Community Structure and Rumor Blocking Ding-Zhu Du University of Texas at Dallas

Outline  Social Network  Online Social Networks  Community Structure  Rumor Blocking 2

Web definition: A network consists of two or more nodes that are linked in order to share resources. What is a Network? 3

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What is Social Network? Wikipedia Definition: Social Structure Nodes: Social actors (individuals or organizations) Links: Social relations 5

Example 1: Friendship Network Nodes: all persons in the world A link exists between two persons if they know each other. 6

Milgram (1967) The experiment: Random people from Nebraska were to send a letter (via intermediaries) to a stock broker in Boston. Could only send to someone with whom they know. Six links were needed. Stanley Milgram ( ) Property of Friendship Six Degrees of Separation 7

Family Friend Family Friend Supervise Friend Roommate Friend 8 Lidong Wu

Chinese Observation 八竿子打不着 形容二者之间关系疏远或毫无关联。 “ 竿 ” 也 作 “ 杆 ” 。 9

“The small world network is a type of mathematical graph in which most nodes are not neighbors of one another, but most nodes can be reached from every other by a small number of hops or steps.”

Example 2: Coauthorship Network Nodes: all publication authors A link exists between two authors if they are coauthors in a publication. 11

Erdős number: is the collaboration distance with mathematician Paul Erd ő s. What is your Erdős number? Erdös number person Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people Erdös number people * Two persons are linked if they are coauthors of an article. Coauthorship Network is a Small World Network 12 Distribution in Dec.2010

My Erdős number is 2. 13

Nodes: all cities with an airport. A link exists between two cities if there exists a direct flight between them. Example 3: Flight Map Is a Small World Network 14

Find a cheap ticket between two given cities. It is a shortest path problem in a social network. Need to add connection information to network. Search Cheap Ticket 15 There are about 28,537 commercial flights in the sky in the U.S. on any given day.

Network Construction AA123 AA456 AA789 Dallas Chicago 16

Network Construction 17 Dallas 8am 9am 1pm 9am 3pm 8am

Network construction Dallas 8am 9am 1pm 9am 3pm 8am 18

Outline  Social Network  Online Social Networks  Community Structure  Rumor Blocking 19

Social Network is online in Internet Facebook: friendship linkedIn: friendship ResearchGate: coauthorship 20

Online Social Networks (OSN) Social influence occurs when one's emotions, opinions, or behaviors are affected by others. Although social influence is possible in the workplace, universities, communities, it is most popular online.

Internet provides a platform to record and to develop social networks 22

What Are OSN Used For? 23

Candidates (left to right) ： Ken Livingstone, Boris Johnson and Brian Paddick. Political Election for Mayor of London (2012) Usage Example /technology/news/ /Twitter-data-predicts- Boris-Johnson-victory.html 24

Prediction of Boris Johnson Victory 25

How to Predict? Analysis posts on Facebook and Twitter: “Sentiment Analysis”. Find 7% more positive sentiment towards Mr. Johnson than Mr. Livingstone. Predict 54% of the vote for Mr. Johnson. Google Insights, tracking web trends, Almost five times more searches for “Boris Johnson” than for “Ken Livingstone” via google.co.uk. Of the total number of web searches for both candidates, 60% were for “Boris Johnson”. 26

Outline  Social Network  Online Social Networks  Community Structure  Rumor Blocking 27

Question 1? Does Six Degrees of Separation imply six degrees of influence? 28

Three Degrees of Influence in friendship network 29

Three Degrees of Influence In Book Connected by Nicholas A. Christakis and James H. Fowler. Nicholas A. ChristakisJames H. Fowler

Three Three Degrees of Influence The influence of actions ripples through networks 3 hops (to and from your friends’ friends’ friends). 31

I am happy! 32

Question 2? How to explain Six Degrees of Separation and Three Degrees of Influence? 33

Community People in a same community share common interests in - clothes, music, beliefs, movies, food, etc. Influence each other strongly. 34

* same color, same community Community without overlap Community with overlap Community Structure 35

two nodes can reach each other in three steps. A few of tied key persons: C, D Member A reaches Member B via A-C-D-B Community Structure 36 In the same community,

Two nodes may have distance more than three. Community Structure 37 For different communities,

Community Structure Two nodes can reach each other by at most six steps. A C B 38 For two overlapping communities,

Outline  Social Network  Online Social Networks  Community Structure  Rumor Blocking 39

8/19/ When misinformation or rumor spreads in social networks, what will happen?

A misinformation said that the president of Syria is dead, and it hit the twitter greatly and was circulated fast among the population, leading to a sharp, quick increase in the price of oil. leads-sharp-increase-price-oil html 8/19/201541

In August, 2012, thousands of people in Ghazni province left their houses in the middle of the night in panic after the rumor of earthquake. e-rumour-sends-thousands-ghazni-streets 8/19/201542

8/19/ People in a same community share common interests in - clothes, music, beliefs, movies, food, etc. Influence each other strongly.

Example is a rumor, 6 is a protector. Step 1: 1--2,3; 6--2,4. 2 and 4 are protected, 3 is infected. 8/19/ rumor protector

Step 2: is protected. Example 8/19/201545

Least Cost Rumor Blocking Problem (LCRB) Bridge ends:  form a vertex set;  belong to neigborhood communities of rumor community;  each can be reached from the rumors before others in its own community. C0 C2 C1 Red node is a rumor; Yellow nodes are bridge ends. 8/19/201546

Construct Rumor Forward Search Trees (RFST) Yellow nodes are bridge ends. 8/19/201547

Hitting Set Based Greedy Algorithm Main idea  Convert to hitting set problem Three stages: For each bridge end, find the shortest distance from it to a rumor infected node construct Bridge End Backward Search Trees (BEBST)— find the set of protector candidates construct protector nodes used in greedy approximation for hitting set problem 8/19/201548

“Prerequisites” 49

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