North Carolina State UniversityDepartment of Computer Science

890 Oval Drive, Raleigh, NC

Algorithms and Protocols on Social Graphs:Real vs Virtual Social Networks

Research Report

Francesco Ficarola, Ph.D. Studentfficaro@ncsu.edu

Who am I?

- I'm 29 and I have a master's degree in Computer Engineering

- I'm a Ph.D. student from Sapienza, University of Rome (Italy)

- I currently work (part-time) for a company on research projects

- I really like photography, nature and science.

Who am I?

- I'm 29 and I have a master's degree in Computer Engineering

- I'm a Ph.D. student from Sapienza, University of Rome (Italy)

- I currently work (part-time) for a company on research projects

- I really like photography, nature and science.

- I really like cultural exchanges

- I won a TEE scholarship to study here for 6 months

- I'd like to improve my English

Why am I here?

Towards a more social world… or not?

… a photo with you …

… a new job …

… video …

Social Networks as networks of contacts

A definition of Social Graph

A social graph is a network of connections and relationships

between people.

Representation

G = (V ,E)

nodeedge

∈ E

∈V

Real and Virtual Social Graphs

Real Social Graph

• Person-to-Person interactions:when individual A physically meets another individual B.

A particular technology must be used to record and measure them.

Virtual Social Graph• Virtual interactions:

- Facebook friendships- Twitter followers- …

Easy tracking by APIs

Real and Virtual Social Graphs

Real Social Graph

• Person-to-Person interactions:when individual A physically meets another individual B.

A particular technology must be used to record and measure them.

Virtual Social Graph• Virtual interactions:

- Facebook friendships- Twitter followers- …

Applications and Related Work

Easy tracking by APIs

- Facebook applications (e.g., games)

- Analysis of activities and friendships

- “Like button” to suggest targeted advertising

- Intel Imotes

- Smartphones

- SocioPatterns projects

bluetooth

Contribution and main goals in few words

- Deployment of several testbeds to collect real interactions

- Analysis of virtual and real social networks

- Population protocols

- Distinct Counting

- Distributed PageRank

- The Wisdom of Crowds

Contribution and main goals in few words

- Deployment of several testbeds to collect real interactions

- Analysis of virtual and real social networks

- Population protocols

- Distinct Counting

- Distributed PageRank

- The Wisdom of Crowds

WHY?

SocioPatterns platform: the OpenBeacon project

The SocioPatterns sensing platform employs wearable electronic badges to

sense sustained face-to-face proximity among people.

Radio Frequency IDentification technology

OpenBeacon Reader

OpenBeacon Tag

Our contribution in detail…

- DIAG experiment - MACRO experiment

Set-up:- Five-day experiment- DIAG LAN- 116 attendees

Set-up: - Two-and-a-half-hour experiment- LAN built by powerline and wifi bridge devices- 114 attendees

python collectorreaders

tags

forwarding data

Brief analysis of our networks

- DIAG experiment - MACRO experiment

Similarity in terms of grouping: triangles and couples

Algorithms and Protocols on Social Graphs

Population Protocols

• Threshold: for any given a Є X, it is true if #a ≥ T, where T is a given threshold

• Modulo: it is true whenever #a ≡ j (mod k), for given j, k

• Comparison: it is true whenever #a ≥ #b, for a, b Є X

a

aa

ba

b

a

a

a

b

b

a

Example set-up12 nodes8 nodes with symbol a4 nodes with symbol bThreshold value: T=7Modulo parameters: j=7, k=4

Example ResultsThreshold: verifiedModulo: not verifiedComparison: verified

Simulation of Population Protocols

- Threshold and Modulo

DIAG Graph MACRO Graph

Erdos-Renyi Random Graph

Simulation of Population Protocols

- Threshold and Modulo

DIAG Graph MACRO Graph

Erdos-Renyi Random Graph

A significant fraction ofnodes (≥ 80%) convergesto the correct outputwell before the finalconvergence time.

Time normalization requiredDIAG experiment : 5 daysMACRO experiment : 2.5 hours

Erdos-Renyi Random Graph

Simulation of Population Protocols

- Threshold and Modulo

DIAG Graph MACRO Graph

A significant fraction ofnodes (≥ 80%) convergesto the correct outputwell before the finalconvergence time.

Time normalization requiredDIAG experiment : 5 daysMACRO experiment : 2.5 hours

The time required by the wholepopulation to stabilize, stronglydepends on the interaction patterns

Faster convergence = Greater density

Simulation of Population Protocols

- Comparison

DIAG Graph MACRO Graph

Erdos-Renyi Random Graph

Similar results to the threshold andmodulo predicates: 80% of nodesconverges to the correct output wellbefore the final convergence time.

Trend curves are pretty similarto the case of the random graph

Populations Protocols on physical devices

Implementation of Population Protocols on physical devices

threshold threshold

[Unexpected result] The threshold predicate directly running on physical devices converges faster than simulations on Netlogo

Implementation of Population Protocols on physical devices

threshold threshold

Sub-Networks and Parallel Computing

counter

Initial network

Populations Protocols on physical devices

[Unexpected result] The threshold predicate directly running on physical devices converges faster than simulations on Netlogo

Algorithms and Protocols on Social Graphs

Distinct Counting: the Flajolet-Martin algorithmfor i = 0, ..., L-1 do M[i] = 0foreach (data item with value x) do

while hash(x, i) = 0 doi = i + 1

M[i] = 1let Z = min{i : M[i] = 0}

return

[0000001]

[0000001] [0000010]

[0000010]

[0000001]OR operator

[0000011] Z = 2

577351.

2≅

ZEstimation

77351.

2Z

The experiment at WSDM 2013

Distinct Counting

Average of 10 simulations on Netlogo Estimations vs true number of nodes

The experiment at WSDM 2013

Distinct Counting

Average of 10 simulations on Netlogo Estimations vs true number of nodes

Estimation (Netlogo): very good approximation of the curve depicting the true number of nodes over time.

Estimation (WSDM): a proof of concept. Running a distributed version of the FM algorithm on devices.

The Wisdom of Crowds

Sir Francis Galton

What does the ox weigh?

• Aggregation

• Diversity of opinion

• Independence

• Decentralization

Crowd

The experiment at WSDM 2013

The Wisdom of Crowds: setup• 73 attendees

• 2 rounds

- In the first round we gave people some questions to be answered alone.

- In the second round we proposed the same set of questions to be answeredafter a social interaction.

• 4 questions

- What was the total value in euro of all the coins thrown at the Trevi fountain in 2011?

- What is the total length (in meters) of the corridor of the Auditorium Antonianum?

- What is the average number of journal papers among the WSDM 2013 participantsaccording to DBLP?

- What was the number of Internet users in New Zealand by the end of 2011?

The experiment at WSDM 2013

The Wisdom of Crowds: preliminary results

Relation between the error made by users in the first round and the improvement in the second one.

Pearsoncoefficient

≈ 1

Algorithms and Protocols on Social Graphs

Adjacency Matrix

=

0111001100001000

dcba

dcba

M

PageRank π

b

c

d

a

Algorithms and Protocols on Social Graphs

PageRank π Adjacency Matrix

=

0111001100001000

dcba

dcba

M

Stochastic Adjacency Matrix

=

031

31

31

0021

21

41

41

41

41

1000

d

c

ba

dcba

Aij

∑ ∑∞

=

−=

0],[1

k j

kki ijAn

ααπ

b

c

d

a

Algorithms and Protocols on Social Graphs

Distributed PageRank p

Ti = generate_tokens(r) ∪ incoming_tokens()foreach token in Ti do:

if rnd(0,1) > α then:Ci = Ci + 1

else:if node is not a dangling node then:

send token to a neighbor j with probability Aijelse:

send token u.a.r. to another noderemove token from Ti

IDEALSAMPLE

b

c

d

a

Stochastic Adjacency Matrix

=

031

31

31

0021

21

41

41

41

41

1000

d

c

ba

dcba

Aij

foreachnodei

Algorithms and Protocols on Social Graphs

Distributed PageRank p

Ti = generate_tokens(r) ∪ incoming_tokens()foreach token in Ti do:

if rnd(0,1) > α then:Ci = Ci + 1

else:if node is not a dangling node then:

send token to a neighbor j with probability Qijelse:

send token u.a.r. to another noderemove token from Ti

FDSAMPLE

b

c

d

a

Modified Adjacency Matrix

=

031

31

31

0021

21

00001000

d

cba

dcba

Qij

foreachnodei

The distributed PageRank

ArXiv HEP-PH citations graphNodes: 34546 Edges: 421578 Dangling nodes: 2393

The distributed PageRank

Performance measures and preliminary results

Average Relative Error: ∑ ==n

i ie

nE

111

wherei

iii

pe

ππ −

=

The distributed PageRank

Performance measures and preliminary results

Precision: the fraction of the top k nodes (ordered according to non increasing πi’ s) that are also among the top k when nodes are ordered according to non increasing pi’ s.

What I'd like to do at NCSU…

- Deployment of other two social experiments:

• Real social experiment SocioPatterns infrastructure

• Virtual social experiment Chat game

- The Wisdom of Crowds in the real and virtual social experiments

- Distributed PageRank in physical devices during real social experiments

Publications

L. Becchetti, L. Bergamini, F. Ficarola, and A. Vitaletti. Population protocols on real social networks (POSTER). In Proceedings of the Fifth Workshop on Social Network Systems, SNS '12, pages 15:1-15:2, New York, NY, USA, 2012. ACM.

L. Becchetti, L. Bergamini, F. Ficarola, and A. Vitaletti. Population protocols on real social networks. In PE-WASUN '12: Proceedings of the 9th ACM workshop on Performance evaluation of wireless ad hoc, sensor, and ubiquitous networks, 2012.

L. Becchetti, L. Bergamini, F. Ficarola, F. Salvatore, and A. Vitaletti. First Experiences with the Implementation and Evaluation of Population Protocols on Physical Devices. In The IEEE International Conference on Cyber, Physical and Social Computing, 2012.

T. Arzilli, F. Ficarola, K. Massri, A. Vitaletti, F. Loriga, I. De Marinis, A. Ferraresi, R. Bloise, and M. Goretti. ProvinciaSense: extending the capillary WiFi infrastructure of Lazio region with static and mobile sensor networks (DEMO). To be appeared in SENSYS '13: Proceedings of the 11th ACM Conference on Embedded Network Sensor Systems, 2013.

L. Becchetti, F. Ficarola, G. Persiano and A. Vitaletti. Decentralized computation of authority scores over an evolving network. To be accepted in WWW '14 Companion: Proceedings of the 23rd international conference companion on World Wide Web.

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