A. Mislove, M. Marcon, K Gummadi, P. Druschel, B. Bhattacharjee

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Measurement and Analysis of Online Social Networks

• A. Mislove, M. Marcon, K Gummadi, P. Druschel, B.
  Bhattacharjee

Presentation by Shahan Khatchadourian Supervisor
Prof. Mariano P. Consens
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Focus

• graphs of online social networks
• how they were obtained
• how they were verified
• how measurement and analysis was performed
• properties of obtained graphs
• why these properties are relevant

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Why study the graphs?

• important to improve existing system and develop
  new applications
• information search
• trusted users
• what is the structure of online social networks
• what are different ways to examine a social
  network when complete data is not available?
• how do they compare with each other and to the
  Web?

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Which graphs?

• Flickr, YouTube, LiveJournal, and Orkut
• All are directed except for Orkut
• Weakly Connected Component (WCC)
• Strongly Connected Component (SCC)

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How are the graphs obtained?

• API
• users
• groups
• forward/backward links
• HTML Screen Scraping

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Summary of graph properties

• small-world
• scale-free
• correlation between indegree and outdegree
• large strongly connected core of high-degree
  nodes surrounded by small clusters of low-degree
  nodes

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Crawling Concerns - Algorithms

• BFS and DFS
• Snowball method underestimates number of
  low-degree nodes. In social networks, they
  underestimate the power-law coefficient, but
  closely match other metrics such as overall
  clustering coefficient.

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Crawling Concerns FW links

• cannot reach entire WCC

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How to Verify Samples

• Obtain a random user sample
• LJ feature which returns 5,000 random users
• Flickr random 8-digit user id generation
• Conduct a crawl using these random users as seeds
• See if these random nodes connect to the original
  WCC
• See what the graph structure of the newly crawled
  graph compares to original

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Crawling Concerns FW links

• no effect on largest WCC

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Crawling Concerns FW links

• increasing the size of the WCC by starting at a
  different seed

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Site YT Flickr LJ Orkut
Users(mill) 1.1 1.8 5.2 3
Links(mill) 4.9 22 72 223
symmetry 79.1 62.0 73.5 100.0
Access (FW Forward-only) (SS HTML screen-scraping) API (users only) FW SS for group info API (users groups) FW API (users groups) FW BW SS for users groups
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Link Symmetry

• even with directed links, there is a high level
  of symmetry
• possibly contributed to by informing users of new
  incoming links
• makes it harder to identify reputable sources due
  to dilution
• possible sol who initiated the link?

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Power-law node degrees

• Orkut deviates
• only 11.3 of network reached (effect of partial
  BFS crawl Snowball method)
• artificial cap of users number of outgoing
  links, leads to a distortion in distribution of
  high degrees
• differs from Web

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Power-law node degrees
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Power-law node degrees
e.g. analysis of top keywords
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Spread of Information
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Power Law affectors

• services, accessibility, features

100
100
mobile users
10-8
10-8
1
1
10000
10000
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Correlation of indegree and outdegree

• over 50 of nodes have indegree within 20 of
  their outdegree

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Path lengths and diameter

• all four networks have short path length
• Broder et al noted if Web were treated as
  undirected graph, path length would drop from 16
  to 7, so what?

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Link degree correlations

• JDD joint degree distribution
• mapping between outdegree and average indegree of
  all nodes connected to nodes of that outdegree
• YouTube different due to extremely popular users
  being connected to by many unpopular users
• Orkut shows bump due to undersampling

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Joint degree distribution and Scale-free behaviour
cap on links
undersampling of low-degree nodes
celebrity-driven nature
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Densely connected core

• removing 10 of core nodes results in breaking up
  graph into millions of very small SCCs
• why an SCC? directed links matter for actual
  communication
• graphs below show results as nodes are removed
  starting with highest-degree nodes (left) and
  path length as graph is constructed beginning
  with highest-degree nodes(right)

Sub logarithmic growth
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Tightly clustered fringe

• based on clustering coefficient
• social network graphs show stronger clustering,
  most likely due to mutual friends

Possibly because personal content is not shared
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Groups

• group sizes follow power-law distribution
• represent tightly clustered communities

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Groups

• Orkut special case maybe because of partial crawl

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Node Value Determination

• Directed Graph, current model
• nodes with many incoming links (hubs) have value
  due to their connection to many users
• it becomes easy to spread important information
  to the other nodes, e.g. DNS
• unhealthy in case of spam or viruses
• in order for a user to send spam, they have
  become a more important node, amass friends

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Node Value Determination

• Link Initiator, requires temporal information
• if user A requests a link with user B, does that
  mean that user B is more important?
• even though graphs have a high level of link
  symmetry, this additional information can offset
  this symmetry
• unfortunately, examined graphs do not have
  temporal information

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Trust

• lendingclub.com, Facebook application
• people are more willing to lend money to friends
  who are linked through a short path
• people are more willing to pay back those who are
  linked through a short path
• no indication of whether this actually works
• does trust increase as degree increases?
• what credit rating and JDD does a person have to
  get a good interest rate?

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Thank you
shahan_at_cs