Sudden emergence of a giant k-core in a random graph
Journal of Combinatorial Theory Series B
Group formation in large social networks: membership, growth, and evolution
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Graph evolution: Densification and shrinking diameters
ACM Transactions on Knowledge Discovery from Data (TKDD)
Measurement and analysis of online social networks
Proceedings of the 7th ACM SIGCOMM conference on Internet measurement
Influence and correlation in social networks
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Proceedings of the forty-first annual ACM symposium on Theory of computing
On the evolution of user interaction in Facebook
Proceedings of the 2nd ACM workshop on Online social networks
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Networks, Crowds, and Markets: Reasoning About a Highly Connected World
Networks, Crowds, and Markets: Reasoning About a Highly Connected World
Proceedings of the 20th international conference on World wide web
Extracting Analyzing and Visualizing Triangle K-Core Motifs within Networks
ICDE '12 Proceedings of the 2012 IEEE 28th International Conference on Data Engineering
Vertex neighborhoods, low conductance cuts, and good seeds for local community methods
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Preventing unraveling in social networks: the anchored k-core problem
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
User engagement: the network effect matters!
Proceedings of the 21st ACM international conference on Information and knowledge management
Arrival and departure dynamics in social networks
Proceedings of the sixth ACM international conference on Web search and data mining
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Given a large social graph, how can we model the engagement properties of nodes? Can we quantify engagement both at node level as well as at graph level? Typically, engagement refers to the degree that an individual participates (or is encouraged to participate) in a community and is closely related to the important property of nodes' departure dynamics, i.e., the tendency of individuals to leave the community. In this paper, we build upon recent work in the field of game theory, where the behavior of individuals (nodes) is modeled by a technology adoption game. That is, the decision of a node to remain engaged in the graph is affected by the decision of its neighbors, and the "best practice" for each individual is captured by its core number - as arises from the k-core decomposition. After modeling and defining the engagement dynamics at node and graph level, we examine whether they depend on structural and topological features of the graph. We perform experiments on a multitude of real graphs, observing interesting connections with other graph characteristics, as well as a clear deviation from the corresponding behavior of random graphs. Furthermore, similar to the well known results about the robustness of real graphs under random and targeted node removals, we discuss the implications of our findings on a special case of robustness - regarding random and targeted node departures based on their engagement level.