1. Evolution Dynamics in social networks
Ashwin Bahulkar1, Boleslaw Szymanski1, Kevin Chan3, Omar Lizardo2, Nitesh Chawla2
1Rensselaer Polytechnic Institute, Troy, NY, USA
Social Cognitive Networks Academic Research Center ( SCNARC)
2University of Notre Dame, Notre Dame, IN, USA
3US Army Research Laboratory
supported by Network Science CTA, ARL
Do we need all the affiliations?
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2. Problems we study
Link Formation and Dissolution in attribute-rich networks
Can we predict the state of a network from node attributes?
Which node attributes -> edges to form and dissolve in networks.
Coevolution of multiple networks
Multiple networks: several networks sharing the same node-set, different relations among nodes.
Coevolution: Do edges occur in one network before they do so in another?
Do edges dissolve in one network before they do so in another?
Can causal inferences be made?

3. Motivation
Influence policy making in schools, organizations, work places.
Bring stability to networks in organizations through policies
We need to know which factors affect evolution of networks

4. NetSense data
Participants: Students from University of NotreDame, from Freshman to Junior years, around 2 years, 200 of them.
Data collected:
Call and message logs between students in the study.
Friendship surveys.
Opinions on social & political issues, student background and university activities for every student.
Frequency:
Opinions were collected in the form of surveys at the beginning of every semester.
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5. Evolving NetSense Networks
Networks are made for every semester of the year: Fall and Spring.
Behavioral Networks : Based on calls, texts, bluetooth interactions made in the semester.
An edge exists if there is a call or text exchange between two nodes. Typical network size ranges from nodes and edges.
We have snapshots for 4 semesters.
Cognitive Network : Based on survey answers by students to “Who are your top friends”.
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6. Node Attributes Student background: Opinions on: Habits and Lifestyle:
Major in the Notre Dame programs
Behavioral traits
Family income, race and religion
Opinions on:
Politics
Abortion and marijuana legalization.
Homosexuality and gay marriage
Habits and Lifestyle:
Drinking habits
Time spent on weekly activities: studying, partying etc.
Classes taken and clubs joined
Change color for santafe and karate
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7. Link Prediction Objectives
Find which attributes are correlated with formation and persistence of observed linked.
Identify disagreements on which attributes are correlated with dissolution of observed links.
We observe “homophily” to a good extent. People tend to form links with people similar to them.
AA: accounts for limited attention of humans
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8. Link Prediction definition
Given a social network, which evolves over time.
Edges are created, and they get dissolved.
Question asked: at a given time, which are the edges that would be created in the future?
Link Dissolution: Which of the existing links will dissolve?

9. Graphs with rich nodes attributes
Traditionally, link prediction done on nodes with less attributes.
Graph topology based methods: no. common neighbors, random walk.
How do you also make use of a rich node attribute set?
Images from nd.edu.

10. Link Prediction using Machine Learning
Link Prediction is a classification problem.
4 networks snapshots: 1st two to learn, 3rd and 4th to test
Positive Examples: Non Existing edges which materialize in the succeeding semester.
Negative Examples: Non Existing edges which do not materialize in the succeeding semester.

11. Link Prediction: an unbalanced problem
Very few positive examples, maybe 100.
Too many negative examples, n(n-1)/2.
Classifiers get overwhelmed with the negative examples.
Very high precision, but poor recall.

12. Features for Link Prediction
Agreement levels for all attributes. There are 26 of these.
Feature value between 0 and 1.
Number of common neighbors for the endpoints of an edge.
Total number of attributes over which the endpoints of an edge “agree” with each other.

13. Machine Learning Techniques Used
Classifiers used: Linear SVM, Linear Regression, Kernel SVM, Random Forests, Naïve Bayes Classifier, Ensemble methods.
Dimensionality Reduction: Needed, since a combination of attributes affects results. SVD(Singular Value Decomposition) performed over the data matrix, features in new space used for classification.
Credits to Los Alamos Laboratory for the figure
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14. Some initial results 76% recall observed, with 75% accuracy.
Can this be improved?
Homophily not always seen!
We need to capture “homophily” in a better way.

15. Individual Preferences of Nodes
Features for machine learning:
Node preferences for each attribute.
For an edge with nodes n1 and n2, for attribute a:
Feature-value (a) = n1->preference * n2-> preference.
Calculate preference of node n1 for attribute-value v:
n1 has n friends with attribute-value v.
Individual Preferences: How anomalous is having n friends ?
Values > 1 indicate preference for, values < indicates preference against.

16. Example of the preference method
Network: 60% liberals, 20% moderates, 20% conservatives
Node 1: liberal
6 friends, 3 liberal and 3 conservatives
Preference: not too against conservatives, maybe doesn’t care enough about politics
Node 2: liberal
6 friends, 5 liberal, 1 moderate
Preference: most are liberal, probably doesn’t prefer conservative friends.
Everyone has different preferences at each attribute

17. Results with the Preference method
We get about 90% recall with good accuracy.

18. Link dissolution results

19. Link Dissolution Link dissolution has been hardly studied.
Link Dissolution Prediction is much harder in social networks.
The clues for dissolution prediction are really much more hidden.

20. Results and Ranking of Attributes
Different attributes for dissolution and creation.
Leave one-attribute out method used.
Behavior
Cognition
Political Views
Parental Income
Common Neighbors
Time Volunteering
Time Exercising
Gay Marriage Legalization
Political Views
Parental Income
Views on homosexuality
Time Camping
Link Creation
Views on Homosexuality
Political Views
Time socializing
Time Partying
Marijuana Legalization
Time socializing
Time in Clubs
Marijuana Legalization
Time Exercising
Time Studying
Link Dissolution

21. Coevolution of Multiple Social Networks
Continuously evolving cognitive and behavioral networks.
Are behavioral edges formed before cognitive edges are formed?
How likely does behavioral edge dissolve after the corresponding edge disappears in the cognitive network?
Cognitive network (red edges) and behavioral network(green edges).

22. Co-Evolution in NetSense
Are communication edges formed before friendship edges are formed?
How likely does communication dissolve after the corresponding edge disappears in the friendship network?
Are there any patterns of communication decay following link dissolution in the friendship network?
Do symmetric friendships differ from asymmetric friendship?
Change color for santafe and karate
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23. Higher communication and the appearance of edges in the friendship network
We can predict future edges with a good accuracy and recall, based on number of calls and texts.
Higher communication corresponds to edge formation in the next semester.
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24. Higher collocation and the appearance of edges in the friendship network
We can predict future edges with a good accuracy and recall, based on number of bluetooth interactions.

25. Friendship Edges and the Strength of Links in the Communication Network
Yes, they do.
Friends have much higher communication than non-friends who communicate.
Newly formed edges communicate less than older edges.
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26. Friendship Edges and the Strength of Links in the Collocation Network
Friends have much higher communication than non-friends who communicate.

27. ROC curve calls vs. text vs. collocations

28. Formation vs. Dissolution
Dissolving edges: They interact less than persistent edges, easy to spot them.
Edges dissolve simultaneously in both networks.
Dissolution is fast, while formation is slow.
We use “recency” to track the speed of dissolution.

29. Temporal Features of different networks
Friendship edges vs. Behavioral edges
Friendship edges: Meet on weekday evenings and weekends.
Behavioral edges: Meet on weekdays.
Edges in different networks can dramatically different properties.

30. Asymmetric edges Asymmetric edges have non-reciprocal behavior
Asymmetric edges communicate and meet less
They don’t survive much

31. Personality traits and behavior
Churn of friends: Nodes with asymmetric edges retain only less friends.
Self-confessed introverts have few friends, more interactions per friend.
Self-confessed extroverts have more friends, less interactions per friend.

32. Slow evolution of edges
Nodes are first connected in the bluetooth network.
More bluetooth interactions -> edge in the communication network
More communication -> edge in the friendship network

33. Evolution of Collaboration Networks
Nodes: Researchers
Edges: Collaborations, writing a paper together.
Sources: DBLP, AMiner collections.
Much larger: about 50,000 nodes, 1 M edges
Evolution of several decades, from

34. Link Prediction in Collaboration Networks
Techniques: Machine Learning based.
Features:
No. common neighbors
No. common keywords
Same country?
Same institute?
Interaction coefficient between the two institutes

35. Results Recall: 70% to 90% Accuracy: 80% to 90%
Predictions are about a million times better than random!

36. Tracking changes in collaboration patterns
6 network snapshots: 1986 to 1990, …
Use the most recent network to train model:
Use and as train set.
and 2011 – 2015 is the test set.
To monitor change in evolution patterns:
Use older models to predict.
Use and as train set
Older the model, lower the performance
Shows how collaboration patterns change over time

37. Conclusion
Different attributes influence formation of edges in networks.
Preference plays an important role in the formation and dissolution of edges
Increasing weight behavior edges -> friendship edge
Formation of edges is slower than dissolution of edges

38. Future Work Group Communication:
Identify communication and interactions among groups.
Why do people join groups? What are the benefits of groups for individuals?
Why do people leave groups? Can you predict such an event?
Do people in a group have similar or diverse personality profiles?

39. Thank you!
Questions?