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2016-present
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A strong Harnack inequality for graphs,
Comm. Analysis and Geometry, 25, no. 3, (2017), 557--588,
(with S.-T. Yau).
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Extreme values of the stationary distribution of random walks on directed graphs
,
Advance in Applied Math., 81, (2016), 128--155,
(with Sinan Aksoy and Xing Peng).
-
A generalized Alon-Boppana bound and weak Ramanujan graphs, Electronic Journal of Combinatorics, 23, (2016), Paper #3.4, (20 pages).
The
version in E-JC.
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Curvature aspects of graphs,
Proc. of AMS, 145 (2017), 2033--2042,
(with F. Bauer, Y. Lin and Y. Liu).
-
The matrix cover polynomial,
J. Combinatorics, 7 (2016), 375--412,
(with R. L. Graham).
2011-2015
- Distributed algorithms for finding local clusters using heat kernel pagerank, WAW, 2015,
LNCS 9479, Springer, 177--189,
(with O. Simpson).
-
A brief survey of PageRank algorithms,
IEEE Transactions on Network Science and Engineering, 1, No. 1, (2015), 38--42.
-
Discrepancy inequalities for directed graphs
,
Discrete Applied Mathematics, 176 (2014) 30-42,
(with F. Kenter).
-
Harnack inequalities for graphs with non-negative Ricci curvature
,
J. Math. Anal. Appl. 415 (2014), 25 -- 32,
(with Yong Lin and S.-T. Yau).
-
From quasirandom graphs to graph limits and graphlets
,
Advances in Applied Math. 56 (2014),
135--174.
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Solving linear systems with boundary conditions using heat kernel pagerank
WAW 2013, LNCS 8305, 203--219,
(with Olivia Simpson).
The journal version appeared in Internet Mathematics, 11 (2015), 449-471.
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A local clustering algorithm for connection graphs
,
WAW 2013, LNCS 8305, 203--219,
(with Mark Kempton).
The journal version appeared in Internet Math., 11 (2015), 333-351.
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Spectral clustering of graphs with general degrees in the extended planted partition model
,
COLT 2012,
Journal of Machine Learning Research, (2012), 1--23,
(with K. Chaudhuri and A. Tsiatas).
-
Multi-commodity allocation for dynamic demands using PageRank vectors
,
WAW2012,
LNCS 7323 (2012), 138--152,
(with P. Horn and J. Hughes).
The journal version appeared in Internet Mathematics, 10 (2014), 49--65.
-
Braess's paradox in expanders
,
Random Structures and Algorithms, 41 (2012), 451--468,
(with S. J. Young and W. Zhao).
-
Hypergraph coloring games and voter models
,
WAW2012, LNCS 7323 (2012), 1--16,
(with Alex Tsiatas).
The
journal version appeared in Internet Mathematics, 10 (2014), 66--86.
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Diameter
of random spanning trees in a given graph ,
Journal of Graph Theory,
69, (2012), 223--240,
(with P. Horn and L. Lu).
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On the spectra of general random graphs,
Electronic Journal of Combinatorics, 18(1),
(2011), P215, 14 pages,
(with M. Radcliffe).
2006-2010
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Graph Theory in the information age
,
Notices of AMS, 57, no. 6, July 2010, 726--732.
This article was translated into Chinese and appeared in
Mathematical Advances in Translation, 3, 2010, 207--213.
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PageRank and random walks on graphs
,
Fete of Combinatorics and Computer Science, (G. O. H. Katona, A. Schrijver and T. Szonyi, Eds.),
Springer, Berlin, (2010), 43--62,
(with Wenbo Zhao).
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Small
spectral gap in the combinatorial Laplacian implies Hamiltonian,
Annals of Combinatorics, 13, (2010), 403--412,
(with S. Butler).
-
PageRank
as a discrete Green's function,
Geometry and Analysis, I, ALM 17, (2010), 285--302.
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A local graph
partitioning algorithm using heat kernel pagerank,
WAW 2009,
LNCS 5427, (2009), 62-75.
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Distributing antidote using PageRank vectors
,
Internet Mathematics, 6, (2009), 237--254,
(with Paul Horn and Alexander Tsiatas).
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The giant component
in a random subgraph of a given graph
,
Proceedings of WAW2009, Lecture Notes in Computer Science 5427, 38--49,
(with P. Horn and L. Lu).
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A whirlwind tour of random graphs
,
a survey article in Encyclopedia on Complex Systems, Springer, 2008.
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A network color game
,
WINE 2008, Lecture Notes in Computer Science, Volume 5385 (2008), 522--530,
(with K. Chaudhuri and M. S. Jamall).
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Quasi-random graphs with
given degree sequences,
Random Structures and Algorithms, 12 (2008), 1--19,
(with R. L. Graham).
-
Four
Cheeger-type inequalities for graph
partitioning algorithms
,
Proceedings of ICCM, II, (2007), 751--772.
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The heat kernel as the pagerank of a graph
,
PNAS, 105 (50), (2007), 19735--19740.
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Local partitioning for directed graphs using PageRank
,
WAW2007, 166--178,
(with R. Andersen and Kevin Lang).
The full paper is in Internet Mathematics, 5 (2008), 3--22.
-
The
spectral gap of a random subgraph of a graph,
the
extended abstract appeared in Proceedings of WAW2006, LNCS 4937 and the complete version is in Internet Math, 4 (2007), 225-244,
(with Paul Horn).
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Detecting sharp
drops in PageRank and a simplified local partitioning algorithm
Theory and Applications of Models of Computation,
Proceedings of TAMC 2007, LNCS 4484, Springer, (2007), 1--12,
(with R. Andersen).
-
Local
graph partitioning using pagerank vectors,
FOCS 2006, 475-486,
(with R. Andersen and K. Lang).
The full paper version,
Using pagerank vectors to locally partition a graph appeared in Internet Mathematics, 4 (2007), 35--64.
-
Random walks and local cuts
in graphs,
Linear Algebra and its Applications, 423 (2007), 22--32.
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The diameter and
Laplacian eigenvalues of directed graphs,
Electronic Journal of Combinatorics 13 (2006), N4, 6 pp.
2001-2005
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Laplacians
and the Cheeger inequality for
directed graphs,
Annals of Combinatorics, 9 (2005), 1--19.
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A spectral Turán theorem,
Combinatorics, Probability and Computing 14 (2005), 755--767.
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Coupling online and offline analyses for random power law graphs,
Internet Mathematics, 1 (2004), 409--461,
(with Lincoln Lu).
-
Discrete isoperimetric inequalities,
Surveys in Differential Geometry IX, International Press, (2004), 53--82.
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Generalizations of Polya's urn problem,
Annals of Combinatorics 7 (2003), 141--153,
(with Shirin Handjani and Doug Jungreis).
- Finding Favorites,
Electronic Colloquium on Computational Complexity, Report No. 78 (2003),
(with Ron Graham, Jia Mao and Andrew Yao).
-
Eigenvalues of random power law graphs,
Annals of Combinatorics 7 (2003), 21--33,
(with Lincoln Lu and Van Vu).
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The spectra of random graphs with given expected degrees,
short version,
Proceedings of National Academy of Sciences 100, no. 11, (2003), 6313--6318,
long version
(with full proofs) Internet Mathematics 1 (2004), 257--275,
(with Lincoln Lu and Van Vu).
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Spectral Partitioning with Indefinite Kernels using the Nyström Extension,
European Conference on Computer Vision, 2002, III, 531--542.
Paper version:
Spectral grouping using the Nyström method,
IEEE Transactions on Pattern Analysis and Machine Intelligence
26, No. 2, (2004), 214--225,
(with Charless Fowlkes, Serge Belongie, and Jitendra Malik).
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A chip-firing game and Dirichlet eigenvalues,
abstract,
Discrete Math 257 (2002), 341--355,
(with Robert Ellis).
1996-2000
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Discrete Green's functions,
abstract,
J. Combinatorial Theory (A) 91 (2000), 191--214,
(with S.-T. Yau).
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Higher eigenvalues and isoperimetric inequalities on
Riemannian manifolds and graphs,
Communications on Analysis and Geometry 8, (2000), 969--1026,
(with A. Grigor'yan and S.-T. Yau).
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On polynomials of spanning trees,
abstract,
Annals of Combinatorics 4 (2000), 13--26,
(with C. Yang).
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Weighted graph Laplacians and isoperimetric inequalities,
Pacific Journal of Mathematics 192 (2000), 257--273,
(with Kevin Oden).
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A Harnack inequality for Dirichlet eigenvalues,
Journal of Graph Theory, 34 (2000), 247--257,
(with S.-T. Yau).
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Spanning trees in subgraphs of lattices,
Comtempory Math. 245, Amer. Math. Soc., Providence, R. I., 1999, 201--219.
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Coverings, heat kernels and spanning trees,
Electronic Journal of Combinatorics 6 (1999), R12, 21 pp,
(with S.-T. Yau).
-
Multidiameters and multiplicities,
European Journal of Combinatorics 20 (1999), 629--640,
(with C. Delorme and P. Sol'e).
-
Logarithmic Sobolev techniques for random walks on graphs,
Emerging Applications of Number Theory, IMA Volumes in Math. and its Applications
109 (eds. D. A. Hejhal et. al.), 175--186, Springer, 1999.
- Isoperimetric inequalities for Cartesian products of graphs,
Combinatorics, Probability and Computing 7 (1998), 141--148,
(with Prasad Tetali).
-
Spectral Graph Theory, (first four chapter)
CBMS Number 92, AMS Publications, 1997, xii+207 pp.
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Stratified random walks on an n-cube,
Random Structures and Algorithms 11 (1997), 199--222,
(with R.L. Graham).
-
Random walks on generating sets of groups,
Electronic Journal of Combinatorics 4 no. 2, (1997) #R7, 14 pp,
(with R. L. Graham).
-
Eigenvalue inequalities for graphs and convex subgraphs,
Communications on Analysis and Geometry 5 (1997), 575--623,
(with S.-T. Yau).
-
A combinatorial trace formula,
Tsing Hua Lectures on Geometry and Analysis,
International Press, Cambridge, Massachusetts, 1997, 107--116,
(with S.-T. Yau)
-
Eigenvalues and diameters for manifolds and graphs,
Tsing Hua Lectures on Geometry and Analysis,
International Press, Cambridge, Massachusetts, 1997, 79--106,
(with A. Grigor'yan and S.-T. Yau).
-
Logarithmic Harnack inequalities,
Mathematical Research Letters 3 (1996), 793--812,
(with S.-T. Yau).
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Laplacians of graphs and Cheeger's inequalities,
in Combinatorics, Paul Erdos is eighty, Vol. 2 (Keszthely, 1993),
Bolyai Math.
Soc., Budapest, 1996, 157--172.
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A combinatorial Laplacian with vertex weights,
Journal of Combinatorial Theory (A) 75 (1996), 316--327,
(with R. P. Langlands).
-
Upper bounds for eigenvalues of the discrete and continuous
Laplace operators,
Advances in Mathematics 117 (1996) 165--178,
(with A. Grigor'yan and S.-T. Yau).
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On sampling with Markov chains,
Random Structures and Algorithms 9 (1996) 55--77.
(with R. L. Graham and S. -T. Yau).
1991-1995
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A Harnack inequality for homogeneous graphs and subgraphs,
Communications on Analysis and Geometry 2
(1994), 627--640,
also in Turkish J. Math. 19 (1995), 273--290,
(with S.-T. Yau).
-
Eigenvalues of graphs,
Proceedings of the International Congress of Mathematicians (Zurich, 1994),
Birkhäuser Verlag, Berlin, 1333--1342.
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Eigenvalues of graphs and Sobolev inequalities,
Combinatorics, Probability and Computing 4 (1995), 11--26,
(with S.-T. Yau).
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Groups and the Buckyball,
in Lie Theory and Geometry: In honor of Bertram Kostant (Eds. J.-L. Brylinski, R. Brylinski, V. Guillemin and V. Kac)
PM 123, Birkhäuser, Boston, 1994, 97--126,
(with Bertram Kostant and Shlomo Sternberg).
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An upper bound on the diameter
of a graph from eigenvalues associated with its Laplacian,
SIAM J. Discrete Math. 7 (1994), 443--457,
(with V. Faber and Thomas A. Manteuffel).
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The Laplacian of a hypergraph,
in Expanding graphs (Princeton, NY, 1992),
DIMACS Ser. Discrete Math. Theoret.
Comput. Sci., 10, Amer. Math. Soc., Providence, RI, 1993, 21--36.
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Mathematics and the Buckyball,
(this is a somewhat different version from the one
that appeared in American Scientist 81, No. 1., (1993) 56--71),
(with Shlomo Sternberg).
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Laplacian and vibrational spectra for homogeneous graphs,
J. Graph Theory 16 (1992), 605--627,
(with Shlomo Sternberg).
1986-1990
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1981-1985
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1975-1980
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1973-1975
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