Markov fundamental tensor and its applications to network analysis

Golnari, Golshan; Boley, Daniel

doi:10.1016/j.laa.2018.11.024

Cited by 6 publications

(7 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Golnari et al [115] use the random walk matrix R(A) for simple and directed connected graphs; in the latter case, A is not symmetric and D is the diagonal matrix of out-degrees. The expected number of visits at a transit node m of a random walk with source node s and a target node t is counted by the fundamental t-matrix F t = [F t sm ] = (I − R(A \tt )) −1 .…”

Section: Spectral Methodsmentioning

confidence: 99%

“…The random walk (rw) equivalents for the distance d (s,t) between a source s and target node t and the local Random Walk ASPL d rw t are provided in [115] as follows:…”

Section: Trmentioning

confidence: 99%

“…The Random Walk Betweenness B rw i counts the times a flow passes through a node on any random walk in a connected network [115,130], where at each time step the transition probability through the outgoing links is proportional to their weights. It is proportional to the Network Criticality τ (Section 8.12), and, in undirected networks with a stationary probability π i = s i 2e , to Strength s i (Section 3.2).…”

Section: Trmentioning

confidence: 99%

“…L + is the Moore-Penrose inverse of the Laplacian L of a connected networks, and u st = [0...1... − 1...0], with 1 and −1 in the s th and t th position, and K(G) the Kirchhoff Index [115]. The random walk begins at source node s and ends at destination node t. At each step, at node i it chooses to travel to the adjacent node j with probability p = w ij s i .…”

Section: Network Criticality (Effective Resistance)mentioning

confidence: 99%

See 3 more Smart Citations

Graph Metrics for Network Robustness—A Survey

Oehlers

Fabian

2021

Mathematics

View full text Add to dashboard Cite

Research on the robustness of networks, and in particular the Internet, has gained critical importance in recent decades because more and more individuals, societies and firms rely on this global network infrastructure for communication, knowledge transfer, business processes and e-commerce. In particular, modeling the structure of the Internet has inspired several novel graph metrics for assessing important topological robustness features of large complex networks. This survey provides a comparative overview of these metrics, presents their strengths and limitations for analyzing the robustness of the Internet topology, and outlines a conceptual tool set in order to facilitate their future adoption by Internet research and practice but also other areas of network science.

show abstract

Section: Spectral Methodsmentioning

confidence: 99%

“…The random walk (rw) equivalents for the distance d (s,t) between a source s and target node t and the local Random Walk ASPL d rw t are provided in [115] as follows:…”

Section: Trmentioning

confidence: 99%

Section: Trmentioning

confidence: 99%

Section: Network Criticality (Effective Resistance)mentioning

confidence: 99%

See 2 more Smart Citations

Graph Metrics for Network Robustness—A Survey

Oehlers

Fabian

2021

Mathematics

View full text Add to dashboard Cite

show abstract

“…It is well known that on an undirected graph (i.e., a graph for which a i j = a ji and c i j = c ji for all (i, j) ∈ E) where edge costs correspond to edge resistances (i.e., c i j = r i j = 1/a i j ; in which case affinities correspond to conductances), both the commute time and commute cost distances are proportional to the resistance distances between corresponding nodes. More exactly, if we denote, for any s-t-pair on an undirected graph, by ∆ res st , ∆ CT st and ∆ CC st , respectively, the resistance, commute time and commute cost distances between s and t, then the following holds [9,20,27]:…”

Section: Definitions and Notationmentioning

confidence: 99%

Maximum likelihood estimation for randomized shortest paths with trajectory data

Kivimäki

Moorter

Panzacchi

et al. 2020

Journal of Complex Networks

View full text Add to dashboard Cite

Randomized shortest paths (RSPs) are tool developed in recent years for different graph and network analysis applications, such as modelling movement or flow in networks. In essence, the RSP framework considers the temperature-dependent Gibbs–Boltzmann distribution over paths in the network. At low temperatures, the distribution focuses solely on the shortest or least-cost paths, while with increasing temperature, the distribution spreads over random walks on the network. Many relevant quantities can be computed conveniently from this distribution, and these often generalize traditional network measures in a sensible way. However, when modelling real phenomena with RSPs, one needs a principled way of estimating the parameters from data. In this work, we develop methods for computing the maximum likelihood estimate of the model parameters, with focus on the temperature parameter, when modelling phenomena based on movement, flow or spreading processes. We test the validity of the derived methods with trajectories generated on artificial networks as well as with real data on the movement of wild reindeer in a geographic landscape, used for estimating the degree of randomness in the movement of the animals. These examples demonstrate the attractiveness of the RSP framework as a generic model to be used in diverse applications.

show abstract

Two-point resistances of symmetric polyhedral networks

Stern

Aravind

2023

Journal of Computational Science

View full text Add to dashboard Cite

Markov fundamental tensor and its applications to network analysis

Cited by 6 publications

References 51 publications

Graph Metrics for Network Robustness—A Survey

Graph Metrics for Network Robustness—A Survey

Maximum likelihood estimation for randomized shortest paths with trajectory data

Two-point resistances of symmetric polyhedral networks

Contact Info

Product

Resources

About