human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "step by step community detection for volume regular graphs"):
  Abstract: Spectral techniques have proved amongst the most effective approaches to graph clustering. However, in general they require explicit computation of the main eigenvectors of a suitable matrix (usually the Laplacian matrix of the graph). #R##N#Recent work (e.g., Becchetti et al., SODA 2017) suggests that observing the temporal evolution of the power method applied to an initial random vector may, at least in some cases, provide enough information on the space spanned by the first two eigenvectors, so as to allow recovery of a hidden partition without explicit eigenvector computations. While the results of Becchetti et al. apply to perfectly balanced partitions and/or graphs that exhibit very strong forms of regularity, we extend their approach to graphs containing a hidden $k$ partition and characterized by a milder form of volume-regularity. We show that the class of $k$-volume regular graphs is the largest class of undirected (possibly weighted) graphs whose transition matrix admits $k$ stepwise eigenvectors (i.e., vectors that are constant over each set of the hidden partition). To obtain this result, we highlight a connection between volume regularity and lumpability of Markov chains. Moreover, we prove that if the stepwise eigenvectors are those associated to the first $k$ eigenvalues and the gap between the $k$-th and the ($k$+1)-th eigenvalues is sufficiently large, the Averaging dynamics of Becchetti et al. recovers the underlying community structure of the graph in logarithmic time, with high probability.

Includes members:
  Member "distributed community detection via metastability of the 2 choices dynamics":
    also connected through other hyperedges:
      (none)
  Member "phase transition of the 2 choices dynamics on core periphery networks":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "distributed community detection via metastability of the 2 choices dynamics")
  Member "eigenvector computation and community detection in asynchronous gossip models":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "understanding filter bubbles and polarization in social networks")
  Member "distributed graph clustering and sparsification":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "distributed community detection via metastability of the 2 choices dynamics")
  Member "find your place simple distributed algorithms for community detection":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "efficient distributed community detection in the stochastic block model")
  Member "partitioning well clustered graphs spectral clustering works":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "approximating spectral clustering via sampling a review")
  Member "exact recovery in the stochastic block model":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "renyi entropy bounds on the active learning cost performance tradeoff")
  Member "spectral redemption in clustering sparse networks":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "approximating spectral clustering via sampling a review")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.DC(Distributed, Parallel, and Cluster Computing)