Measurement and Analysis of Online Social Networks Alan Mislove,Massimiliano Marcon, Krishna P. Gummadi, Peter Druschel, Bobby Bhattacharjee Presented.

Measurement and Analysis of Online Social Networks

Alan Mislove,Massimiliano Marcon, Krishna P. Gummadi, Peter Druschel, Bobby Bhattacharjee

Presented by Aleksandra Potapova

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

What was studied?

• Flickr• YouTube• LiveJournal,• Orkut

Why should we perform measurements and analysis in social networks?

• To design future online social network based systems

• To understand the impact of online social networks on the Internet

• To reduce the number of spam • To improve security aspect

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Summary of graph properties

• small-world• power-law• scale-free• correlation between indegree and outdegree• large strongly connected core of high-degree

nodes surrounded by small clusters of low-degree nodes

Crawling Algorithms for large graphs

• BFS and DFS• Snowball method(crawling only small subset

of a graph by ending BFS early): – Partial BFS craws overestimate node degree and

underestimate the level of symmetry.– In social networks, they underestimate the power-

law coefficient, but closely match other metrics such as overall clustering coefficient.

How social networks should be crawled?

• The focus of the paper – WCC– Forward and reverse links should be used

How the graphs were obtained?

• API– users– groups– forward/backward links

• HTML Screen Scraping

How to Verify Samples

1. Obtain a random user sample– LJ: feature which returns 5,000 random users– Flickr: random 8-digit user id generation

2. Conduct a crawl using these random users as seeds3. See if these random nodes connect to the original

WCC4. See what the graph structure of the newly crawled

graph compares to original

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

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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 user’s number of outgoing links,

leads to a distortion in distribution of high degrees

• differs from Web

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Power-law node degrees

Power-law node degrees

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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

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Link degree correlations

• JDD: joint degree distribution(how often nodes of different degree connect to each other)

• Knn --- mapping between outdegree and average indegree of all nodes connected to nodes of that outdegree– Used for aproxmation of JDD

• YouTube different due to extremely popular users being connected to by many unpopular users

• Orkut shows bump due to undersampling

Measurement and Analysis of Online Social Networks 20

Joint degree distribution and Scale-free behaviour

undersamplingof low-degreenodes celebrity-driven

nature

cap on links

Measurement and Analysis of Online Social Networks 21

Densely connected core• removing 10% of core nodes results in breaking up graph into millions of

very small SCCs• 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

Measurement and Analysis of Online Social Networks 22

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

Measurement and Analysis of Online Social Networks 23

Groups

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

Measurement and Analysis of Online Social Networks 24

Groups

• Orkut special case maybe because of partial crawl

Measurement and Analysis of Online Social Networks 25

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

• Questions?