human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "community detection thresholds and the weak ramanujan property"
  Abstract: Decelle et al.\cite{Decelle11} conjectured the existence of a sharp threshold for community detection in sparse random graphs drawn from the stochastic block model. Mossel et al.\cite{Mossel12} established the negative part of the conjecture, proving impossibility of meaningful detection below the threshold. However the positive part of the conjecture remained elusive so far. Here we solve the positive part of the conjecture. We introduce a modified adjacency matrix $B$ that counts self-avoiding paths of a given length $\ell$ between pairs of nodes and prove that for logarithmic $\ell$, the leading eigenvectors of this modified matrix provide non-trivial detection, thereby settling the conjecture. A key step in the proof consists in establishing a {\em weak Ramanujan property} of matrix $B$. Namely, the spectrum of $B$ consists in two leading eigenvalues $\rho(B)$, $\lambda_2$ and $n-2$ eigenvalues of a lower order $O(n^{\epsilon}\sqrt{\rho(B)})$ for all $\epsilon>0$, $\rho(B)$ denoting $B$'s spectral radius. $d$-regular graphs are Ramanujan when their second eigenvalue verifies $|\lambda|\le 2 \sqrt{d-1}$. Random $d$-regular graphs have a second largest eigenvalue $\lambda$ of $2\sqrt{d-1}+o(1)$ (see Friedman\cite{friedman08}), thus being {\em almost} Ramanujan. Erd\H{o}s-R\'enyi graphs with average degree $d$ at least logarithmic ($d=\Omega(\log n)$) have a second eigenvalue of $O(\sqrt{d})$ (see Feige and Ofek\cite{Feige05}), a slightly weaker version of the Ramanujan property. However this spectrum separation property fails for sparse ($d=O(1)$) Erd\H{o}s-R\'enyi graphs. Our result thus shows that by constructing matrix $B$ through neighborhood expansion, we regularize the original adjacency matrix to eventually recover a weak form of the Ramanujan property.

Connected through hyperedge HE-1 (induced by source paper "from tree matching to sparse graph alignment"):
  with members:
    - "analysis of a canonical labeling algorithm for the alignment of correlated erd h o s r enyi graphs"
    - "spectral alignment of graphs"
    - "maximum quadratic assignment problem reduction from maximum label cover and lp based approximation algorithm"
    - "de anonymizing social networks"

Connected through hyperedge HE-2 (induced by source paper "power up robust graph convolutional network against evasion attacks based on graph powering"):
  with members:
    - "mixhop higher order graph convolutional architectures via sparsified neighborhood mixing"
    - "adversarial attacks on graph neural networks via meta learning"
    - "a comprehensive survey on graph neural networks"
    - "can adversarial network attack be defended"
    - "graph powering and spectral robustness"
    - "graph neural networks a review of methods and applications"
    - "zero shot recognition via semantic embeddings and knowledge graphs"
    - "adversarial attack on graph structured data"

Connected through hyperedge HE-3 (induced by source paper "mean field theory of graph neural networks in graph partitioning"):
  with members:
    - "graphrnn generating realistic graphs with deep auto regressive models"
    - "algorithmic detectability threshold of the stochastic block model"
    - "deriving neural architectures from sequence and graph kernels"
    - "the computer science and physics of community detection landscapes phase transitions and hardness"
    - "neural message passing for quantum chemistry"
    - "node2vec scalable feature learning for networks"
    - "semi supervised classification with graph convolutional networks"
    - "learning convolutional neural networks for graphs"

Connected through hyperedge HE-4 (induced by source paper "accuracy memory tradeoffs and phase transitions in belief propagation"):
  with members:
    - "the circuit complexity of inference"
    - "communication complexity of estimating correlations"
    - "geometric lower bounds for distributed parameter estimation under communication constraints"
    - "reducibility and computational lower bounds for problems with planted sparse structure"
    - "inference under information constraints i lower bounds from chi square contraction"
    - "extractor based time space lower bounds for learning"
    - "secret key generation with limited interaction"
    - "fast learning requires good memory a time space lower bound for parity learning"

Connected through hyperedge HE-5 (induced by source paper "planted models for k way edge and vertex expansion"):
  with members:
    - "semi random graphs with planted sparse vertex cuts algorithms for exact and approximate recovery"
    - "multisection in the stochastic block model using semidefinite programming"
    - "learning communities in the presence of errors"
    - "how robust are reconstruction thresholds for community detection"
    - "partitioning well clustered graphs spectral clustering works"
    - "constant factor approximation for balanced cut in the pie model"
    - "approximation algorithms for hypergraph small set expansion and small set vertex expansion"
    - "exact recovery in the stochastic block model"

Connected through hyperedge HE-6 (induced by source paper "statistical guarantees for local graph clustering"):
  with members:
    - "flow based local graph clustering with better seed set inclusion"
    - "capacity releasing diffusion for speed and locality"
    - "an optimization approach to locally biased graph algorithms"
    - "parallel local graph clustering"
    - "a simple and strongly local flow based method for cut improvement"
    - "heat kernel based community detection"
    - "flow based algorithms for local graph clustering"
    - "on semidefinite relaxations for the block model"

Connected through hyperedge HE-7 (induced by source paper "local statistics semidefinite programming and community detection"):
  with members:
    - "a tight degree 4 sum of squares lower bound for the sherrington kirkpatrick hamiltonian"
    - "vector colorings of random ramanujan and large girth irregular graphs"
    - "computational hardness of certifying bounds on constrained pca problems"
    - "the lov asz theta function for random regular graphs and community detection in the hard regime"
    - "learning from untrusted data"
    - "avoiding imposters and delinquents adversarial crowdsourcing and peer prediction"
    - "semidefinite programs on sparse random graphs and their application to community detection"
    - "exact recovery in the stochastic block model"

Connected through hyperedge HE-8 (induced by source paper "the sdp value for random two eigenvalue csps"):
  with members:
    - "the threshold for sdp refutation of random regular nae 3sat"
    - "the lov asz theta function for random regular graphs and community detection in the hard regime"
    - "sum of squares lower bounds for refuting any csp"
    - "the backtracking survey propagation algorithm for solving random k sat problems"
    - "strongly refuting random csps below the spectral threshold"
    - "semidefinite programs on sparse random graphs and their application to community detection"
    - "a composition theorem for parity kill number"
    - "spectral redemption in clustering sparse networks"

Question: Please tell me which class the center node 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.SI(Social and Information Networks)