SOCIAL NETWORKS AN ENHANCED MODEL

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SOCIAL NETWORKS AN ENHANCED MODEL

• Project Presentation (ECE 568)
• Swapnil Dipankar
• Steve Adegbite
• Chaowu Lin
• Sameer Pai

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Social Networks - Introduction

• Early formalizations of sociometric research was
  first conceived by Jacob Moreno in 1934, but
  Social Network Analysis began to come into
  prominence in 1967 by the work of Stanley Migram
  who was a Social Psychologist at Harvard
  University.
• Stanley Migram conducted experiments in Omaha,
  Nebraska, Wichita and Kansas independently.
• His work is now commonly referred to as the six
  degrees of separation which is also known as
  the small world phenomenon.

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Social Networks Introduction (Continued)

• What is a Social Network?
• A Social network comprises a set of people with a
  similar pattern of interaction among them.

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Social Networks Introduction (Continued)

• However, over the past few years, researchers
  have extended the concept of Social Networking
  from viewpoint of restricting its application to
  only people to even a broader perspective
  especially in the field of distributed computing
  which involves the dispersing and searching for
  information which plays a very vital role in the
  management of knowledge.

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Social Networks Introduction (Continued)

• Social Networks primarily contain
• A set of entities.
• Associations between them.

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Social Networks Introduction (Continued)
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Social Networks Introduction (Continued)
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Social Networks Introduction (Continued)

• Thus a Social Network could be more appropriately
  defined as a network that consists of nodes
  (often referred to as actors or entities such as
  people, organizations or simply objects that are
  linked by binary relations such as social
  relations, dependencies or the need for exchange.

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Examples of Present day Social Networks

• Friendster (www.friendster.com)
• Tribe (www.tribe.net)
• Ryze (www.ryze.org)
• Google (www.google.com)
• Always On (www.alwayson-network.com)
• Linked In (www.linkedin.com)
• Just to mention a few.

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Current Social Network Models

• Generally speaking, Social Network models may be
  classified based on the nature of their origin.
  This method of taxonomy was initiated by John
  Skvoretz in 1991.
• The two main groups are
• Theoretical models.
• Methodological models.
• However, methodological model are more prevalent
  because theoretical models involve a very high
  level of complexity. Furthermore, most theories
  in Social Sciences are not formally stated. As a
  result, the underlying logic for its accurate
  representation can be extremely difficult to
  derive.

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Underlying Assumptions in Current Models

• Due to the fact that researchers are currently
  developing new interests and insights into the
  various applications of Social Networks, a myriad
  number of approaches exists for its analysis
  depending on each researchers area of interest.
  However, to limit not only the level of
  complexity but also the number of parameters to
  be estimated there are two main assumptions that
  are common to all models
• The Homogeneity Assumption This states that a
  particular effect does not depend on the
  identities of the node involved.
• The Markov Assumption This states that edges or
  arcs can be conditionally dependent only if they
  share at least one node in the original graph.

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Motivation and Applications of Social Networks

• The small world phenomenon constitutes a basic
  property of the Web which offers great
  importance. An example of this graph structure is
  in the Google Search engine.
• Social Networking is used to optimize the speed
  of search and Quality of Service in the Peer to
  Peer environment. A typical example of this is in
  the Gnutella P2P protocol.
• It increases the productivity and overall
  efficiency of enterprises by providing them
• the right information (documents)
• the right people (experts)

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Problems/Issues of Concern With Present Social
Network Models

• A more efficient implementation of referrals to
  improve the search of information. This has two
  main bifurcations
• Distributed Trust and Reputation Management.
• Knowledge Management.
• A means of retaining all users thereby fostering
  a continual growth.
• The need for a suitable business model.

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Trust and Accountability Available Models

• As the social communities and P2P networks
  continue to spruce up and thrive the networks,
  the problem of resource allocation continues to
  grow.
• Problems in resource allocation come up
  constantly in offering computer services.
• Traditionally they have been solved by making
  users accountable for their use of resources.
• Such accountability in distributed or
  peer-to-peer systems requires careful planning
  and discipline.

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Available Models (Continued)

• The main goal of accountability is to maximize a
  server's utility to the overall system while
  minimizing its potential threat. There are two
  ways to minimize the threat.
• One approach is to limit the risk (in bandwidth
  used, disk space lost, or whatever) to an amount
  roughly equivalent to the benefit from the
  transaction. This suggests
• Fee-for-service.
• Micro-payment model.
• The other approach is to make our risk
  proportional to our trust in the other parties.
  This calls for a reputation system.

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Reputation Model

• Features
• During each exchange, a server risks some amount
  of resources proportional to its trust that the
  result will be satisfactory.
• As a server's reputation grows, other nodes
  become more willing to make larger payments to
  it.
• The micro-payment approach of small, successive
  exchanges is no longer necessary.

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Reputation Model - Problems

• If the system allows impermanent and pseudonymous
  identities, reputation systems require careful
  development.
• If an adversary can gain positive attributes too
  easily and establish a good reputation, she can
  damage the system.
• Pseudo-spoofing - Establish many seemingly
  distinct identities that all secretly collaborate
  with each other.
• Conversely, if a well-intentioned server can
  incur negative points easily from short-lived
  operational problems, it can lose reputation too
  quickly.

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Our Approach The Grameen Model

• Also called the micro-credit scheme.
• Candidate for a loan must form a group with at
  least four other people who are not family
  members.
• Two members of the group originally receive a
  loan, and if they do well, the others then
  receive loans.
• The loan has to be returned back by the group and
  not by the individual borrower.

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The Grameen Model (Continued)
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The Grameen Model (Continued)

• Advantages of the Grameen Model
• First, the Grameen design provides strong
  incentive for good borrowers to join together,
  since they don't want to risk losing a loan
  because of one failure or troublemaker. The fact
  that they cannot join with other family members
  removes one sort of pressure to dilute group
  quality.
• Second, the members of the group have an
  incentive to monitor one another's activities
  actively. They can provide advice, assistance,
  education and, if necessary, insurance. The group
  members themselves are in the best position to
  know whether a recipient is slacking off or has
  just had a run of bad luck, and they have great
  incentives to monitor their behavior in an honest
  and helpful way.
• Third, all of this selection, monitoring,
  educating and insuring is done not by high-paid
  professionals, but by the peasants themselves.
  The transactions costs of using groups are far,
  far lower than are the transactions costs for
  traditional bank loans.

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Grameen Model and Social Networks-Relations
Social Network Group 2
Social Network Group 1
Social Network Group 3
Social Network Group n
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Our Social Network Model

• Subdivisions of problems
• Introduction of members into a Group.
• Induction of a Group into the Social Network.
• Trust and Accountability.
• Monitoring of the Groups in the Social Network.

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Our Model (Continued)

• Introduction of individuals in a group based on
  common interests and goals.
• Integration of group into the social network
• Trust and accountability issues.
• Establishing the authenticity of the Groups.
• Adding CC number or SSN as a part of the
  password.
• Establishing authenticity through SMS.

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Mathematics of Available Model

• Mathematical Model Classification
• Methodological Models.
• Theoretical Models.
• Our Mathematical Model and algorithm
• Random Graph Model - Random graphs with
  arbitrary degree distributions.

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Mathematics of Available Model
An Example of standard random graph. In this
case the number of vertices N is 16
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Mathematics of our Model

• Definition of Symbols
• N - Total nodes or vertices.
• p - The independent probability of a connecting
  edge for each pair of vertices.
• pk - Degree distributions.
• k - A random number drawn independent from the
  distribution pk for each vertex.
• Z - The average degree of a vertex in the
  network.

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Mathematics of our Model

• A vertex in a Random Graph.
• Binomial distribution
• when z (N-1) p

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Mathematics of Our Model

• Generating function G0(x)
• Instead of working directly with the degree
  distribution
• Example
• Average degree z of a vertex in the
  network

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Mathematics of Our Social Network

• Degree Distribution
• A power-law distribution characterized by the
  exponent
• An exponential cutoff characterized by the cutoff
  length
• Constant c is fixed by the requirement that the
  distribution be normalized.

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Mathematics of Our Social Network
Frequency
Degree distributions of our social networks
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Mathematics of Our Social Network

• Gives
• Where is the nth poly
  logarithm of x, Thus
• Substituting into Eq.3 , we then get

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Result and Future Work

• Our derivations are still going on.
• The interpretations and deductions from the
  mathematical model are yet to be made.
• We need to consider algorithm for social
  networks and the accountability and trust.
• If possible, run a simulation of our model.

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References

• M. E. J. Newman, D. J. Watts, and S. H. Strogatz
  -Random graph models of social networks.
• John Skvoretz - Complexity Theory and Models
  for Social Networks.
• Ulrik Brandes1 and Dorothea Wagner - Analysis
  and Visualization of Social Networks.
• Prabhakar Raghavan - Social Networks from the
  Web to the Enterprise.
• Yamini Upadrashta - Emerging Social Networks in
  Peer-to-Peer Systems.
• Bin Yu and Munindar P. Singh - Searching Social
  Networks.
• http//www.grameen-info.org/
• http//www.telecommons.com/villagephone/biblio.htm
  l
• Roger Dingledine, David Molnar Peer-To-Peer
  Harnessing the Power of Disruptive Technologies.