Peer Centralityin Socially-Informed P2P Topologies

Nicolas Kourtellis, Adriana Iamnitchi

Department of Computer Science & EngineeringUniversity of South Florida

Tampa, USA

11th IEEE International Conference on Peer-to-Peer ComputingKyoto, Japan, 2011

Social and Socially-aware Applications

Applications collect social information: Location, collocation, history of interactions, etc.

Use it for recommendations, inferring trust, etc. How is this information stored and mined?

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Internet Applications Mobile Applications

Social Graphs and P2P Networks

User social graph over particular activity edges Users’ peers organized into a P2P network Users store their data (edges) on particular peers

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Motivational Example

G’s 2-hop neighborhood? Social graph traversals translate to many P2P

lookups

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=> B, C, E, A, D, F, I

Motivation

Peers acquire particular network properties due to users storing their data on them. E.g., peer 2 more central than peer 1

Application performance affected by projection of social graph on P2P network.

How does the topology of the social graph affect the P2P routing? 5

Projection Graphs: help us study the network properties of the peers.

Projection Graph Model

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ProjectionGraph (PG)

P2P Overlay

SocialGraph (SG)

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Outline

Motivation Projection Graph Model Social Network Centrality Metrics

Degree Node Betweenness Edge Betweenness

Centrality Calculation Limitations Research Questions Experimental Setup Experimental Results Impacts on Applications & Systems

Degree Centrality

Direct connections of a node with others Useful to identify nodes that:

Can contact directly many others with a message broadcast and perform as network hubs in a graph

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Node Betweenness Centrality

Shortest paths between two nodes that pass through a third node, over all shortest paths between the two nodes.

Useful to identify nodes that: Control communication over indirect routes Can host data caches for reduced latency to locate

data

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Edge Betweenness Centrality

Shortest paths between two nodes that pass through an edge, over all shortest paths between the two nodes.

Useful to identify edges that: Connect distant parts of network Can monitor and block malware traffic

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Centrality Calculation: Not easy!

Limiting factors in calculation of peer measures: Users keep their data private (encrypted, etc.) Users allow access only to their peer Intractable number of shortest paths in large

graphs Unavailability of data due to peer churn

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Research Questions

Assuming that users allow access to their centrality scores in the social graph (SG): How well can we approximate the centrality scores

of their peers in the projection graph (PG)? How do the cumulative centrality scores of users

associate with the centrality scores of their peers? How does the number of users storing data per

peer affect the centrality scores of their peers?

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Outline

Motivation Projection Graph Model Social Network Centrality Metrics

Degree Node Betweenness Edge Betweenness

Calculation Problems Research Questions Experimental Setup Experimental Results Impacts on Applications & Systems

Experimental Setup

Community Detection: a recursive version of the Louvain algorithm

Each community mapped on a peer Merged communities to reach average size 10, 20, …, 1000

users/peer Community sizes exhibit social structure of power-law

nature Calculate & compare centralities for SGs & PGs 14

Social Network Number of Users Number of Edges

gnutella04 10,876 39,994

gnutella31 62,561 147,878

enron 33,696 180,811

epinions 75,877 405,739

slashdot 82,168 504,230

Comparison of Centrality Scores

Turning point: Centralities of peers reach max P2P network exhibits optimal structuring Maximum opportunity for peers to influence information

flows through them.

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Users/Peervs.

Degree

Users/Peervs.

Node Betweenness

Users/PeerVs.

Edge Betweenness

Correlation of Centrality Scores

Before turning point: PG resembles closely SG Correlation of SG and PG

metrics is highest Degree and Node

Betweenness estimated by local info (cumulative scores)

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After turning point: PG topology loses social

properties A highly connected clique Peers acquire equal

importance in graph traversal

Users/Peervs.

Degree

Users/Peervs.

Node Betweenness

Users/Peervs.

Edge Betweenness

Finding High Betweenness Peers

Such peers affect system performance and security. Difficult to identify (network scale, peer churn, etc.) Can we identify such peers, knowing the top

betweenness users?

Top 5% betweenness centrality users => top betweenness centrality peers with 80–90% accuracy 17

Users/Peer(Top-N% users)

Users/Peer(Top-N% communities)

Impact on Applications & Systems

Target high degree peers to: Decrease search time Increase breadth of search and diversity of results

Target high betweenness peers to: Monitor information flow and collect traces Place data caches and indexes of data location Quarantine malware outbursts Disseminate software patches

Tackle P2P churn Predict centrality of peers to allocate resources

Reduce overlay overhead Enhance routing tables with P2P edges for faster &

more secure peer discovery18

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Thank you!

This work was supported by NSF Grants:CNS 0952420 and CNS 0831785

http://www.cse.usf.edu/dsg/nkourtel@mail.usf.edu

Projection Graphs

Community Size Distribution

Degree Distribution

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Approximation of Peer Betweenness

Top 5% betweenness centrality users => top betweenness centrality peers with 80–90% accuracy 21

1. Pick top-N% betweenness users.2. Identify set U of their peers.3. Pick k=|U| top betweenness peers,

set P.4. Compare sets U & P, find peer

overlap.

1. Pick set C communities in top-N% cumulative score of betweenness.

2. Pick q=|C| top-N% betweenness peers, set P.

3. Compare sets C & P, find peer overlap.

P2P Social Networks and Services

P2P Systems that could benefit from this work: Commercial Efforts:

Diaspora FreedomBox EnThinnai

Academic Efforts: Prometheus LifeSocial.KOM Vis-à-Vis Safebook PeerSoN Tribler F2F Turtle Sprout 22