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Introduction to Social Network Analysis
Ramasuri Narayanam
IBM Research, IndiaEmail ID: [email protected]
07-July-2017
Ramasuri Narayanam (IBM Research) 07-July-2017 1 / 39
Outline of the Presentation
1 Introduction to Social Networks
2 Key Tasks in Social Network Analysis
Ramasuri Narayanam (IBM Research) 07-July-2017 2 / 39
Introduction to Social Networks
Social Networks: Introduction
Recently there is a significant interest from research community to studysocial networks since:
Such networks are fundamentally different from technologicalnetworks
Networks are powerful primitives to model several real world scenariossuch as interactions among individuals/objects
Ramasuri Narayanam (IBM Research) 07-July-2017 3 / 39
Introduction to Social Networks
Social Networks: Introduction (Cont.)
Social networks are ubiquitous and have many applications:
For targeted advertising
Monetizing user activities on on-line communities
Job finding through personal contacts
Predicting future events
E-commerce and e-business
For Propagating trusts in web communities
. . .
———————–M.S. Granovetter. The Strength of Weak Ties. American Journal of Sociology, 1973.
Ramasuri Narayanam (IBM Research) 07-July-2017 4 / 39
Introduction to Social Networks
Example 1: Web Graph
Nodes: Static web pagesEdges: Hyper-links
——————–Reference: Prabhakar Raghavan. Graph Structure of the Web: A Survey. In Proceedingsof LATIN, pages 123-125, 2000.Ramasuri Narayanam (IBM Research) 07-July-2017 5 / 39
Introduction to Social Networks
Example 2: Friendship Networks
Friendship Network
Nodes: FriendsEdges: Friendship——————Reference: Moody 2001
Subgraph of Email Network
Nodes: IndividualsEdges: Email Communication——————Reference: Schall 2009
Ramasuri Narayanam (IBM Research) 07-July-2017 6 / 39
Introduction to Social Networks
Example 3: Weblog Networks
Nodes: BlogsEdges: Links
——————–Reference: Hurst 2007
Ramasuri Narayanam (IBM Research) 07-July-2017 7 / 39
Introduction to Social Networks
Example 4: Co-authorship Networks
Nodes: Scientists Edges: Co-authorship
——————–Reference: M.E.J. Newman. Coauthorship networks and patterns of scientific
collaboration. PNAS, 101(1):5200-5205, 2004Ramasuri Narayanam (IBM Research) 07-July-2017 8 / 39
Introduction to Social Networks
Example 5: Citation Networks
Nodes: Journals Edges: Citation
——————–Reference: http://eigenfactor.org/
Ramasuri Narayanam (IBM Research) 07-July-2017 9 / 39
Introduction to Social Networks
Social Networks - Definition
Social Network: A social system made up of individuals andinteractions among these individuals
Represented using graphs
Nodes - Friends, Publications, Authors, Organizations, Blogs, etc.Edges - Friendship, Citation, Co-authorship, Collaboration, Links, etc.
——————–S.Wasserman and K. Faust. Social Network Analysis. Cambridge University Press,
Cambridge, 1994
Ramasuri Narayanam (IBM Research) 07-July-2017 10 / 39
Introduction to Social Networks
Social Networks are Different from Computer Networks
Social networks differ from technological and biological networks in twoimportant ways:
1 non-trivial clustering or network transitivity, and
2 the phenomenon of degree correlation due to the existence of groupsor components in the network
————————————————————————————
M. E. J. Newman, Assortative mixing in networks. Phys. Rev. Lett. 89,208701, 2002.
M. E. J. Newman and Juyong Park. Why social networks are different fromother types of networks. Physical Review E 68, 036122, 2003.
Ramasuri Narayanam (IBM Research) 07-July-2017 11 / 39
Introduction to Social Networks
Courtesy: M. E. J. Newman and M. Girvan. Finding and evaluating communitystructure in networks. Phys. Rev. E 69, 026113, 2004.
Ramasuri Narayanam (IBM Research) 07-July-2017 12 / 39
Introduction to Social Networks
Social Network Analysis (SNA)
Study of structural and communication patterns− degree distribution, density of edges, diameter of the network
Two principal categories:Node/Edge Centric Analysis:
Centrality measures such as degree, betweeneness, stress, closenessAnomaly detectionLink prediction, etc.
Network Centric Analysis:Community detectionGraph visualization and summarizationFrequent subgraph discoveryGenerative models, etc.
——————–U. Brandes and T. Erlebach. Network Analysis: Methodological Foundations.
Springer-Verlag Berlin Heidelberg, 2005.Ramasuri Narayanam (IBM Research) 07-July-2017 13 / 39
Introduction to Social Networks
Why is SNA Important?
To understand complex connectivity and communication patternsamong individuals in the network
To determine the structure of networks
To determine influential individuals in social networks
To understand how social network evolve
To determine outliers in social networks
To design effective viral marketing campaigns for targeted advertising
. . .
Ramasuri Narayanam (IBM Research) 07-July-2017 14 / 39
Next Part of the Presentation
1 Introduction to Social Networks
2 Key Tasks in Social Network Analysis
Ramasuri Narayanam (IBM Research) 07-July-2017 15 / 39
Key Tasks in Social Network Analysis
A Few Key SNA Tasks
1 Measures to rank nodes (or edges)
2 Community detection
3 Link prediction problem
4 Inferring social networks from social events
5 Viral marketing
6 Graph Visualization
7 Design of incentives in networks
8 Determining implicit social hierarchy
9 Network formation
10 Sparsification of social networks (with purpose)
11 . . .
Ramasuri Narayanam (IBM Research) 07-July-2017 16 / 39
Key Tasks in Social Network Analysis
Task 1: Centrality Measures
Significant amount of attention in the analysis of social networks isdevoted to understand the centrality measures
A centrality measure essentially ranks nodes/edges in a given networkbased on either their positional power or their influence over thenetwork;
Some well known centrality measures:
Degree centralityCloseness centralityClustering coefficientBetweenness centralityEigenvector centrality, etc.
Ramasuri Narayanam (IBM Research) 07-July-2017 17 / 39
Key Tasks in Social Network Analysis
Task 1: Centrality Measures
Significant amount of attention in the analysis of social networks isdevoted to understand the centrality measures
A centrality measure essentially ranks nodes/edges in a given networkbased on either their positional power or their influence over thenetwork;
Some well known centrality measures:
Degree centralityCloseness centralityClustering coefficientBetweenness centralityEigenvector centrality, etc.
Ramasuri Narayanam (IBM Research) 07-July-2017 17 / 39
Key Tasks in Social Network Analysis
Task 1: Centrality Measures
Significant amount of attention in the analysis of social networks isdevoted to understand the centrality measures
A centrality measure essentially ranks nodes/edges in a given networkbased on either their positional power or their influence over thenetwork;
Some well known centrality measures:
Degree centralityCloseness centralityClustering coefficientBetweenness centralityEigenvector centrality, etc.
Ramasuri Narayanam (IBM Research) 07-July-2017 17 / 39
Key Tasks in Social Network Analysis
Task 1: Centrality Measures
Significant amount of attention in the analysis of social networks isdevoted to understand the centrality measures
A centrality measure essentially ranks nodes/edges in a given networkbased on either their positional power or their influence over thenetwork;
Some well known centrality measures:
Degree centralityCloseness centralityClustering coefficientBetweenness centralityEigenvector centrality, etc.
Ramasuri Narayanam (IBM Research) 07-July-2017 17 / 39
Key Tasks in Social Network Analysis
Degree Centrality
Degree Centrality: The degree of a node in a undirected andunweighted graph is the number of nodes in its immediateneighborhood.
Rank nodes based on the degree of the nodes in the network
Freeman, L. C. (1979). Centrality in social networks: Conceptualclarification. Social Networks, 1(3), 215-239
Degree centrality (and its variants) are used to determine influentialseed sets in viral marketing through social networks
Ramasuri Narayanam (IBM Research) 07-July-2017 18 / 39
Key Tasks in Social Network Analysis
Degree Centrality (Cont.)
Degree Centrality
Node 1 2 3 4 5 6 7 8 9 10
Value 1 3 2 3 2 3 3 1 2 2
Rank 9 1 5 1 5 1 1 9 5 5
Ramasuri Narayanam (IBM Research) 07-July-2017 19 / 39
Key Tasks in Social Network Analysis
Closeness Centrality
The farness of a node is defined as the sum of its shortest distancesto all other nodes;
The closeness centrality of a node is defined as the inverse of itsfarness;
The more central a node is in the network, the lower its total distanceto all other nodes.
Ramasuri Narayanam (IBM Research) 07-July-2017 20 / 39
Key Tasks in Social Network Analysis
Closeness Centrality (Cont.)
Closeness Centrality
Node 1 2 3 4 5 6 7 8 9 10
Value 134
126
127
121
119
119
123
131
129
125
Rank 10 6 7 3 1 1 4 9 8 5
Ramasuri Narayanam (IBM Research) 07-July-2017 21 / 39
Key Tasks in Social Network Analysis
Clustering Coefficient
It measures how dense is the neighborhood of a node.
The clustering coefficient of a node is the proportion of links betweenthe vertices within its neighborhood divided by the number of linksthat could possibly exist between them.
D. J. Watts and S. Strogatz. Collective dynamics of ’small-world’networks. Nature 393 (6684): 440442 , 1998.
Clustering coefficient is used to design network formation models
Ramasuri Narayanam (IBM Research) 07-July-2017 22 / 39
Key Tasks in Social Network Analysis
Clustering Coefficient (Cont.)
Clustering Coefficient
Node 1 2 3 4 5 6 7 8 9 10
Value 0 13 1 1
3 0 0 0 0 0 0
Rank 3 2 1 2 3 3 3 3 3 3
Ramasuri Narayanam (IBM Research) 07-July-2017 23 / 39
Key Tasks in Social Network Analysis
Betweeness Centrality
Between Centrality: Vertices that have a high probability to occuron a randomly chosen shortest path between two randomly chosennodes have a high betweenness.
Formally, betweenness of a node v is given by
CB(v) =∑
s 6=v 6=t
σs,t(v)
σs,t
where σs,t(v) is the number of shortest paths from s to t that passthrough v and σs,t is the number of shortest paths from s to t.L. Freeman. A set of measures of centrality based upon betweenness.Sociometry, 1977.Betweenness centrality is used to determine communities in socialnetwoks (Reference: Girvan and Newman (2002)).
Ramasuri Narayanam (IBM Research) 07-July-2017 24 / 39
Key Tasks in Social Network Analysis
Betweenness Centrality (Cont.)
Betweenness Centrality
Node 1 2 3 4 5 6 7 8 9 10
Value 0 8 0 18 20 21 11 0 1 6
Rank 8 5 8 3 2 1 4 8 7 6
Ramasuri Narayanam (IBM Research) 07-July-2017 25 / 39
Key Tasks in Social Network Analysis
A Simple Observation
ID Degree Closeness Clustering Betweenness EigenvectorCentrality Centrality Centrality Centrality Centrality
1 9 10 3 8 92 1 6 2 5 23 5 7 1 8 34 1 3 2 3 15 5 1 3 2 56 1 1 3 1 37 1 4 3 4 68 9 9 3 8 109 5 8 3 7 8
10 5 5 3 6 7
Ramasuri Narayanam (IBM Research) 07-July-2017 26 / 39
Key Tasks in Social Network Analysis
Task 2: Community Detection
Based on Link Structure in the Social Network:
Determining dense subgraphs in social graphsGraph partitioningDetermining the best subgraph with maximum number of neighborsOverlapping community detection
Based on Activities over the Social Network
Determine action communities in social networksOverlapping community detection
J. Leskovec, K.J. Lang, and M.W. Mahoney. Empirical comparison ofalgorithms for network community detection. In WWW 2010.
Ramasuri Narayanam and Y. Narahari. A Game Theory Inspired,Decentralized, Local Information based Algorithm for CommunityDetection in Social Graphs. To appear in International Conference onPattern Recognition (ICPR), 2012.
Ramasuri Narayanam (IBM Research) 07-July-2017 27 / 39
Key Tasks in Social Network Analysis
Task 3: Link Prediction Problem
Given a snapshot of a social network, can we infer which newinteractions among its members are likely to occur in the near future?
D. Liben-Nowell and J. Kleinberg. The link prediction problem forsocial networks. In CIKM 2003.
Ramasuri Narayanam (IBM Research) 07-July-2017 28 / 39
Key Tasks in Social Network Analysis
Task 3: Link Prediction Problem
Given a snapshot of a social network, can we infer which newinteractions among its members are likely to occur in the near future?
D. Liben-Nowell and J. Kleinberg. The link prediction problem forsocial networks. In CIKM 2003.
Ramasuri Narayanam (IBM Research) 07-July-2017 28 / 39
Key Tasks in Social Network Analysis
Task 3: Link Prediction Problem
Given a snapshot of a social network, can we infer which newinteractions among its members are likely to occur in the near future?
D. Liben-Nowell and J. Kleinberg. The link prediction problem forsocial networks. In CIKM 2003.
Ramasuri Narayanam (IBM Research) 07-July-2017 28 / 39
Key Tasks in Social Network Analysis
Task 4: Inferring Social Networks From Social Events
In the traditional link prediction problem, a snapshot of a socialnetwork is used as a starting point to predict (by means ofgraph-theoretic measures) the links that are likely to appear in thefuture.
Predicting the structure of a social network when the network itself istotally missing while some other information (such as interest groupmembership) regarding the nodes is available.
V. Leroy, B. Barla Cambazoglu, F. Bonchi. Cold start link prediction.In SIGKDD 2010.
Ramasuri Narayanam (IBM Research) 07-July-2017 29 / 39
Key Tasks in Social Network Analysis
Task 5: Viral Marketing
With increasing popularity of online social networks, viral Marketing -the idea of exploiting social connectivity patterns of users topropagate awareness of products - has got significant attention
In viral marketing, within certain budget, typically we give freesamples of products (or sufficient discounts on products) to certainset of influential individuals and these individuals in turn possiblyrecommend the product to their friends and so on
It is very challenging to determine a set of influential individuals,within certain budget, to maximize the volume of information cascadeover the network
P. Domingos and M. Richardson. Mining the network value ofcustomers. In ACM SIGKDD, pages 5766, 2001.
Ramasuri Narayanam (IBM Research) 07-July-2017 30 / 39
Key Tasks in Social Network Analysis
Task 5: Viral Marketing (Cont.)
Often not only positive opinions about the products, but also negativeopinions may emerge and propagate over the social network.
How to choose the initial seeds for viral marketing in the presence ofboth positive and negative opinions?
W. Chen, A. Collins, R. Cummings, T. Ke, Z. Liu, D. Rincon, X. Sun,Y. Wang, W. Wei, and Y. Yuan. Influence maximization in socialnetworks when negative opinions may emerge and propagate. In SDM2011.
How to choose the initial seeds for viral marketing of products in thepresence of competing products already in the market?
X. He, G. Song, W. Chen, and Q. Jiang. Influence blockingmaximization in social networks under the competitive linearthreshold model. In SDM, 2012.
Ramasuri Narayanam (IBM Research) 07-July-2017 31 / 39
Key Tasks in Social Network Analysis
Task 5: Viral Marketing (Cont.)
Viral Marketing with Product Dependencies
Often cross-sell or up-sell is possible among the products
Product specific costs for promoting the products have to beconsidered
Since a company often has budget constraints, the initial seeds haveto be chosen within a given budget
Ramasuri Narayanam and Amit A. Nanavati. Viral marketing withproduct cross-sell through social networks. To appear inECML-PKDD, 2012.
Ramasuri Narayanam (IBM Research) 07-July-2017 32 / 39
Key Tasks in Social Network Analysis
Task 6: Graph Visualization
Ramasuri Narayanam (IBM Research) 07-July-2017 33 / 39
Key Tasks in Social Network Analysis
Task 6: Graph Visualization
Ramasuri Narayanam (IBM Research) 07-July-2017 33 / 39
Key Tasks in Social Network Analysis
Task 6: Graph Visualization
Ramasuri Narayanam (IBM Research) 07-July-2017 33 / 39
Key Tasks in Social Network Analysis
Task 7: Design of Incentives in Networks
Users pose queries to the network itself, rather than posing queries toa centralized system.
At present, the concept of incentive based queries is used in variousquestion-answer networks such as Yahoo! Answers, Orkuts AskFriends, etc.
In the above contexts, only the person who answers the query isrewarded, with no reward for the intermediaries. Since individuals areoften rational and intelligent, they may not participate in answeringthe queries unless some kind of incentives are provided.
It is also important to consider the quality of the answer to the query,when incentives are involved.
J. Kleinberg and P. Raghavan. Query incentive networks. InProceedings of 46th IEEE FOCS, 2005.
Ramasuri Narayanam (IBM Research) 07-July-2017 34 / 39
Key Tasks in Social Network Analysis
Task 8: Determining Implicit Social Hierarchy
Social stratification refers to the hierarchical classification ofindividuals based on power, position, and importance
The popularity of online social networks presents an opportunity tostudy social hierarchy for different types of large scale networks
M. Gupte, P. Shankar, J. Li, S. Muthukrishnan, and L. Iftode.Finding hierarchy in directed online social networks. In theProceedings of World Wide Web (WWW) 2011.
Ramasuri Narayanam (IBM Research) 07-July-2017 35 / 39
Key Tasks in Social Network Analysis
Task 9: Network Formation
More often links among individuals in social networks form by choicenot by chance
These links capture the associated social and economic incentives
How to model the formation of social networks in the presence ofstrategic individuals (or organizations)?
What are the networks that will emerge due to the dynamics ofnetwork formation and what their characteristics are likely to be?
Matthew O. Jackson. Social and Economic Networks. PrincetonUniversity Press, Princeton and Oxford, 2008
Ramasuri Narayanam and Y. Narahari. Topologies of StrategicallyFormed Social Networks Based on a Generic Value Function -Allocation Rule Model. Social Networks, 33(1), 2011
Ramasuri Narayanam (IBM Research) 07-July-2017 36 / 39
Key Tasks in Social Network Analysis
Task 10: Sparsification of Social Networks
Real world social networks are very large in the sense that theycontain millions of nodes and billions of edges
Certain applications associated with social network data need outputquickly. In particular, they can compromise even on the solutionquality till some extent but not on the execution time requirements
The above leads to an interesting and challenging research problem,namely sparsification of social networks
Using the sparse social graphs, we perform SNA and again map theseresults back to the original network if required
V. Satuluri, S. Parthasarathy, Y. Ruan. Local graph sparsification forscalable clustering. In SIGMOD, 2011.
M. Mathioudakis, F. Bonchi, C. Castillo, A. Gionis, A. Ukkonen.Sparsification of influence networks. In SIGKDD 2011.
Ramasuri Narayanam (IBM Research) 07-July-2017 37 / 39
Key Tasks in Social Network Analysis
Emerging Challenges in SNA
Availability of Auxiliary Data
Recent applications witness data related to not only who is connectedto whom, but also the activities performed by the users
Availability of Large Data Sets
Technological advancements made it easy to collect network data setswith very large sizes
Dynamic Nature of the Network Data Sets
The structure of the network changes over time due to user activity
Strategic Behavior of Users
More often the nodes in the social network are individuals ororganizationsSuch entities more often exhibit strategic behaviorGame theory and mechanism design can naturally model such scenarios
Nature of the Recent Applications
Privacy Related Issues
Ramasuri Narayanam (IBM Research) 07-July-2017 38 / 39
Thank You
Ramasuri Narayanam (IBM Research) 07-July-2017 39 / 39