
2016present

A strong Harnack inequality for graphs,
Comm. Analysis and Geometry, to appear,
(with S.T. Yau).

Extreme values of the stationary distribution of random walks on directed graphs
,
Advance in Applied Math., 81, (2016), 128155,
(with Sinan Aksoy and Xing Peng).

A generalized AlonBoppana bound and weak Ramanujan graphs, Electric Journal of Combinatorics, 23, (2016), Paper #3.4, (20 pages).

Curvature aspects of graphs,
Proc. of AMS, to appear,
(with F. Bauer, Y. Lin and Y. Liu).

The matrix cover polynomial,
J. Combinatorics, 7 (2016), 375412,
(with R. L. Graham).
20112015
 Distributed algorithms for finding local clusters using heat kernel pagerank, WAW, 2015,
LNCS 9479, Springer, 177189,
(with O. Simpson).

A brief survey of PageRank algorithms,
IEEE Transactions on Network Science and Engineering, 1, No. 1, (2015), 3842.

Discrepancy inequalities for directed graphs
,
Discrete Applied Mathematics, 176 (2014) 3042,
(with F. Kenter).

Harnack inequalities for graphs with nonnegative 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),
135174.

Solving linear systems with boundary conditions using heat kernel pagerank
WAW 2013, LNCS 8305, 203219,
(with Olivia Simpson).
The journal version appeared in Internet Mathematics, 11 (2015), 449471.

A local clustering algorithm for connection graphs
,
WAW 2013, LNCS 8305, 203219,
(with Mark Kempton).
The journal version appeared in Internet Math., 11 (2015), 333351.

Spectral clustering of graphs with general degrees in the extended planted partition model
,
COLT 2012,
Journal of Machine Learning Research, (2012), 123,
(with K. Chaudhuri and A. Tsiatas).

Multicommodity allocation for dynamic demands using PageRank vectors
,
WAW2012,
LNCS 7323 (2012), 138152,
(with P. Horn and J. Hughes).
The journal version appeared in Internet Mathematics, 10 (2014), 4965.

Braess's paradox in expanders
,
Random Structures and Algorithms, 41 (2012), 451468,
(with S. J. Young and W. Zhao).

Hypergraph coloring games and voter models
,
WAW2012, LNCS 7323 (2012), 116,
(with Alex Tsiatas).
The
journal version appeared in Internet Mathematics, 10 (2014), 6686.

Diameter
of random spanning trees in a given graph ,
Journal of Graph Theory,
69, (2012), 223240,
(with P. Horn and L. Lu).

On the spectra of general random graphs,
Electronic Journal of Combinatorics, 18(1),
(2011), P215, 14 pages,
(with M. Radcliffe).
20062010
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Graph Theory in the information age
,
Notices of AMS, 57, no. 6, July 2010, 726732.
This article was translated into Chinese and appeared in
Mathematical Advances in Translation, 3, 2010, 207213.

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), 4362,
(with Wenbo Zhao).

Small
spectral gap in the combinatorial Laplacian implies Hamiltonian,
Annals of Combinatorics, 13, (2010), 403412,
(with S. Butler).

PageRank
as a discrete Green's function,
Geometry and Analysis, I, ALM 17, (2010), 285302.

A local graph
partitioning algorithm using heat kernel pagerank,
WAW 2009,
LNCS 5427, (2009), 6275.

Distributing antidote using PageRank vectors
,
Internet Mathematics, 6, (2009), 237254,
(with Paul Horn and Alexander Tsiatas).

The giant component
in a random subgraph of a given graph
,
Proceedings of WAW2009, Lecture Notes in Computer Science 5427, 3849,
(with P. Horn and L. Lu).

A whirlwind tour of random graphs
,
a survey article in Encyclopedia on Complex Systems, Springer, 2008.

A network color game
,
WINE 2008, Lecture Notes in Computer Science, Volume 5385 (2008), 522530,
(with K. Chaudhuri and M. S. Jamall).

Quasirandom graphs with
given degree sequences,
Random Structures and Algorithms, 12 (2008), 119,
(with R. L. Graham).

Four
Cheegertype inequalities for graph
partitioning algorithms
,
Proceedings of ICCM, II, (2007), 751772.

The heat kernel as the pagerank of a graph
,
PNAS, 105 (50), (2007), 1973519740.

Local partitioning for directed graphs using PageRank
,
WAW2007, 166178,
(with R. Andersen and Kevin Lang).
The full paper is in Internet Mathematics, 5 (2008), 322.

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), 225244,
(with Paul Horn).

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), 112,
(with R. Andersen).

Local
graph partitioning using pagerank vectors,
FOCS 2006, 475486,
(with R. Andersen and K. Lang).
The full paper version,
Using pagerank vectors to locally partition a graph appeared in Internet Mathematics, 4 (2007), 3564.

Random walks and local cuts
in graphs,
Linear Algebra and its Applications, 423 (2007), 2232.

The diameter and
Laplacian eigenvalues of directed graphs,
Electronic Journal of Combinatorics 13 (2006), N4, 6 pp.
20012005
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Laplacians
and the Cheeger inequality for
directed graphs,
Annals of Combinatorics, 9 (2005), 119.

A spectral Turán theorem,
Combinatorics, Probability and Computing 14 (2005), 755767.

Coupling online and offline analyses for random power law graphs,
Internet Mathematics, 1 (2004), 409461,
(with Lincoln Lu).

Discrete isoperimetric inequalities,
Surveys in Differential Geometry IX, International Press, (2004), 5382.

Generalizations of Polya's urn problem,
Annals of Combinatorics 7 (2003), 141153,
(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), 2133,
(with Lincoln Lu and Van Vu).

The spectra of random graphs with given expected degrees,
short version,
Proceedings of National Academy of Sciences 100, no. 11, (2003), 63136318,
long version
(with full proofs) Internet Mathematics 1 (2004), 257275,
(with Lincoln Lu and Van Vu).

Spectral Partitioning with Indefinite Kernels using the Nyström Extension,
European Conference on Computer Vision, 2002, III, 531542.
Paper version:
Spectral grouping using the Nyström method,
IEEE Transactions on Pattern Analysis and Machine Intelligence
26, No. 2, (2004), 214225,
(with Charless Fowlkes, Serge Belongie, and Jitendra Malik).

A chipfiring game and Dirichlet eigenvalues,
abstract,
Discrete Math 257 (2002), 341355,
(with Robert Ellis).
19962000
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Discrete Green's functions,
abstract,
J. Combinatorial Theory (A) 91 (2000), 191214,
(with S.T. Yau).

Higher eigenvalues and isoperimetric inequalities on
Riemannian manifolds and graphs,
Communications on Analysis and Geometry 8, (2000), 9691026,
(with A. Grigor'yan and S.T. Yau).

On polynomials of spanning trees,
abstract,
Annals of Combinatorics 4 (2000), 1326,
(with C. Yang).

Weighted graph Laplacians and isoperimetric inequalities,
Pacific Journal of Mathematics 192 (2000), 257273,
(with Kevin Oden).

A Harnack inequality for Dirichlet eigenvalues,
Journal of Graph Theory, 34 (2000), 247257,
(with S.T. Yau).

Spanning trees in subgraphs of lattices,
Comtempory Math. 245, Amer. Math. Soc., Providence, R. I., 1999, 201219.

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), 629640,
(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.), 175186, Springer, 1999.
 Isoperimetric inequalities for Cartesian products of graphs,
Combinatorics, Probability and Computing 7 (1998), 141148,
(with Prasad Tetali).

Spectral Graph Theory, (first four chapter)
CBMS Number 92, AMS Publications, 1997, xii+207 pp.

Stratified random walks on an ncube,
Random Structures and Algorithms 11 (1997), 199222,
(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), 575623,
(with S.T. Yau).

A combinatorial trace formula,
Tsing Hua Lectures on Geometry and Analysis,
International Press, Cambridge, Massachusetts, 1997, 107116,
(with S.T. Yau)

Eigenvalues and diameters for manifolds and graphs,
Tsing Hua Lectures on Geometry and Analysis,
International Press, Cambridge, Massachusetts, 1997, 79106,
(with A. Grigor'yan and S.T. Yau).

Logarithmic Harnack inequalities,
Mathematical Research Letters 3 (1996), 793812,
(with S.T. Yau).

Laplacians of graphs and Cheeger's inequalities,
in Combinatorics, Paul Erdos is eighty, Vol. 2 (Keszthely, 1993),
Bolyai Math.
Soc., Budapest, 1996, 157172.

A combinatorial Laplacian with vertex weights,
Journal of Combinatorial Theory (A) 75 (1996), 316327,
(with R. P. Langlands).

Upper bounds for eigenvalues of the discrete and continuous
Laplace operators,
Advances in Mathematics 117 (1996) 165178,
(with A. Grigor'yan and S.T. Yau).

On sampling with Markov chains,
Random Structures and Algorithms 9 (1996) 5577.
(with R. L. Graham and S. T. Yau).
19911995
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A Harnack inequality for homogeneous graphs and subgraphs,
Communications on Analysis and Geometry 2
(1994), 627640,
also in Turkish J. Math. 19 (1995), 273290,
(with S.T. Yau).

Eigenvalues of graphs,
Proceedings of the International Congress of Mathematicians (Zurich, 1994),
Birkhäuser Verlag, Berlin, 13331342.

Eigenvalues of graphs and Sobolev inequalities,
Combinatorics, Probability and Computing 4 (1995), 1126,
(with S.T. Yau).

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, 97126,
(with Bertram Kostant and Shlomo Sternberg).

An upper bound on the diameter
of a graph from eigenvalues associated with its Laplacian,
SIAM J. Discrete Math. 7 (1994), 443457,
(with V. Faber and Thomas A. Manteuffel).

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, 2136.

Mathematics and the Buckyball,
(this is a somewhat different version from the one
that appeared in American Scientist 81, No. 1., (1993) 5671),
(with Shlomo Sternberg).

Laplacian and vibrational spectra for homogeneous graphs,
J. Graph Theory 16 (1992), 605627,
(with Shlomo Sternberg).
19861990
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19811985
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19751980
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19731975
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