Inferring Peer Centralityin Socially-Informed P2P Systems

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

Socially-aware Applications

Applications collect and use social information: Location, collocation, history of interactions, etc. Build (implicit/explicit) social network of users Use: reduce spam, provide recommendations, etc.

Wide range of system architectures How does the social network of users affect the load

in a P2P architecture?

2Decentralization of user social data

• MobiClique• Yarta• ...

• PeerSoN• LifeSocial.KOM• Safebook• Prometheus• …

P2P Networks

Company Servers

MobileDevices

Social Graphs & P2P Networks

Users connected with application-specific edges User-contributed peers form a P2P network User social graph is partitioned into subgraphs &

stored on peers

Questions: How do applications traverse a distributed social graph? What does it mean for the P2P routing?

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Invite user G’s 2-hop hiking contacts to a trip

Social graph traversals => many P2P lookups

Application performance affected by projection of social graph on peers

Application Example

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=> 1-hop={B, C, E} 2-hops={A, D, F, I}

How do the properties of the projection graph compare with the properties of the social graph projected?

Projection Graph

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ProjectionGraph (PG)

P2P Overlay

SocialGraph (SG)

Projection Graph Model

Uses: Study properties of peers such as centrality Study how the social graph topology affects P2P

routing & system performance6

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Outline

Motivation Projection Graph Model Social Network Centrality Metrics

Degree Centrality Node Betweenness Centrality Edge Betweenness Centrality

Centrality Calculation: Limitations Experimental Questions Experimental Methodology Experimental Results Impacts on Applications & Systems

Number of edges of a node High degree centrality peers: Network Hubs

Can be targeted to directly influence many other peers with a message broadcast or distribute a search query

Degree Centrality

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Node Betweenness Centrality

Measures the extent to which a node lies on the shortest path between two other nodes

High betweenness centrality peers: Control communication between distant peers Can host data caches for reduced latency to locate

data

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Edge Betweenness Centrality

Measures the extent to which an edge lies on the shortest path between two nodes

High betweenness centrality edges: Connect distant parts of P2P network Can be monitored to block malware traffic

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Calculating Peer Centrality

Challenging because of: Limited access to user data (e.g., privacy settings) P2P network scale Peer churn

Through experimental analysis on the social and projection graph, we investigate how to circumvent these limitations

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Experimental Questions

Can we approximate the centrality of peers using the centrality scores of their users?

How does the number of users storing data per peer affect the centrality scores of their peers? Social graph is less dynamic than the P2P network Calculate infrequently centrality score of users & use it

to estimate their peer’s centrality

Spoiler Alert! [1, ~150] users/peer: Can estimate degree &

betweenness centrality of peers with good accuracy

Above 150 users/peer: The projection graph becomes highly connected => peers do not differentiate in centrality

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Naturally-formed communities offer incentives for resource sharing 1 community subgraph mapped per peer

Projection graphs generated from 5 real social graphs

Communities detected via recursive Louvain algorithm* Varied average community size: 5,10,20,…,1000 users/peer

Calculate correlation of centralities of users and their peers Compare average centralities of users and their peers Identify top centrality peers from their users’ scores

Experimental Methodology

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Social Network Users 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

*V. D. Blondel et al, “Fast unfolding of communities in large networks”,Journal of Statistical Mechanics: Theory and Experiment, vol. 10, 2008.

Correlation of Centrality Scores

[1-150] users/peer: Projection graph resembles

closely social graph Highest correlation of social &

projection graph metrics Degree & node betweenness

estimated from local information (cumulative scores)

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After 150 users/peer: Projection graph topology

loses social properties Highly connected network Peers participate equally

in graph traversal

Users/Peervs.

Degree

Users/Peervs.

Node Betweenness

Users/Peervs.

Edge Betweenness

Comparison of Centrality Scores

Increase number of users/peer turning point in projection graph More connections with other peers

increase peer degree & betweenness to maximum More social edges within peers

decrease edge betweenness to minimum 15

Users/Peervs.

Degree

Users/Peervs.

Node Betweenness

Users/PeerVs.

Edge Betweenness

Finding High Betweenness Peers

Placing data caches on high betweenness peers can reduce latency to locate data

Can we identify such peers, knowing the top betweenness users or communities?

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

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Users/Peer Users/Peer

With Top-N% users With Top-N% communities

Summary of Findings

[1, ~150] users/peer: Projection graph resembles closely social graph Highest correlation of social & projection graph metrics Degree & node betweenness can be estimated from

local information (cumulative scores of users) Cannot estimate well edge betweenness

Above 150 users/peer: Projection graph topology loses social properties A highly connected projection graph No differentiation in peer centrality

Top betweenness centrality users can pinpoint the top betweenness centrality peers with good accuracy

Overall: Applications can calculate infrequently centrality score of users to estimate peer centrality Social graph changes slowly compared to P2P network

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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