Analyzing the Facebook friendship graph

Analyzing the Facebook friendship graph

S. Catanese1, P. De Meo1,2, E. Ferrara3, G. Fiumara1 and A.Provetti1,4

1Dept. of Physics, Informatics Section, University of Messina

2Dept. of Computer Sciences, Vrije Universiteit Amsterdam

3Dept. of Mathematics, University of Messina

3Oxford-Man Institute, University of Oxford

Int’l Conf. on Web Intelligence, Mining and SemanticsMay 26th 2011, Sogndal

Catanese, De Meo, Ferrara, Fiumara & Provetti ()Analyzing the Facebook friendship graph WIMS11 1 / 43

Outline

1 MotivationMain objectiveThe Basic ProblemClassic Work

2 Our Results/ContributionData Extraction and CleaningData AnalysisMain Results

3 Future Issues


Outline



3 Future Issues


Main objective

Extract a (partial) graph of friendship relations from FacebookI starting from the friendlist of a real userI accessing only publicly accessible data of Facebook users

using:I a wrapper (for extraction, cleaning and normalization of data)I a tool for graph visualization and analysis

developed by some of us


Main objective





Main objective





Outline



3 Future Issues


Social NetworksA Taxonomy

Social Networks (SN)Described with graphs representing users and relationships amongthem

Organizational NetworksCollaboration NetworksCommunication NetworksFriendship NetworksOnline Social Networks (OSNs) [1]:

I Social Communities: Facebook, MySpace, etc.I Social Bookmarking: Digg, Delicious, etc.I Content Sharing: YouTube, Flickr, etc.


Social NetworksA Taxonomy

Social Networks (SN)Described with graphs representing users and relationships amongthem

Organizational NetworksCollaboration NetworksCommunication NetworksFriendship NetworksOnline Social Networks (OSNs) [1]:

I Social Communities: Facebook, MySpace, etc.I Social Bookmarking: Digg, Delicious, etc.I Content Sharing: YouTube, Flickr, etc.


Social NetworksExamples

fig1-a.png

Figure: Organizational Network

fig1-c.png

Figure: Friendship Network

fig1-b.png

Figure: Collaboration Network

fig1-d.png

Figure: Online Social Network


Mining Online Social NetworksMotivation

Is the distribution of friendship computable?

Calculating graph properties of OSNs

Exploiting new algorithms in following tasks:

I Walking through a large graph (e.g. BFS, MHRW, etc.)I Data compression (matrix decomposition, quadtrees, etc.)I Efficient visualization of large graphsI Clustering data (Fruchterman-Reingold, Harel-Koren, etc.)I Optimize efficiency in metrics evaluation (e.g. All-Pairs

Shortest-Paths related: BC, CC, diameter, etc.)

Studying the scalability of the problem

Investigating similarities between OSNs and real-life SNs






































Mining Online Social NetworksPros and Cons

Pros:I Large-scale studies of phenomena and behaviors impossible beforeI Relations among users are clearly definedI Data can be automatically acquiredI Huge amount of information can be minedI Several levels of granularity can be established

Cons:I Large-scale mining issuesI Computational and algorithmic challengesI Online friendship 6= Real-life friendshipI Bias of data depends on visiting algorithm [2]


Mining Online Social NetworksPros and Cons

Pros:I Large-scale studies of phenomena and behaviors impossible beforeI Relations among users are clearly definedI Data can be automatically acquiredI Huge amount of information can be minedI Several levels of granularity can be established

Cons:I Large-scale mining issuesI Computational and algorithmic challengesI Online friendship 6= Real-life friendshipI Bias of data depends on visiting algorithm [2]


Outline



3 Future Issues


Classic Work on (online or offline) SNs

Milgram, Travers [3]: the Small World problem (1969-70)Zachary [4]: ’mining’ and modeling real-life SNs (1980)Kleinberg [5]: the small world problem from an algorithmicperspective (2000)Golbeck et al. [6]: social networks vs OSNs (2005)Barabasi [7], Leskovec [8], Shneiderman [9], etc.: all focusing onOSNs and their analysis (nowadays)

I Online Social Network Analysis and ToolsI Large-scale data mining from OSNsI Visualization of large graphsI Bias of data acquired from OSNsI Dynamics and evolution of OSNs


















Outline



3 Future Issues


Mining the Facebook graphVisiting Algorithm

BFS approach: starting from a single seed (aFB profile), visiting friend-lists of nodes in orderof discovering.

Pros:

Optimal solution for unw. und. graphs

Implementation is easy and intuitive

Cons:

Introduces bias in incomplete visits

Challenges:

FB anti-data mining policies

fig2.png

Figure: Breadth-firstsearch (3rd sub-level)

1 Seed

2-4 Friends

5-8 Friends of friends

9-12 Friends of fr. of fr.


Mining the Facebook graphDesign of the Mining Agent

Figure: State Diagram of the Data Mining Process


Mining the Facebook graphArchitecture

Java applicationFirefox browser embeddedXPCOM/XULRunner interface

Web pages spiderWrapper

fig10.png


Mining the Facebook graphHow the Agent Works

Agent Initialization:FB authentication → Seed friend-list pageSelection an example friend → XPath extractionWrapper generation and adaptationWrapper execution → Generation of the queue

Agent Execution:Load FIFO queueFor all the user profiles in the queue:

I Visit friend-list page of the current userF Extract friends (nodes) and save friendships (edges)F Insert unvisited profiles in the queue

I Visit ’next pages’ of the friend-listI Cycle the process


Mining the Facebook graphHandling DataPossible representations of vis-ited nodes and edges:

Adjacency listAdjacency matrix

fig5.png

fig11.png

Possible representation of BFSvisit for unvisited nodes:

FIFO queue

fig8.png


Mining the Facebook graphCleaning Data

removing duplicate nodesexploiting hash tables

relinking edges

deleting parallel edges

Data cleaning: O(n) time (optimal)

fig9.png

Structured Format: Clean datais saved under the XML structureGraphML

fig6.png


Mining the Facebook graphAgent Running

fig7.png


Outline



3 Future Issues


Network Analysis MetricsTypes of Networks

Classifications of several types of networks exist. They affect metricsand maps generated in order to reflect their interpretation.

Networks member’s point of viewI EgocentricI PartialI Full

Networks entity’s point of viewI UnimodalI MultimodalI BimodalI Affiliation

Multiplex networks






Multiplex networks






Multiplex networks


Network Analysis MetricsFacebook Friendship NetworkFacebook characteristics:

Egocentric networks: the term ego denotes a person connectedto everyone (alter) in the networkUnweighted, undirected network:

I 1.0 degree

I 1.5 degree

I 2.0 degree

fig12.png

Shows a natural effect of clustering around different areas of aperson’s life: friends, classmates, workmates, family ecc.




I 1.0 degree

I 1.5 degree

I 2.0 degree

fig12.png





I 1.0 degree

I 1.5 degree

I 2.0 degree

fig12.png



Network Analysis MetricsMeasures

Network metricsAllow analysts to systematically dissect the social world, creating abasis on which to compare networks, track changes in a network overtime and determine the relative position of individuals and clusterswithin the network.

Research focuses on:I Structure of the whole graph;I Large sub-graphs;I Identifying individual nodes of particular interest;I Analyze the whole graph aggregated over its entire lifetime;I To slice the network into units of time to explore the progression of

the development of the network.

A starting point: list from Perer and Shneiderman


Network Analysis MetricsMeasures

Network metricsAllow analysts to systematically dissect the social world, creating abasis on which to compare networks, track changes in a network overtime and determine the relative position of individuals and clusterswithin the network.

Research focuses on:I Structure of the whole graph;I Large sub-graphs;I Identifying individual nodes of particular interest;I Analyze the whole graph aggregated over its entire lifetime;I To slice the network into units of time to explore the progression of

the development of the network.

A starting point: list from Perer and Shneiderman


Network Analysis MetricsMeasures - Perer and Shneiderman List

Overall network metrics: number of nodes, number of edges,density, diameter ecc;Node rankings: degree, betweenness and closeness centrality;Edge rankings: weight, betweenness centrality;Node rankings in pairs: degree vs. betweenness, plotted on ascatter gram;Edge rankings in pairs;Cohesive subgroups: finding communities;Multiplexity: analyzing comparisons among different edge types.


Analyzing Social NetworksVisual Analysis: Motivation

Visualizing Social NetworksConstructing visual images of social networks provides insights aboutthe structure of a network, so as representing a visual support forexplaining network phenomena [10].

Graph drawing issues:I As network complexity increases, its illegibility increases as well;I Interactive operations on nodes, such as filtering or manual

placement, are needed


Analyzing Social NetworksBetter-quality Network Visualization

Readability Metrics (RMs)RMs measure how much understandable is the graph drawing (such asthe number of edge crossings or occluded nodes in the drawing) [11].

Each algorithm attempts to find an optimal layout of the graph,often according to a set of readability metrics;A simple interim set of guidelines might aspire to the fourprinciples of NetViz Nirvana [12]:

I Every vertex is visible;I Every vertex’s degree is countable;I Every edge can be followed from source to destination;I Clusters and outliers are identifiable.

Approach: layout and filtering techniques.














SNA ToolsSome Powerful Tools and Libraries Adopted

GUESS focuses on improving the interactive exploration ofgraphs.NodeXL developed as an add-in to the Microsoft Excel 2007spreadsheet software, provides tools for network overview,discovery and exploration.LogAnalysis helps forensic analysts in visual statistical analysisof mobile phone traffic networks.Jung and Prefuse provide Java APIs implementing algorithmsand methods for building applications for graphical visualizationand SNA for graphs.A list of other SNA tools for extract, analyze and display socialmedia networks can be found on International Network for SocialNetwork Analysis (INSNA) site 1.

1http://www.insna.org/software/index.htmlCatanese, De Meo, Ferrara, Fiumara & Provetti ()Analyzing the Facebook friendship graph WIMS11 27 / 43

Outline



3 Future Issues


Facebook Network AnalysisNodeXL - Overall Metrics

Graph Type: UndirectedVertices: 547,302Unique Edges: 836,468Edges With Duplicates: 0Total Edges: 836,468Self-Loops: 0Connected Components: 2Single-Vertex Connected Components: 0Maximum Vertices in a Connected Component: 546,733Maximum Edges in a Connected Component: 835.9Maximum Geodesic Distance (Diameter): 10Average Geodesic Distance: 5.00

Table: Overall Network Metrics


Facebook Network AnalysisNodeXL - Miscellaneous Metrics

Minimum Maximum Average MedianDegree 1 4,958 3.057 1.000PageRank 0.269 2,120.268 1.000 0.491Clustering Coefficient 0.000 1.000 0.053 0.000Eigenvector Centrality 0.000 0.003 0.000 0.000

Table: Miscellaneous Metrics


Facebook Network GraphLogAnalysis Force Directed Filtered View (25K Nodes Sub-graph)

fig7cat.png


Facebook Network GraphLogAnalysis Force Directed Filtered View (2.0 degree)

fig8cat.png


Facebook Network GraphLogAnalysis Force Directed Aggregate Filtered View (2.0 Degree)

fig9cat.png


Facebook Network GraphNodeXL Visualization (25K Nodes Sub-graph)

fig10cat.png


Facebook Network GraphNodeXL Filtered Visualization (25K Nodes Sub-graph)

fig11cat.png


Facebook Network GraphNodeXL Filtered Visualization (25K Nodes Sub-graph)

fig12cat.png


Metrics Importance: Betweenness CentralityTop 25 Nodes Ordered by BC (25K Nodes Sub-graph)

fig4.png


Future Issues

Enrich the sample (currently 5 million nodes and 15 million edges)Refine features and metrics thanks to larger sampleStudy communities emerging from the overall graphImplement parallel techniques to speed-up metrics calculationsDetermine scaling (-up and -down) coefficientsHow visiting algorithms affect extracted dataDynamic (i.e., temporal) evolution of the graph


Thank you


For Further Reading I

R. KumarOnline social networks: modeling and miningProc. of the 2nd ACM International Conference on Web Search and DataMining, 2009

M. Kurant, A. Markopoulou, P. ThiranOn the bias of BFSArxiv preprint arXiv:1004.1729, 2010

S. Milgram, J. TraversAn experimental study of the small world problemSociometry, 32(4), 1969

W. ZacharyA language for modeling and simulating social processPhD Thesis, 1980


For Further Reading II

J. KleinbergThe small-world phenomenon: an algorithm perspectiveProc. of the 32nd ACM symposium on Theory of computing, 2000

J. Golbeck et al.Social networks appliedIEEE Intelligent Systems, 20(1), 2005

A.L. Barabasi et al.Linked: the new science of networksAmerican Journal of Physics, 71(4), 2003

J. LeskovecDynamics of large networksPhD Thesis, 2008


For Further Reading IIIB. ShneidermanAnalyzing (social media) networks with NodeXLProc. of the 4th International Conference on Communities andTechnologies, 2009

L.C. FreemanVisualizing Social NetworksJournal of Social Structure, 2000

B. Shneiderman, C. DunneImproving Graph Drawing Readability by Incorporating ReadabilityMetrics: A Software Tool for Network AnalystsUniversity of Maryland, HCIL Tech Report HCIL-2009-13, May 2009

B. Shneiderman, A. ArisNetwork Visualization with Semantic SubstratesIeee Symposium on Information Visualization and Ieee Trans,Visualization and Computer Graphics 12 (5) (2006) 733-740


For Further Reading IV


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Analyzing the Facebook friendship graph

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