How to schedule a cascade in an arbitrary graph
Proceedings of the 13th ACM Conference on Electronic Commerce
Complex contagion and the weakness of long ties in social networks: revisited
Proceedings of the fourteenth ACM conference on Electronic commerce
Cascading behavior in social and economic networks
Proceedings of the fourteenth ACM conference on Electronic commerce
Information cascade at group scale
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Algorithms, networks, and social phenomena
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
On the inapproximability of minimizing cascading failures under the deterministic threshold model
Information Processing Letters
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The spread of a cascading failure through a network is an issue that comes up in many domains: in the contagious failures that spread among financial institutions during a financial crisis, through nodes of a power grid or communication network during a widespread outage, or through a human population during the outbreak of an epidemic disease. Here we study a natural model of threshold contagion: each node is assigned a numerical threshold drawn independently from an underlying distribution, and it will fail as soon as its number of failed neighbors reaches this threshold. Despite the simplicity of the formulation, it has been very challenging to analyze the failure processes that arise from arbitrary threshold distributions, even qualitative questions concerning which graphs are the most resilient to cascading failures in these models have been difficult to resolve. Here we develop a set of new techniques for analyzing the failure probabilities of nodes in arbitrary graphs under this model, and we compare different graphs according to the maximum failure probability of any node in the graph when thresholds are drawn from a given distribution. We find that the space of threshold distributions has a surprisingly rich structure when we consider the risk that these thresholds induce on different graphs: small shifts in the distribution of the thresholds can favor graphs with a maximally clustered structure (i.e., cliques), those with a maximally branching structure (trees), or even intermediate hybrids.