{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:49:38Z","timestamp":1759063778303},"publisher-location":"Berlin, Heidelberg","reference-count":15,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642180088"},{"type":"electronic","value":"9783642180095"}],"license":[{"start":{"date-parts":[[2010,1,1]],"date-time":"2010-01-01T00:00:00Z","timestamp":1262304000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010]]},"DOI":"10.1007\/978-3-642-18009-5_8","type":"book-chapter","created":{"date-parts":[[2010,12,2]],"date-time":"2010-12-02T10:31:28Z","timestamp":1291285888000},"page":"74-85","source":"Crossref","is-referenced-by-count":18,"title":["Random Walks on Digraphs, the Generalized Digraph Laplacian and the Degree of Asymmetry"],"prefix":"10.1007","author":[{"given":"Yanhua","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhi-Li","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"8_CR1","unstructured":"Aldous, D., Fill, J.A.: Reversible markov chains and random walks on graphs, http:\/\/www.stat.berkeley.edu\/~aldous\/RWG\/book.html"},{"key":"8_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0653-8","volume-title":"Matrix Analysis","author":"R. Bhatia","year":"1997","unstructured":"Bhatia, R.: Matrix Analysis. Springer, Heidelberg (1997)"},{"key":"8_CR3","unstructured":"Boley, D., Ranjan, G., Zhang, Z.-L.: An asymmetric laplacian for a directed graph. University of minnesota computer science department technical report: Tr09-009 (2009)"},{"key":"8_CR4","first-page":"240","volume-title":"SIAM Workshop on Analytic Algorithmics and Combinatorics (ANALCO)","author":"S. Boyd","year":"2005","unstructured":"Boyd, S., Ghosh, A., Prabhakar, B., Shah, D.: Mixing times for random walks on geometric random graphs. In: SIAM Workshop on Analytic Algorithmics and Combinatorics (ANALCO), Vancouver, pp. 240\u2013249. SIAM, Philadelphia (2005)"},{"issue":"1-7","key":"8_CR5","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/S0169-7552(98)00110-X","volume":"30","author":"S. Brin","year":"1998","unstructured":"Brin, S., Page, L.: The anatomy of a large-scale hypertextual web search engine. Computer Networks and ISDN Systems\u00a030(1-7), 107\u2013117 (1998)","journal-title":"Computer Networks and ISDN Systems"},{"key":"8_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00026-005-0237-z","volume":"9","author":"F.R.K. Chung","year":"2005","unstructured":"Chung, F.R.K.: Laplacians and the cheeger inequality for directed graphs. Annals of Combinatorics\u00a09, 1\u201319 (2005)","journal-title":"Annals of Combinatorics"},{"key":"8_CR7","unstructured":"Chung, F.R.K.: Spectral Graph Theory. In: CBMS Regional Conference Series in Mathematics, vol. 92 (2006)"},{"key":"8_CR8","doi-asserted-by":"crossref","unstructured":"Chung, F.R.K., Yau, S.T.: Discrete green\u2019s functions. Journal of Combinatorial Theory, Series A, 191\u2013214 (July 2000)","DOI":"10.1006\/jcta.2000.3094"},{"issue":"1","key":"8_CR9","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1214\/aoap\/1177005981","volume":"1","author":"J.A. Fill","year":"1991","unstructured":"Fill, J.A.: Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process. Ann. Appl. Probab.\u00a01(1), 62\u201387 (1991)","journal-title":"Ann. Appl. Probab."},{"key":"8_CR10","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810817","volume-title":"Matrix Analysis","author":"R. Horn","year":"1985","unstructured":"Horn, R., Johnson, C.R.: Matrix Analysis, 1st edn. Cambridge University Press, Cambridge (1985)","edition":"1"},{"key":"8_CR11","unstructured":"Jerrum, M., Son, J.-B.: Spectral gap and log-sobolev constant for balanced matroids. In: The 43rd Annual IEEE Symposium on Foundations of Computer Science, FOCS 2002 (2002)"},{"key":"8_CR12","doi-asserted-by":"crossref","unstructured":"Li, Y., Zhang, Z.-L.: Random walks on diagraphs, the generalized digraph laplacian and the degree of asymmetry. Technical Report. CSE Department of University of Minnesota (2010), http:\/\/www.cs.umn.edu\/~yanhua\/","DOI":"10.1007\/978-3-642-18009-5_8"},{"key":"8_CR13","first-page":"1","volume":"2","author":"L. Lov\u00e0sz","year":"1993","unstructured":"Lov\u00e0sz, L.: Random walks on graphs: A survey. Combinatorics\u00a02, 1\u201346 (1993)","journal-title":"Combinatorics"},{"key":"8_CR14","doi-asserted-by":"crossref","unstructured":"Mihail, M.: Conductance and convergence of markov chains-a combinatorial treatment of expanders. In: Proceedings of FOCS 1989, pp. 526\u2013531 (1989)","DOI":"10.1109\/SFCS.1989.63529"},{"key":"8_CR15","first-page":"1036","volume-title":"Proceedings of the 22nd International Conference on Machine Learning, ICML 2005","author":"D. Zhou","year":"2005","unstructured":"Zhou, D., Huang, J., Sch\u00f6lkopf, B.: Learning from labeled and unlabeled data on a directed graph. In: Proceedings of the 22nd International Conference on Machine Learning, ICML 2005, pp. 1036\u20131043. ACM, New York (2005)"}],"container-title":["Lecture Notes in Computer Science","Algorithms and Models for the Web-Graph"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-18009-5_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,6]],"date-time":"2019-06-06T15:07:27Z","timestamp":1559833647000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-18009-5_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"ISBN":["9783642180088","9783642180095"],"references-count":15,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-18009-5_8","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2010]]}}}