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Community Detection and Modularity

In the context of community detection in complex networks, which of the following statements most accurately describes the "resolution limit" inherent in modularity (Q) optimization? Answer Options: A. The resolution limit refers to the inability of the Girvan-Newman algorithm to efficiently recalculate edge betweenness in large-scale networks, thus preventing its practical application. B. The resolution limit refers exclusively to divisive methods, indicating that iterative edge removal always fragments the network into individual components before a maximum of modularity can be achieved. C. The resolution limit is an artifact of the configuration model used in the modularity formula, causing the method to fail to detect small communities, even if they are strongly internally connected (such as cliques), favoring their merging into larger communities to maximize the overall Q. D. The resolution limitation states that modularity (Q) will always assign a negative value to any ...

Growth Mechanisms and the Persistence of Degree Correlation


The persistence of assortativity in a network, that is, the tendency for degree correlation to be maintained over time or in the face of perturbations, is intrinsically related to:

A. The existence of a k-core with a high degree of internal connectivity that protects high-degree nodes from random failures.

B. The preferential attachment rule in network growth, where new nodes connect proportionally to the degree of existing nodes, as long as this rule is modified to explicitly penalize or favor connections between nodes of similar degrees.

C. A strong positive correlation between a node's degree and its betweenness centrality, ensuring that hubs remain key bridges.

D. The structural robustness exhibited by disassortative networks against attacks targeting hubs, preserving their overall structure.

E. None of the above.

Original idea by: Juan Jose Rodriguez Rodriguez

Comentários

  1. Caro Juan, não estudamos a persistência de correlações de graus ao longo do tempo. Creio que esta questão caia um pouco fora do nosso conteúdo.

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