Scale-free percolation in continuous space: quenched degree and clustering coefficient

AbstractSpatial random graphs capture several important properties of real-world networks. We prove quenched results for the continuous-space version of scale-free percolation introduced in [14]. This is an undirected inhomogeneous random graph whose vertices are given by a Poisson point process in $\mathbb{R}^d$. Each vertex is equipped with a random weight, and the probability that two vertices are connected by an edge depends on their weights and on their distance. Under suitable conditions on the parameters of the model, we show that, for almost all realizations of the point process, the degree distributions of all the nodes of the graph follow a power law with the same tail at infinity. We also show that the averaged clustering coefficient of the graph is self-averaging. In particular, it is almost surely equal to the annealed clustering coefficient of one point, which is a strictly positive quantity.

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Directed random geometric graphs

Journal of Complex Networks ◽

10.1093/comnet/cnz006 ◽

2019 ◽

Vol 7 (5) ◽

pp. 792-816

Author(s):

Jesse Michel ◽

Sushruth Reddy ◽

Rikhav Shah ◽

Sandeep Silwal ◽

Ramis Movassagh

Keyword(s):

Real World ◽

Word Association ◽

Graph Model ◽

Small World ◽

Geometric Graph ◽

Clustering Coefficient ◽

Random Geometric Graph ◽

Random Geometric Graphs ◽

Scale Free ◽

Small World Property

Abstract Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet and the network of followers on Twitter among many others. The challenge, however, is to create a network model that has many of the properties of real-world networks such as power-law degree distributions and the small-world property. To meet these challenges, we introduce the Directed Random Geometric Graph (DRGG) model, which is an extension of the random geometric graph model. We prove that it is scale-free with respect to the indegree distribution, has binomial outdegree distribution, has a high clustering coefficient, has few edges and is likely small-world. These are some of the main features of aforementioned real-world networks. We also empirically observed that word association networks have many of the theoretical properties of the DRGG model.

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The Fractional Preferential Attachment Scale-Free Network Model

Entropy ◽

10.3390/e22050509 ◽

2020 ◽

Vol 22 (5) ◽

pp. 509

Author(s):

Rafał Rak ◽

Ewa Rak

Keyword(s):

Network Model ◽

Real World ◽

Degree Distribution ◽

Preferential Attachment ◽

Clustering Coefficient ◽

Node Degree ◽

Scale Free Network ◽

Scale Free ◽

Degree Correlation ◽

Free Network

Many networks generated by nature have two generic properties: they are formed in the process of preferential attachment and they are scale-free. Considering these features, by interfering with mechanism of the preferential attachment, we propose a generalisation of the Barabási–Albert model—the ’Fractional Preferential Attachment’ (FPA) scale-free network model—that generates networks with time-independent degree distributions p ( k ) ∼ k − γ with degree exponent 2 < γ ≤ 3 (where γ = 3 corresponds to the typical value of the BA model). In the FPA model, the element controlling the network properties is the f parameter, where f ∈ ( 0 , 1 ⟩ . Depending on the different values of f parameter, we study the statistical properties of the numerically generated networks. We investigate the topological properties of FPA networks such as degree distribution, degree correlation (network assortativity), clustering coefficient, average node degree, network diameter, average shortest path length and features of fractality. We compare the obtained values with the results for various synthetic and real-world networks. It is found that, depending on f, the FPA model generates networks with parameters similar to the real-world networks. Furthermore, it is shown that f parameter has a significant impact on, among others, degree distribution and degree correlation of generated networks. Therefore, the FPA scale-free network model can be an interesting alternative to existing network models. In addition, it turns out that, regardless of the value of f, FPA networks are not fractal.

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Network robustness improvement via long-range links

Computational Social Networks ◽

10.1186/s40649-019-0073-2 ◽

2019 ◽

Vol 6 (1) ◽

Cited By ~ 1

Author(s):

Vincenza Carchiolo ◽

Marco Grassia ◽

Alessandro Longheu ◽

Michele Malgeri ◽

Giuseppe Mangioni

Keyword(s):

Complex Networks ◽

Long Range ◽

Real World ◽

Network Robustness ◽

Scale Free ◽

Area Of Interest ◽

Before And After ◽

Significant Area ◽

Better Than

AbstractMany systems are today modelled as complex networks, since this representation has been proven being an effective approach for understanding and controlling many real-world phenomena. A significant area of interest and research is that of networks robustness, which aims to explore to what extent a network keeps working when failures occur in its structure and how disruptions can be avoided. In this paper, we introduce the idea of exploiting long-range links to improve the robustness of Scale-Free (SF) networks. Several experiments are carried out by attacking the networks before and after the addition of links between the farthest nodes, and the results show that this approach effectively improves the SF network correct functionalities better than other commonly used strategies.

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Words, constructions and corpora: Network representations of constructional semantics for Mandarin space particles

Corpus Linguistics and Linguistic Theory ◽

10.1515/cllt-2020-0012 ◽

2020 ◽

Vol 0 (0) ◽

Cited By ~ 1

Author(s):

Alvin Cheng-Hsien Chen

Keyword(s):

Clustering Coefficient ◽

Linguistic Knowledge ◽

Scale Free ◽

Network Analyses ◽

Semantic Fields ◽

Text Corpora ◽

Quantitative Properties ◽

Local Clustering Coefficient ◽

Linguistic Units

AbstractIn this study, we aim to demonstrate the effectiveness of network science in exploring the emergence of constructional semantics from the connectedness and relationships between linguistic units. With Mandarin locative constructions (MLCs) as a case study, we extracted constructional tokens from a representative corpus, including their respective space particles (SPs) and the head nouns of the landmarks (LMs), which constitute the nodes of the network. We computed edges based on the lexical similarities of word embeddings learned from large text corpora and the SP-LM contingency from collostructional analysis. We address three issues: (1) For each LM, how prototypical is it of the meaning of the SP? (2) For each SP, how semantically cohesive are its LM exemplars? (3) What are the emerging semantic fields from the constructional network of MLCs? We address these questions by examining the quantitative properties of the network at three levels: microscopic (i.e., node centrality and local clustering coefficient), mesoscopic (i.e., community) and macroscopic properties (i.e., small-worldness and scale-free). Our network analyses bring to the foreground the importance of repeated language experiences in the shaping and entrenchment of linguistic knowledge.

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Maximal assortative matching for real-world network graphs, random network graphs and scale-free network graphs

Vietnam Journal of Computer Science ◽

10.1007/s40595-016-0066-0 ◽

2016 ◽

Vol 3 (3) ◽

pp. 151-179 ◽

Cited By ~ 2

Author(s):

Natarajan Meghanathan

Keyword(s):

Real World ◽

Random Network ◽

Assortative Matching ◽

Scale Free Network ◽

Scale Free ◽

Free Network

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Downlink SINR Statistics in OFDM-Based Optical Attocell Networks with a Poisson Point Process Network Model

2015 IEEE Global Communications Conference (GLOBECOM) ◽

10.1109/glocom.2015.7417221 ◽

2015 ◽

Cited By ~ 6

Author(s):

Cheng Chen ◽

Dushyantha Basnayaka ◽

Harald Haas

Keyword(s):

Point Process ◽

Network Model ◽

Poisson Point Process

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SCALE-FREE AND SMALL-WORLD PROPERTIES OF A SPECIAL HIERARCHICAL NETWORK

Fractals ◽

10.1142/s0218348x19500105 ◽

2019 ◽

Vol 27 (02) ◽

pp. 1950010

Author(s):

DAOHUA WANG ◽

YUMEI XUE ◽

QIAN ZHANG ◽

MIN NIU

Keyword(s):

Degree Distribution ◽

Path Length ◽

Small World ◽

Average Path Length ◽

Clustering Coefficient ◽

Hierarchical Network ◽

Scale Free

Many real systems behave similarly with scale-free and small-world structures. In this paper, we generate a special hierarchical network and based on the particular construction of the graph, we aim to present a study on some properties, such as the clustering coefficient, average path length and degree distribution of it, which shows the scale-free and small-world effects of this network.

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