Spectrum of walk matrix for Koch network and its application
Journal of Chemical Physics, ISSN: 0021-9606, Vol: 142, Issue: 22, Page: 224106
2015
- 18Citations
- 8Captures
Metric Options: Counts1 Year3 YearSelecting the 1-year or 3-year option will change the metrics count to percentiles, illustrating how an article or review compares to other articles or reviews within the selected time period in the same journal. Selecting the 1-year option compares the metrics against other articles/reviews that were also published in the same calendar year. Selecting the 3-year option compares the metrics against other articles/reviews that were also published in the same calendar year plus the two years prior.
Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Example: if you select the 1-year option for an article published in 2019 and a metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019. If you select the 3-year option for the same article published in 2019 and the metric category shows 90%, that means that the article or review is performing better than 90% of the other articles/reviews published in that journal in 2019, 2018 and 2017.
Citation Benchmarking is provided by Scopus and SciVal and is different from the metrics context provided by PlumX Metrics.
Metrics Details
- Citations18
- Citation Indexes18
- 18
- CrossRef16
- Captures8
- Readers8
Article Description
Various structural and dynamical properties of a network are encoded in the eigenvalues of walk matrix describing random walks on the network. In this paper, we study the spectra of walk matrix of the Koch network, which displays the prominent scale-free and small-world features. Utilizing the particular architecture of the network, we obtain all the eigenvalues and their corresponding multiplicities. Based on the link between the eigenvalues of walk matrix and random target access time defined as the expected time for a walker going from an arbitrary node to another one selected randomly according to the steady-state distribution, we then derive an explicit solution to the random target access time for random walks on the Koch network. Finally, we corroborate our computation for the eigenvalues by enumerating spanning trees in the Koch network, using the connection governing eigenvalues and spanning trees, where a spanning tree of a network is a subgraph of the network, that is, a tree containing all the nodes.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84934986691&origin=inward; http://dx.doi.org/10.1063/1.4922265; http://www.ncbi.nlm.nih.gov/pubmed/26071700; https://pubs.aip.org/jcp/article/142/22/224106/564486/Spectrum-of-walk-matrix-for-Koch-network-and-its; http://scitation.aip.org/content/aip/journal/jcp/142/22/10.1063/1.4922265; http://scitation.aip.org/limit_exceeded.html
AIP Publishing
Provide Feedback
Have ideas for a new metric? Would you like to see something else here?Let us know