An Extended Correlation Dimension of Complex Networks.

Sheng Zhang, Wenxiang Lan, Weikai Dai, Feng Wu, Caisen Chen

Abstract read

In one paragraph

Article in Entropy (Basel, Switzerland), 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

0numbers the graph read from it

0cells of the map it votes in

0citing papers in PubMed

–field-weighted citation impact

1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

The trial behind it

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Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.

3 · Its place in the literature

Who cites it

0 citing papers in PubMed.

No citing paper in PubMed yet.

4 · The record

Corrections and comments

PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

5 authors.

Sheng ZhangSchool of Information Engineering, Nanchang Hangkong University, 696 Fenghe South Avenue, Nanchang 330063, China.

Wenxiang LanSchool of Information Engineering, Nanchang Hangkong University, 696 Fenghe South Avenue, Nanchang 330063, China.

Weikai DaiSchool of Information Engineering, Nanchang Hangkong University, 696 Fenghe South Avenue, Nanchang 330063, China.

Feng WuSchool of Information Engineering, Nanchang Hangkong University, 696 Fenghe South Avenue, Nanchang 330063, China.

Caisen ChenMilitary Exercise and Training Center, Academy of Army Armored Force, Beijing 100072, China.

Funding

Nanchang Hangkong University graduate innovation special foundation YC2020035National Natural Science Foundation of China 61661037National Natural Science Foundation of China U1836101Science and Technology Project of Jiangxi Province Education Department GJJ170575

6 · The paper itself

Abstract

Fractal and self-similarity are important characteristics of complex networks. The correlation dimension is one of the measures implemented to characterize the fractal nature of unweighted structures, but it has not been extended to weighted networks. In this paper, the correlation dimension is extended to the weighted networks. The proposed method uses edge-weights accumulation to obtain scale distances. It can be used not only for weighted networks but also for unweighted networks. We selected six weighted networks, including two synthetic fractal networks and four real-world networks, to validate it. The results show that the proposed method was effective for the fractal scaling analysis of weighted complex networks. Meanwhile, this method was used to analyze the fractal properties of the Newman-Watts (NW) unweighted small-world networks. Compared with other fractal dimensions, the correlation dimension is more suitable for the quantitative analysis of small-world effects.

Indexed as

correlation dimensionfractal propertysmall-world networkweighted networks

Identifiers

PMID34205073

DOI10.3390/e23060710

PMCPMC8229313

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.