Resistance‐distance matrix: A computational algorithm and its application

Babić, Darko; Klein, Douglas J.; Lukovits, István; Nikolić, Sonja; Trinajstić, Nenad

doi:10.1002/qua.10057

Cited by 117 publications

(60 citation statements)

References 43 publications

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“…Because v can be obtained using matrix techniques that do not require inverting the reduced conductance matrix, very large networks can be solved using this method. Other algorithms (e.g., Babic et al 2002;Vast et al 2005) allow computation of all resistance distances with a single matrix inversion and may be more efficient for moderate-sized networks with large numbers of pairwise resistances to calculate.…”

Section: Calculating the Resistance Distancementioning

confidence: 99%

Isolation by Resistance

McRae¹

2006

Evolution

955

944

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Abstract. Despite growing interest in the effects of landscape heterogeneity on genetic structuring, few tools are available to incorporate data on landscape composition into population genetic studies. Analyses of isolation by distance have typically either assumed spatial homogeneity for convenience or applied theoretically unjustified distance metrics to compensate for heterogeneity. Here I propose the isolation-by-resistance (IBR) model as an alternative for predicting equilibrium genetic structuring in complex landscapes. The model predicts a positive relationship between genetic differentiation and the resistance distance, a distance metric that exploits precise relationships between random walk times and effective resistances in electronic networks. As a predictor of genetic differentiation, the resistance distance is both more theoretically justified and more robust to spatial heterogeneity than Euclidean or least cost path-based distance measures. Moreover, the metric can be applied with a wide range of data inputs, including coarse-scale range maps, simple maps of habitat and nonhabitat within a species' range, or complex spatial datasets with habitats and barriers of differing qualities. The IBR model thus provides a flexible and efficient tool to account for habitat heterogeneity in studies of isolation by distance, improve understanding of how landscape characteristics affect genetic structuring, and predict genetic and evolutionary consequences of landscape change.Key words. Gene flow, graph theory, isolation by distance, isolation by resistance, landscape connectivity, landscape genetics, resistance distance. The emerging study of how landscape features affect microevolutionary processes (landscape genetics; Manel et al. 2003) will require tools that explicitly incorporate landscape heterogeneity into analyses of gene flow and genetic differentiation. Landscape characteristics may modify gene flow between pairs of subpopulations directly by affecting dispersal rates among them or indirectly by affecting the spatial arrangement of and dispersal rates among intervening subpopulations. Yet, few models are capable of integrating landscape data into predictions of population structure.For example, models of isolation by distance (Wright 1943) are among the most widely applied tools in studies of genetic differentiation in natural populations. These models have provided powerful means to explain population structure (e.g., Rousset 1997Rousset , 2000Sumner et al. 2001;Rueness et al. 2003), investigate departures from migration-drift equilibrium (Slatkin 1993;Hutchison and Templeton 1999), and address ecological questions such as whether dispersal synchronizes the dynamics of populations separated by long distances (Schwartz et al. 2002). Yet, such analyses assume homogeneous, unbounded populations, ignoring effects of range boundaries and of variation in demographic parameters within species' ranges (Maruyama 1970;Slatkin and Maruyama 1975). As Slatkin (1985) noted, most real populations are neither hom...

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Section: Calculating the Resistance Distancementioning

confidence: 99%

Isolation by Resistance

McRae¹

2006

Evolution

955

944

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“…[8] The resistance distances attracted extensive attention of numerous mathematicians, due to its wide applications. [9][10][11][12][13][14] For more information on resistance distances of graphs, the readers are referred to the most recent papers. [15][16][17][18][19][20][21][22][23][24][25][26][27][28] It is of interest to study some graph operations, such as the Cartesian product, the Kronecker product, the corona, the edge corona, etc.…”

Section: B(g) T B(g) = 2i M + A(l(g))mentioning

confidence: 99%

The {1}-inverse of the Laplacian of subdivision-vertex and subdivision-edge coronae with applications

Liu

Pan

2016

Linear and Multilinear Algebra

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“…The resistance distance between two vertices u and v of graph G, denoted by R G (u, v), is originally defined to be the effective resistance between the corresponding two nodes u and v in the electrical network. More results and devolvement can be found in [1][2][3]25,36,42].…”

Section: Tablementioning

confidence: 87%

“…In this paper, we proved the following: Theorem 1.1. Let G be a unicyclic graph of order n. Then D R (G) 1 3 (2n 3 − 28n + 54). The equality holds if and only if G ∼ = F n , where F n is the funnel obtained from K 3 and the path P n−2 by identifying a vertex of K 3 with one pendent vertex of P n−2 , depicted in Fig.…”

Section: Tablementioning

confidence: 99%

The unicyclic graphs with maximum degree resistance distance

2015

Applied Mathematics and Computation

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Resistance‐distance matrix: A computational algorithm and its application

Cited by 117 publications

References 43 publications

Isolation by Resistance

Isolation by Resistance

The {1}-inverse of the Laplacian of subdivision-vertex and subdivision-edge coronae with applications

The unicyclic graphs with maximum degree resistance distance

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