Community Detection in Social Networks: Algorithms and Techniques, Slides of Computer Networks

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Lecture 8

Communities

Communities

 Community: “subsets of actors among whom there are relatively strong, direct, intense, frequent or positive ties.” -- Wasserman and Faust, Social Network Analysis, Methods and Applications

 Community is a set of actors interacting with each other frequently a.k.a. group, subgroup, module, cluster

 A set of people without interaction is NOT a community  e.g. people waiting for a bus at station but don’t talk to each other

Community Detection

 Community Detection: “formalize the strong social groups based on the social network properties”  a.k.a. grouping, clustering, finding cohesive subgroups

 Given: a social network  Output: community membership of (some) actors

 Some social media sites allow people to join groups

 Not all sites provide community platform  Not all people join groups

Community Detection

 Network interaction provides rich information about the relationship between users  Is it necessary to extract groups based on network topology?  Groups are implicitly formed  Can complement other kinds of information  Provide basic information for other tasks

 Applications  Understanding the interactions between people  Visualizing and navigating huge networks  Forming the basis for other tasks such as data mining

Classification

 User Preference or Behavior can be represented as class labels

• Whether or not clicking on an ad
• Whether or not interested in certain topics
• Subscribed to certain political views
• Like/Dislike a product

 Given  A social network  Labels of some actors in the network

 Output  Labels of remaining actors in the network

Visualization after Prediction

: Smoking : Non-Smoking :? Unknown

Predictions 6: Non-Smoking 7: Non-Smoking 8: Smoking 9: Non-Smoking 10: Smoking

Viral Marketing/Outbreak Detection

 Users have different social capital (or network values) within a social network, hence, how can one make best use of this information?

 Viral Marketing: find out a set of users to provide coupons and promotions to influence other people in the network so benefit is maximized

 Outbreak Detection: monitor a set of nodes that can help detect outbreaks or interrupt the infection spreading (e.g., H1N1 flu)

 Goal: given a limited budget, how to maximize the overall benefit?

An Example of Viral Marketing

 Find the coverage of the whole network of nodes with the minimum number of nodes

 How to realize it – an example  Basic Greedy Selection: Select the node that maximizes the utility, remove the node and then repeat

• Select Node 1
• Select Node 8
• Select Node 7

Node 7 is not a node with high centrality!

Node-Centric Community Detection

Community

Detection

Node- Centric

Group- Centric

Network- Centric

Hierarchy- Centric

Node-Centric Community Detection

 Nodes satisfy different properties

 Complete Mutuality  cliques  Reachability of members  k-clique, k-clan, k-club  Nodal degrees  k-plex, k-core  Relative frequency of Within-Outside Ties  LS sets, Lambda sets

 Commonly used in traditional social network analysis

Geodesic

 Reachability is calibrated by the Geodesic distance

 Geodesic: a shortest path between two nodes (12 and 6)  Two paths: 12-4-1-2-5-6, 12-10-  12-10-6 is a geodesic

 Geodesic distance: #hops in geodesic between two nodes  e.g., d(12, 6) = 2, d(3, 11)=

 Diameter: the maximal geodesic distance for any 2 nodes in a network  #hops of the longest shortest path

Diameter = 5

Reachability: k-clique, k-club

 Any node in a group should be reachable in k hops

 k-clique: a maximal subgraph in which the largest geodesic distance between any nodes <= k

 A k-clique can have diameter larger than k within the subgraph  e.g., 2-clique {12, 4, 10, 1, 6}  Within the subgraph d(1, 6) = 3

 k-club: a substructure of diameter <= k  e.g., {1,2,5,6,8,9}, {12, 4, 10, 1} are 2-clubs

Within-Outside Ties: LS sets

 LS sets: Any of its proper subsets has more ties to other nodes in the group than outside the group  Too strict, not reasonable for network analysis

 A relaxed definition is k-component

 Require the computation of edge-connectivity between any pair of nodes via minimum-cut, maximum-flow algorithm  1-component is a connected component

Recap of Node-Centric Communities

 Each node has to satisfy certain properties  Complete mutuality  Reachability  Nodal degrees  Within-Outside Ties

 Limitations:  Too strict, but can be used as the core of a community  Not scalable, commonly used in network analysis with small-size network  Sometimes not consistent with property of large-scale networks  e.g., nodal degrees for scale-free networks