147:
22:
1312:
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1369:
806:. The concept of biased random walks on a graph has attracted the attention of many researchers and data companies over the past decade especially in the transportation and
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There are a variety of applications using biased random walks on graphs. Such applications include control of diffusion, advertisement of products on
1750:
1383:, explaining dispersal and population redistribution of animals and micro-organisms, community detections, wireless networks, and search engines.
1576:
R. Lambiotte; R. Sinatra; J.-C. Delvenne; T.S. Evans; M. Barahona; V. Latora (Dec 2010). "Flow graphs: interweaving dynamics and structure".
1454:; Renaud Lambiotte; Vincenzo Nicosia; Vito Latora (March 2011). "Maximal-entropy random walks in complex networks with limited information".
86:
791:
is a time path process in which an evolving variable jumps from its current state to one of various potential new states; unlike in a pure
58:
770:
65:
2052:
72:
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830:
823:
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54:
1307:{\displaystyle C(i)={\tfrac {{\text{Total number of shortest paths through }}i}{\text{Total number of shortest paths}}}}
653:
382:
802:
in order to extract their symmetries when the network is too complex or when it is not large enough to be analyzed by
105:
1417:
727:
310:
1402:
623:
1186:
or even it might be explained as an intrinsic characteristic of a node. In case of a fair random walk on graph
613:
608:
1323:
763:
722:
239:
1807:"Use of Data-Biased Random Walks on Graphs for the Retrieval of Context-Specific Networks from Genomic Data"
819:
568:
412:
359:
174:
79:
1451:
603:
1427:
1412:
732:
638:
633:
598:
397:
295:
234:
320:
1709:
1515:
J. Gómez-Gardeñes; V. Latora (Dec 2008). "Entropy rate of diffusion processes on complex networks".
2042:
2018:
2014:(ed. W. Cook, L. Lovász, and P. Seymour). Providence, RI: Amer. Math. Soc., pp. 399–441, 1995.
1446:
756:
658:
618:
125:
882:
516:
2047:
2037:
1422:
1212:
739:
558:
325:
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is the total number of the shortest paths between all pairs of nodes that pass through the node
1704:
1392:
1257:
1183:
643:
628:
543:
822:
based on the particular purpose of the analysis. A common representation of the mechanism for
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1161:
1138:
744:
563:
533:
422:
377:
1063:
1883:
1818:
1595:
1534:
1473:
1317:
Based on the above equation, the recurrence time to a node in the biased walk is given by:
511:
392:
8:
1397:
1050:{\displaystyle T_{ij}^{\alpha }={\frac {\alpha _{i}A_{ij}}{\sum _{k}\alpha _{k}A_{kj}}},}
548:
417:
407:
402:
254:
199:
189:
1887:
1822:
1599:
1538:
1477:
1113:
859:
836:
1980:
1953:
1934:
1899:
1873:
1864:
J.K. Ochab; Z. Burda (Jan 2013). "Maximal entropy random walk in community detection".
1841:
1806:
1787:
1764:
Adal, K.M. (June 2010). "Biased random walk based routing for mobile ad hoc networks".
1744:
1732:
1619:
1585:
1558:
1524:
1497:
1463:
1239:
1178:
can be interpreted differently. It might be implied as the attraction of a person in a
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1846:
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There have been written many different representations of the biased random walks on
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Biased random walks on a graph provide an approach for the structural analysis of
1917:
Beraldi, Roberto (Apr 2009). "Biased Random Walks in
Uniform Wireless Networks".
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1970:
1952:
Da-Cheng Nie; Zi-Ke Zhang; Qiang Dong; Chongjing Sun; Yan Fu (July 2014).
2007:
1930:
792:
1954:"Information Filtering via Biased Random Walk on Coupled Social Network"
1699:
Chung, Zhao, Fan, Wenbo (2010). "PageRank and Random Walks on Graphs".
1675:
Fair and biased random walks on undirected graphs and related entropies
803:
528:
485:
475:
2017:
Anne-Marie
Kermarrec, Erwan Le Merrer, Bruno Sericola, Gilles Trédan,
1703:. Bolyai Society Mathematical Studies. Vol. 20. pp. 43–62.
693:
249:
146:
21:
2019:"Evaluating the Quality of a Network Topology through Random Walks"
1878:
1590:
1529:
1468:
1766:
2010 International
Conference on Intelligent and Advanced Systems
1805:
Kakajan
Komurov; Michael A. White; Prahlad T. Ram (Aug 2010).
1135:
In fact, the steps of the walker are biased by the factor of
795:, the probabilities of the potential new states are unequal.
1514:
1636:
1090:
represents the topological weight of the edge going from
1671:
1286:
1326:
1269:
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1215:
1192:
1164:
1141:
1116:
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958:
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915:
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839:
1256:. In fact the walker prefers the nodes with higher
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1306:
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1198:
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1049:
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2029:
1640:Mathematical Analysis of Urban Spatial Networks
833:, a walker takes a step from the current node,
764:
1866:The European Physical Journal Special Topics
1749:: CS1 maint: multiple names: authors list (
1291:Total number of shortest paths through
1698:
1155:which may differ from one node to another.
1763:
1701:Fete of Combinatorics and Computer Science
771:
757:
1979:
1969:
1877:
1840:
1830:
1708:
1589:
1528:
1467:
879:Assuming that each node has an attribute
106:Learn how and when to remove this message
1158:Depending on the network, the attribute
1916:
1364:{\displaystyle r_{i}={\frac {1}{C(i)}}}
1209:In case of shortest paths random walks
2030:
42:Please improve this article by adding
1919:IEEE Transactions on Mobile Computing
909:the probability of jumping from node
1637:Blanchard, P; Volchenkov, D (2008).
15:
13:
1672:Volchenkov D; Blanchard P (2011).
14:
2064:
2000:
1418:Random walk closeness centrality
145:
118:Structural analysis of a network
20:
1945:
1910:
1374:
55:"Biased random walk on a graph"
1857:
1798:
1757:
1692:
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1630:
1569:
1508:
1440:
1355:
1349:
1299:Total number of shortest paths
1279:
1273:
1:
2053:Social information processing
1433:
789:biased random walk on a graph
44:secondary or tertiary sources
1958:The Scientific World Journal
1832:10.1371/journal.pcbi.1000889
902:{\displaystyle \alpha _{i},}
7:
1896:10.1140/epjst/e2013-01730-6
1719:10.1007/978-3-642-13580-4_3
1678:. Birkhäuser. p. 380.
1428:Travelling salesman problem
1413:Maximal entropy random walk
1403:Kullback–Leibler divergence
1386:
1260:which is defined as below:
1229:{\displaystyle \alpha _{i}}
10:
2069:
2012:Combinatorial Optimization
1774:10.1109/ICIAS.2010.5716181
1608:10.1103/PhysRevE.84.017102
1547:10.1103/PhysRevE.78.065102
1486:10.1103/PhysRevE.83.030103
1206:is one for all the nodes.
2021:in Gadi Taubenfeld (ed.)
2008:"Graph Entropy: A Survey"
1661:– via ResearchGate.
1649:10.1007/978-3-540-87829-2
624:Exponential random (ERGM)
291:Informational (computing)
813:
311:Scientific collaboration
1423:Social network analysis
1199:{\displaystyle \alpha }
1171:{\displaystyle \alpha }
1148:{\displaystyle \alpha }
740:Category:Network theory
260:Preferential attachment
1393:Betweenness centrality
1365:
1308:
1258:betweenness centrality
1250:
1230:
1200:
1184:betweenness centrality
1172:
1149:
1127:
1104:
1084:
1083:{\displaystyle A_{ij}}
1051:
943:
923:
903:
873:
850:
629:Random geometric (RGG)
31:relies excessively on
2023:Distributed Computing
1366:
1309:
1251:
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1201:
1173:
1150:
1128:
1105:
1085:
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944:
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745:Category:Graph theory
1931:10.1109/TMC.2008.151
1452:Jesús Gómez-Gardeñes
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1139:
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956:
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837:
1971:10.1155/2014/829137
1888:2013EPJST.216...73O
1823:2010PLSCB...6E0889K
1600:2011PhRvE..84a7102L
1539:2008PhRvE..78f5102G
1478:2011PhRvE..83c0103S
1398:Community structure
976:
804:statistical methods
549:Degree distribution
200:Community structure
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1304:
1302:
1246:
1226:
1196:
1168:
1145:
1126:{\displaystyle i.}
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1017:
959:
939:
919:
899:
872:{\displaystyle i.}
869:
849:{\displaystyle j,}
846:
733:Network scientists
659:Soft configuration
1783:978-1-4244-6623-8
1728:978-3-642-13579-8
1685:978-0-8176-4903-6
1658:978-3-540-87828-5
1578:Physical Review E
1517:Physical Review E
1456:Physical Review E
1359:
1301:
1300:
1292:
1249:{\displaystyle i}
1103:{\displaystyle j}
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1008:
942:{\displaystyle i}
922:{\displaystyle j}
824:undirected graphs
800:undirected graphs
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609:Bianconi–Barabási
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321:Artificial neural
296:Telecommunication
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1811:PLOS Comput Biol
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1768:. pp. 1–6.
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831:undirected graph
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644:Stochastic block
634:Hyperbolic (HGN)
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275:Social influence
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2043:Social networks
2028:
2027:
2006:Gábor Simonyi,
2003:
1998:
1997:
1950:
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1911:
1862:
1858:
1817:(8): e1000889.
1803:
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1784:
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1742:
1741:
1729:
1710:10.1.1.157.7116
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1513:
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1448:Roberta Sinatra
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838:
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834:
826:is as follows:
816:
808:social networks
785:network science
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680:Boolean network
654:Maximum entropy
604:Barabási–Albert
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438:
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215:Controllability
180:Complex network
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639:Hierarchical
594:Random graph
442: /
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413:Neighborhood
255:Transitivity
235:Optimization
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793:random walk
685:agent based
599:Erdős–Rényi
240:Reciprocity
205:Percolation
190:Small-world
2032:Categories
1964:: 829137.
1434:References
712:Categories
569:Efficiency
564:Modularity
544:Clustering
529:Centrality
517:Algorithms
341:Dependency
316:Biological
195:Scale-free
66:newspapers
33:references
1879:1208.3688
1872:: 73–81.
1745:cite book
1705:CiteSeerX
1591:1012.1211
1530:0712.0278
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1218:α
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383:Component
301:Transport
250:Homophily
210:Evolution
185:Contagion
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1387:See also
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672:Dynamics
586:Topology
559:Distance
496:Weighted
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466:Complete
370:Features
331:Semantic
126:a series
124:Part of
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360:Graphs
306:Social
163:Theory
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2010:. In
1935:S2CID
1900:S2CID
1874:arXiv
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1525:arXiv
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814:Model
709:Lists
539:Motif
486:Multi
476:Hyper
453:Types
393:Cycle
175:Graph
87:JSTOR
73:books
1986:PMID
1962:2014
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1778:ISBN
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