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ITHEA Classification Structure > E. Data  > E.1 DATA STRUCTURES 
ITHEA Classification Structure > G. Mathematics of Computing  > G.2 DISCRETE MATHEMATICS  > G.2.1 Combinatorics 
ITHEA Classification Structure > G. Mathematics of Computing  > G.2 DISCRETE MATHEMATICS  > G.2.2 Graph Theory 
LOGARITHMIC DISTANCES IN GRAPHS
By: Pavel Chebotarev (3041 reads)
Rating: (1.00/10)

Abstract: The walk distances in graphs are defined as the result of appropriate transformations of the P1 k=0(tA)k proximity measures, where A is the weighted adjacency matrix of a graph and t is a sufficiently small positive parameter. The walk distances are graph-geodetic; moreover, they converge to the shortest path distance and to the so-called long walk distance as the parameter t approaches its limiting values. Furthermore, the logarithmic forest distances which are known to generalize the resistance distance and the shortest path distance are a specific subclass of walk distances. On the other hand, the long walk distance is equal to the resistance distance in a transformed graph.

Keywords: graph distances, walk distances, logarithmic forest distances, transitional measure, Laplacian matrix, resistance distance, network

ACM Classification Keywords: G.2.2 Graph Theory – Network problems; E.1 Data Structures – Graphs and networks; C.2.1 Network Architecture and Design – Network topology

Link:

LOGARITHMIC DISTANCES IN GRAPHS

Pavel Chebotarev

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p03.pdf

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E.1 DATA STRUCTURES
article: MAIN DIFFERENCES BETWEEN MAP/REDUCE AND COLLECT/REPORT PARADIGMS · ЦЕЛОСТНОСТЬ ОБРАЗОВ: О МОДЕЛИРОВАНИИ СМЫСЛА И ПОНИМАНИЯ · LARGE VLSI ARRAYS – POWER AND ARCHITECTURAL PERSPECTIVES · CONSTRUCTION OF MORPHOSYNTACTIC DISTANCE ON SEMANTIC STRUCTURES · MEMBRANE STRUCTURE SIMPLIFICATION · SEMANTIC CONSTRUCTION OF UNIVOCAL LANGUAGE · КОГНИТИВНАЯ СЕМИОТИКА В ПРОЦЕССАХ ... · LOGARITHMIC DISTANCES IN GRAPHS · REPRESENTING TREE STRUCTURES BY NATURAL NUMBERS · BUILDING DATA WAREHOUSES USING NUMBERED INFORMATION SPACES ·
G.2.1 Combinatorics
article: RANDOMIZED SET SYSTEMS CONSTRAINED BY THE DISCRETE TOMOGRAPHY · A NEW ALGORITM FOR THE LONGEST COMMON SUBSEQUENCE PROBLEM · ON THE STRUCTURE OF MAXIMUM INDEPENDENT SETS IN BIPARTITE GRAPHS · SOME PROPERTIES IN MULTIDIMENSIONAL MULTIVALUED DISCRETE TORUS · ON PROBLEM OF ADEQUACY OF MULTISET MATHEMATICAL MODELS · SPREADING THE MOORE - PENROSE PSEUDO INVERSE ON MATRICES EUCLIDEAN SPACES: ... · VECTORS AND MATRIXES IN GROUPING INFORMATION PROBLEM · CHOICE OF DIAGNOSTIC DECISION MAKING IN MEDICINE AND INTERVENTION MISTAKE ... · RECURRENT PROCEDURE IN SOLVING THE GROUPING INFORMATION PROBLEM IN APPLIED... · ‘FEATURE VECTORS’ IN GROUPING INFORMATION PROBLEM IN APPLIED MATHEMATICS: .. · DECOMPOSITION METHODS FOR LARGE-SCALE TSP · ON THE DISCRETIZATION OF DISTANCE GEOMETRY PROBLEMS · REGULAR INVERSIVE POLYTOPES · LOGARITHMIC DISTANCES IN GRAPHS · FUZZY SETS AS A MEAN FOR UNCERTAINTY HANDLING: MATH, APPLIED MATH, HEURISTICS · FUZZY SETS: MATH, APPLIED MATH, HEURISTICS? PROBLEMS AND INTERPRETATIONS · CROSS INTERSECTION SEQUEL OF DISCRETE ISOPERIMETRY1 · GENERATING MORE BOUNDARY ELEMENTS OF SUBSET PROJECTIONS · MULTICRITERION PROBLEMS ON THE COMBINATORIAL SET OF POLYARRANGEMENTS · CHAIN SPLIT OF PARTIALLY ORDERED SET OF K-SUBSETS · SOLVING LARGE SYSTEMS OF BOOLEAN EQUATIONS · LAGRANGEAN APPROXIMATION FOR COMBINATORIAL INVERSE PROBLEMS · MULTICRITERION PROBLEMS ON THE COMBINATORIAL SET OF POLYARRANGEMENTS · DESCRIPTION REDUCTION FOR RESTRICTED SETS OF (0,1) MATRICES 1 · DECOMPOSITION OF BOOLEAN FUNCTIONS – RECOGNIZING A GOOD SOLUTION BY TRACES · THE BOUNDARY DESCRIPTORS OF THE n-DIMENSIONAL UNIT CUBE SUBSET PARTITIONING1 · RANDOMIZED PARALLELIZATION – A NEW METHOD FOR SOLVING ... · OPTIMIZATION OF ATM TELECOMMUNICATION NETWORKS · VECTOR COMBINATORIAL PROBLEMS IN A SPACE OF COMBINATIONS ... ·
G.2.2 Graph Theory
article: INFORMATION FLOWS ENHANCEMENT FOR AIS TOURISM AUTOMATED INFORMATION SYSTEM · CONVEXITY RELATED ISSUES FOR THE SET OF HYPERGRAPHIC SEQUENCES · ONTOLOGY OF EDUCATIONAL STANDARDS · THE IMPROVEMENT OF THE PROCESS OF PROVIDING GOVERMENT SERVICES IN MULTIFUNCTIONA · INTERFERENCE MINIMIZATION IN PHYSICAL MODEL OF WIRELESS NETWORKS · Criteria investigations in ant colony optimization algorithm for travelling ... · CRITERIA INVESTIGATIONS IN ANT COLONY OPTIMIZATION ALGORITHM FOR TRAVELLING SALE · CHOICE OF DIAGNOSTIC DECISION MAKING IN MEDICINE AND INTERVENTION MISTAKE ... · LOGARITHMIC DISTANCES IN GRAPHS · MODIFIED BRANCH AND BOUND ALGORITHM FOR SOLVING THE HAMILTONIAN RURAL ... ·
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