scholarly journals Optimisation of the coalescent hyperbolic embedding of complex networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bianka Kovács ◽  
Gergely Palla
Keyword(s):  
Small World ◽  
Hyperbolic Distance ◽  
Greedy Routing ◽  
Scale Free ◽  
Recent Approach ◽  
Strong Motivation ◽  
Angular Coordinates ◽  
Small World Property ◽  
Logarithmic Loss ◽  
Hyperbolic Embedding

AbstractSeveral observations indicate the existence of a latent hyperbolic space behind real networks that makes their structure very intuitive in the sense that the probability for a connection is decreasing with the hyperbolic distance between the nodes. A remarkable network model generating random graphs along this line is the popularity-similarity optimisation (PSO) model, offering a scale-free degree distribution, high clustering and the small-world property at the same time. These results provide a strong motivation for the development of hyperbolic embedding algorithms, that tackle the problem of finding the optimal hyperbolic coordinates of the nodes based on the network structure. A very promising recent approach for hyperbolic embedding is provided by the noncentered minimum curvilinear embedding (ncMCE) method, belonging to the family of coalescent embedding algorithms. This approach offers a high-quality embedding at a low running time. In the present work we propose a further optimisation of the angular coordinates in this framework that seems to reduce the logarithmic loss and increase the greedy routing score of the embedding compared to the original version, thereby adding an extra improvement to the quality of the inferred hyperbolic coordinates.

scholarly journals Directed random geometric graphs

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.

scholarly journals Complex network description of the ionosphere

2018 ◽  
Vol 25 (1) ◽  
pp. 233-240
Author(s):  
Shikun Lu ◽  
Hao Zhang ◽  
Xihai Li ◽  
Yihong Li ◽  
Chao Niu ◽  
...  
Keyword(s):  
Complex Network ◽  
Hypothesis Test ◽  
Small World ◽  
Dynamic Processes ◽  
Electron Content ◽  
Vertical Total Electron Content ◽  
Total Electron ◽  
Scale Free ◽  
Probabilistic Graph ◽  
Small World Property

Abstract. Complex networks have emerged as an essential approach of geoscience to generate novel insights into the nature of geophysical systems. To investigate the dynamic processes in the ionosphere, a directed complex network is constructed, based on a probabilistic graph of the vertical total electron content (VTEC) from 2012. The results of the power-law hypothesis test show that both the out-degree and in-degree distribution of the ionospheric network are not scale-free. Thus, the distribution of the interactions in the ionosphere is homogenous. None of the geospatial positions play an eminently important role in the propagation of the dynamic ionospheric processes. The spatial analysis of the ionospheric network shows that the interconnections principally exist between adjacent geographical locations, indicating that the propagation of the dynamic processes primarily depends on the geospatial distance in the ionosphere. Moreover, the joint distribution of the edge distances with respect to longitude and latitude directions shows that the dynamic processes travel further along the longitude than along the latitude in the ionosphere. The analysis of “small-world-ness” indicates that the ionospheric network possesses the small-world property, which can make the ionosphere stable and efficient in the propagation of dynamic processes.

DYNAMICS BEHAVIORS OF WEIGHTED LOCAL-WORLD EVOLVING NETWORKS WITH EXTENDED LINKS

2009 ◽  
Vol 20 (11) ◽  
pp. 1719-1735 ◽  
Author(s):  
GUANGHUI WEN ◽  
ZHISHENG DUAN
Keyword(s):  
Weak Interactions ◽  
Small World ◽  
Local Information ◽  
Scale Free ◽  
Evolving Networks ◽  
Free Behavior ◽  
Small World Property ◽  
Evolving Model ◽  
Analytical Expressions ◽  
Good Agreement

In this paper, we present a local-world evolving model to characterize weighted networks. By introducing the extended links to mimic the weak interactions between the nodes in different local-worlds, the model yields scale-free behavior as well as the small-world property, as confirmed in many real networks. With the increase of the local information, the generated network undergoes a transition from assortative to disassortative, meanwhile the small-world property is preserved. It indicates that the small-world property is a universal characteristic in our model. The numerical simulation results are in good agreement with the analytical expressions.

scholarly journals The inherent community structure of hyperbolic networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bianka Kovács ◽  
Gergely Palla
Keyword(s):  
Community Structure ◽  
Random Graphs ◽  
Small World ◽  
Label Propagation ◽  
Hyperbolic Distance ◽  
Scale Free ◽  
Wide Range ◽  
Community Finding ◽  
Optimisation Model ◽  
Low Dimensional

AbstractA remarkable approach for grasping the relevant statistical features of real networks with the help of random graphs is offered by hyperbolic models, centred around the idea of placing nodes in a low-dimensional hyperbolic space, and connecting node pairs with a probability depending on the hyperbolic distance. It is widely appreciated that these models can generate random graphs that are small-world, highly clustered and scale-free at the same time; thus, reproducing the most fundamental common features of real networks. In the present work, we focus on a less well-known property of the popularity-similarity optimisation model and the $${\mathbb {S}}^1/{\mathbb {H}}^2$$ S 1 / H 2 model from this model family, namely that the networks generated by these approaches also contain communities for a wide range of the parameters, which was certainly not an intention at the design of the models. We extracted the communities from the studied networks using well-established community finding methods such as Louvain, Infomap and label propagation. The observed high modularity values indicate that the community structure can become very pronounced under certain conditions. In addition, the modules found by the different algorithms show good consistency, implying that these are indeed relevant and apparent structural units. Since the appearance of communities is rather common in networks representing real systems as well, this feature of hyperbolic models makes them even more suitable for describing real networks than thought before.

Research on the Coal Logistics Network's Property Based on the Complex System Theory of Supply Chain

2013 ◽  
Vol 869-870 ◽  
pp. 251-255
Author(s):  
Li Jun Liu ◽  
Xiao Ji Guan
Keyword(s):  
Complex System ◽  
System Theory ◽  
Supply Chain ◽  
Complex Network ◽  
Small World ◽  
Practical Significance ◽  
Logistics Network ◽  
Scale Free ◽  
Small World Property ◽  
Coal Enterprises

This article puts forward the practical significance of studying the complex characteristic of coal logistics network from the coal resource effective utilization and rational allocation. According to the characteristics of coal enterprises, the coal logistics network is defined as the complex network system. Based on the complex system theory of the supply chain, the coal logistics network is analysed separately from the complexity of node and structure, the small word property as well as the scale-free property and it is pointed out that the coal network has complex network structure, the small world property and the scale-free property.

STOCHASTIC EVOLVING MODEL FOR COMPLEX NETWORKS

2004 ◽  
Vol 18 (23) ◽  
pp. 1157-1164 ◽  
Author(s):  
HYUN-JOO KIM ◽  
YEON-MU CHOI ◽  
JIN MIN KIM
Keyword(s):  
Control Parameter ◽  
Small World ◽  
Network Size ◽  
Clustering Coefficient ◽  
Scale Free ◽  
Hierarchical Topology ◽  
Free Behavior ◽  
Small World Property ◽  
Evolving Model ◽  
High Degree

We introduce an evolving complex network model, where a new vertex is added and new edges between already existing vertices are added with a control parameter p. The model shows the characteristics of real networks such as small-world property, high degree of clustering, scale-free behavior in degree distribution, and hierarchical topology. We obtain the various values of degree exponent γ in the range 2<γ≤3 by adjusting the parameter p and find that the degree exponent decreases logarithmically with p. In addition, the clustering coefficient is tunable by changing the control parameter p, and the average path length L is proportional to ln ( ln N) with nonzero p, where N is the network size.

scholarly journals Hyperbolic mapping of human proximity networks

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Marco A. Rodríguez-Flores ◽  
Fragkiskos Papadopoulos
Keyword(s):  
Physical Space ◽  
Hyperbolic Distance ◽  
Greedy Routing ◽  
Epidemic Spreading ◽  
Arrival Times ◽  
Close Range ◽  
Zero Degree ◽  
New Perspective ◽  
Hyperbolic Mapping ◽  
Hyperbolic Embedding

AbstractHuman proximity networks are temporal networks representing the close-range proximity among humans in a physical space. They have been extensively studied in the past 15 years as they are critical for understanding the spreading of diseases and information among humans. Here we address the problem of mapping human proximity networks into hyperbolic spaces. Each snapshot of these networks is often very sparse, consisting of a small number of interacting (i.e., non-zero degree) nodes. Yet, we show that the time-aggregated representation of such systems over sufficiently large periods can be meaningfully embedded into the hyperbolic space, using methods developed for traditional (non-mobile) complex networks. We justify this compatibility theoretically and validate it experimentally. We produce hyperbolic maps of six different real systems, and show that the maps can be used to identify communities, facilitate efficient greedy routing on the temporal network, and predict future links with significant precision. Further, we show that epidemic arrival times are positively correlated with the hyperbolic distance from the infection sources in the maps. Thus, hyperbolic embedding could also provide a new perspective for understanding and predicting the behavior of epidemic spreading in human proximity systems.

scholarly journals Hyperbolic disc embedding of functional human brain connectomes using resting state fMRI

2021 ◽  
Author(s):  
Wonseok Whi ◽  
Seunggyun Ha ◽  
Hyejin Kang ◽  
Dong Soo Lee
Keyword(s):  
Resting State ◽  
Brain Networks ◽  
Small World ◽  
Resting State Fmri ◽  
Hyperbolic Distance ◽  
Functional Brain ◽  
Scale Free ◽  
Functional Brain Networks ◽  
Individual Scale ◽  
The Brain

The brain presents a real complex network of modular, small-world, and hierarchical nature, which are features of non-Euclidean geometry. Using resting-state functional magnetic resonance imaging (rs-fMRI), we constructed a scale-free binary graph for each subject, using internodal time-series correlation of regions-of-interest (ROIs) as a proximity measure. The resulted network could be embedded onto manifolds of various curvature and dimensions. While maintaining the fidelity of embedding (low distortion, high mean average precision), functional brain networks were found to be best represented in the hyperbolic disc. Using a popularity-similarity optimization model (PSOM) on the hyperbolic plane, we reduced the dimension of the network into 2-D hyperbolic space and were able to efficiently visualize the internodal connections of the brain, preserving proximity as distances and angles on the PSOM discs. Each individual PSOM disc revealed decentralized nature of information flow and anatomic relevance. Using the hyperbolic distance on the PSOM disc, we could detect the anomaly of network in autistic spectrum disorder (ASD) subjects. This procedure of embedding grants us a reliable new framework for studying functional brain networks and the possibility of detecting anomalies of the network in the hyperbolic disc on an individual scale.

Top Museums on Instagram

2019 ◽  
Vol 3 (2) ◽  
pp. 18-42 ◽  
Author(s):  
Vasiliki G. Vrana ◽  
Dimitrios A. Kydros ◽  
Evangelos C. Kehris ◽  
Anastasios-Ioannis T. Theocharidis ◽  
George I. Kavavasilis
Keyword(s):  
Social Network ◽  
Network Analysis ◽  
Small World ◽  
Marketing Strategies ◽  
The Other ◽  
Small World Network ◽  
Scale Free ◽  
Centrality Metrics ◽  
Photo Sharing ◽  
Visualization Algorithms

Pictures speak louder than words. In this fast-moving world where people hardly have time to read anything, photo-sharing sites become more and more popular. Instagram is being used by millions of people and has created a “sharing ecosystem” that also encourages curation, expression, and produces feedback. Museums are moving quickly to integrate Instagram into their marketing strategies, provide information, engage with audience and connect to other museums Instagram accounts. Taking into consideration that people may not see museum accounts in the same way that the other museum accounts do, the article first describes accounts' performance of the top, most visited museums worldwide and next investigates their interconnection. The analysis uses techniques from social network analysis, including visualization algorithms and calculations of well-established metrics. The research reveals the most important modes of the network by calculating the appropriate centrality metrics and shows that the network formed by the museum Instagram accounts is a scale–free small world network.

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