Bob’s town
Bob, a farmer in Nebraska
Maya, who grew up in Boston
Six Degrees
of Separation
With Lashawn

6. Result of Small-World Experiment
Short paths exist between individuals in a large social network
Ordinary people can find these short paths

7. Searchability The property of being able to find a target quickly
Has been shown to exist in certain specific classes of networks that either possess
a certain fraction of hubs or
are built upon an underlying geometric lattice which acts as a proxy for “social space"

8. Proposed Model
A model for a social network that is based upon plausible social structures and offers an explanation for the phenomenon of searchability
Follows from 6 contentions about Social Networks

9. 1. Identity of Individuals
Sets of characteristics which Individuals attribute to themselves and others (social groups)

10. 2. Hierarchically Network
Individuals cluster, the world hierarchically into a series of layers,
top layer accounts for the entire world and
deeper layer represents a cognitive division into a greater number of increasingly specific groups

11. Hierarchy: Measuring Social Distance
Similarity xij between individuals i and j as the height of their lowest common ancestor level
xij = 1, if i and j belong to the same group.
g: group size, l: depth, b: branching ratio.

12. 3. Group Membership α measure of homophily
Basis for social interaction, and acquaintanceship
a link distance x with probability of acquaintance between nodes i and j
α is a tunable parameter, and c is a normalizing constant
α measure of homophily
If : all links will be as short as possible
If : individual is equally likely to interact with any other (yielding a uniform random graph)

13. 4. Multi-dimensional Clustering
Individuals hierarchically cluster the social world in more than one way (dimensional)
Example: by geography and by occupation
A node's identity is then as an H-dimensional coordinate vector vi , where vhi is the position of node i in the h th dimension.

14. 5. Social Distance
individuals construct a measure of “social distance" yij, the minimum ultrametric distance over all dimensions between two nodes i and j.

15. 6. Individual local Information
Individuals have two kinds of partial information
Social distance
measured globally but which is not a true distance
Network paths
generate true distances but which are known only locally

16. Research Objective
Determine the conditions under which the average length <L> of a message chain connecting a randomly selected sender s to a random target t is small.
p: message failure probability
q: probability of message reaching its target
r: fixed number (threshold)

17. Result
Searchable networks occupy a broad region of parameter space (α,H)
corresponds to choices of the model parameters
Model suggests that searchability is a generic property of real-world social networks.

18. Result Example (H-α) The region of searchable networks shrinks with N
r = 0.05, p = 0.25, b = 2, g = 100, z = g -1 = 99
N = (solid), N = (dot-dash), and N = (dash)
The region of searchable networks shrinks with N

19. Result Example q(H)
q: probability of message reaching its target, H: # of dimensions
α = 0 (squares) and α = 2 (circles) for the N = , threshold r = 0.05.
Empty symbols indicate the network is searchable (q ≥ r)
The best performance over the largest interval of α is achieved for H = 2 or 3

20. Compare the distribution of chain lengths
n(L): the number of completed chains of length L
Bar graph: original small-world experiment
P = 0.25, H = 2, z = 300, g = 100, For α = 1 and b = 10
Average chain length <L> ~ 6.7 near to original Small-World Experiment <L> ~ 6.5

21. Conclusion Model can apply to any data structure in which
data elements exhibit quantifiable characteristics analogous to our notion of identity, and
similarity between two elements can be judged along more than one dimension.
Efficient decentralized searches can be conducted utilizing simple, greedy algorithms
providing only that the characteristics of the target element and the current element's immediate neighbors are known.
location of data files in peer-to-peer networks, pages on the World Wide Web, information in distributed databases

22. Thank you
&
Best wishes