The Subnetwork Investigation of Scale-Free Networks Based on the Self-Similarity

2021 ◽  
Author(s):  
Wenting Wang ◽  
Shijie Shi ◽  
Xianghua Fu
Keyword(s):  
The Self ◽  
Self Similarity ◽  
Scale Free ◽  
Scale Free Networks

scholarly journals Antigen receptor repertoires of one of the smallest known vertebrates

2021 ◽  
Vol 7 (1) ◽  
pp. eabd8180
Author(s):  
Orlando B. Giorgetti ◽  
Prashant Shingate ◽  
Connor P. O’Meara ◽  
Vydianathan Ravi ◽  
Nisha E. Pillai ◽  
...  
Keyword(s):  
Immune Responses ◽  
Antigen Receptor ◽  
Fundamental Property ◽  
Cell Receptor ◽  
Immune Reactivity ◽  
Self Similarity ◽  
Frequency Distributions ◽  
Scale Free ◽  
Scale Free Networks ◽  
Incomplete Sampling

The rules underlying the structure of antigen receptor repertoires are not yet fully defined, despite their enormous importance for the understanding of adaptive immunity. With current technology, the large antigen receptor repertoires of mice and humans cannot be comprehensively studied. To circumvent the problems associated with incomplete sampling, we have studied the immunogenetic features of one of the smallest known vertebrates, the cyprinid fish Paedocypris sp. “Singkep” (“minifish”). Despite its small size, minifish has the key genetic facilities characterizing the principal vertebrate lymphocyte lineages. As described for mammals, the frequency distributions of immunoglobulin and T cell receptor clonotypes exhibit the features of fractal systems, demonstrating that self-similarity is a fundamental property of antigen receptor repertoires of vertebrates, irrespective of body size. Hence, minifish achieve immunocompetence via a few thousand lymphocytes organized in robust scale-free networks, thereby ensuring immune reactivity even when cells are lost or clone sizes fluctuate during immune responses.

Evaluation of invulnerability of scale-free networks using total information of local sub-graph

2018 ◽  
Vol 29 (08) ◽  
pp. 1850075
Author(s):  
Tingyuan Nie ◽  
Xinling Guo ◽  
Mengda Lin ◽  
Kun Zhao
Keyword(s):  
Mutual Information ◽  
Complex Network ◽  
Fundamental Problem ◽  
The Self ◽  
Practical Significance ◽  
Scale Free ◽  
Total Information ◽  
Scale Free Networks ◽  
Influential Nodes ◽  
Definition Of

The quantification for the invulnerability of complex network is a fundamental problem in which identifying influential nodes is of theoretical and practical significance. In this paper, we propose a novel definition of centrality named total information (TC) which derives from a local sub-graph being constructed by a node and its neighbors. The centrality is then defined as the sum of the self-information of the node and the mutual information of its neighbor nodes. We use the proposed centrality to identify the importance of nodes through the evaluation of the invulnerability of scale-free networks. It shows both the efficiency and the effectiveness of the proposed centrality are improved, compared with traditional centralities.

SMALL-WORLD AND SCALE-FREE PROPERTIES OF THE n-DIMENSIONAL SIERPINSKI CUBE NETWORKS

Fractals ◽  
2020 ◽  
Vol 28 (01) ◽  
pp. 2050001
Author(s):  
CHENG ZENG ◽  
MENG ZHOU ◽  
YUMEI XUE
Keyword(s):  
Small World ◽  
The Self ◽  
Self Similarity ◽  
Scale Free ◽  
Evolving Networks

In this paper, we construct evolving networks from [Formula: see text]-dimensional Sierpinski cube. Using the self-similarity of Sierpinski cube, we show the evolving networks have scale-free and small-world properties.

THE SCALE-FREE AND SMALL-WORLD PROPERTIES OF COMPLEX NETWORKS ON SIERPINSKI-TYPE HEXAGON

Fractals ◽  
2020 ◽  
Vol 28 (03) ◽  
pp. 2050054
Author(s):  
KUN CHENG ◽  
DIRONG CHEN ◽  
YUMEI XUE ◽  
QIAN ZHANG
Keyword(s):  
Power Law ◽  
Path Length ◽  
Small World ◽  
The Self ◽  
Renewal Theorem ◽  
Self Similarity ◽  
Scale Free ◽  
Power Law Exponent ◽  
Self Similar ◽  
Encoding Method

In this paper, a network is generated from a Sierpinski-type hexagon by applying the encoding method in fractal. The criterion of neighbor is established to quantify the relationships among the nodes in the network. Based on the self-similar structures, we verify the scale-free and small-world effects. The power-law exponent on degree distribution is derived to be [Formula: see text] and the average clustering coefficients are shown to be larger than [Formula: see text]. Moreover, we give the bounds of the average path length of our proposed network from the renewal theorem and self-similarity.

scholarly journals Detecting different topologies immanent in scale-free networks with the same degree distribution

2019 ◽  
Vol 116 (14) ◽  
pp. 6701-6706 ◽  
Author(s):  
Dimitrios Tsiotas
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Network Topology ◽  
Degree Distribution ◽  
Growth Process ◽  
Preferential Attachment ◽  
Self Similarity ◽  
Scale Free ◽  
Scale Free Networks ◽  
Definition Of

The scale-free (SF) property is a major concept in complex networks, and it is based on the definition that an SF network has a degree distribution that follows a power-law (PL) pattern. This paper highlights that not all networks with a PL degree distribution arise through a Barabási−Albert (BA) preferential attachment growth process, a fact that, although evident from the literature, is often overlooked by many researchers. For this purpose, it is demonstrated, with simulations, that established measures of network topology do not suffice to distinguish between BA networks and other (random-like and lattice-like) SF networks with the same degree distribution. Additionally, it is examined whether an existing self-similarity metric proposed for the definition of the SF property is also capable of distinguishing different SF topologies with the same degree distribution. To contribute to this discrimination, this paper introduces a spectral metric, which is shown to be more capable of distinguishing between different SF topologies with the same degree distribution, in comparison with the existing metrics.

scholarly journals Fractality and self-similarity in scale-free networks

2007 ◽  
Vol 9 (6) ◽  
pp. 177-177 ◽  
Author(s):  
J S Kim ◽  
K-I Goh ◽  
B Kahng ◽  
D Kim
Keyword(s):  
Self Similarity ◽  
Scale Free ◽  
Scale Free Networks
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