scholarly journals Properties of latent variable network models

2016 ◽  
Vol 4 (4) ◽  
pp. 407-432 ◽  
Author(s):  
RICCARDO RASTELLI ◽  
NIAL FRIEL ◽  
ADRIAN E. RAFTERY
Keyword(s):  
Latent Variable ◽  
Broad Class ◽  
Network Models ◽  
Small World ◽  
Clustering Coefficient ◽  
Analytic Expressions ◽  
Network Properties ◽  
Degree Correlations ◽  
Heavy Tailed ◽  
Special Case

AbstractWe derive properties of latent variable models for networks, a broad class of models that includes the widely used latent position models. We characterize several features of interest, with particular focus on the degree distribution, clustering coefficient, average path length, and degree correlations. We introduce the Gaussian latent position model, and derive analytic expressions and asymptotic approximations for its network properties. We pay particular attention to one special case, the Gaussian latent position model with random effects, and show that it can represent the heavy-tailed degree distributions, positive asymptotic clustering coefficients, and small-world behaviors that often occur in observed social networks. Finally, we illustrate the ability of the models to capture important features of real networks through several well-known datasets.

A NETWORK MODEL GENERATED FROM THE RECURSIVE GRAPH BASED ON POLYGON

2013 ◽  
Vol 24 (09) ◽  
pp. 1350062 ◽  
Author(s):  
YUANYUAN SUN ◽  
KAINING HOU ◽  
YUJIE ZHAO
Keyword(s):  
Real Life ◽  
Network Models ◽  
Small World ◽  
Mapping Method ◽  
Clustering Coefficient ◽  
Research Fields ◽  
Network Diameter ◽  
Degree Correlations ◽  
New Perspective ◽  
Small World Property

The study of network models is one of the most challenging research fields among the studies of complex networks, which have been the hot research topics in recent decades. In this paper, we construct a deterministic network by a mapping method based on a recursive graph, and analyze its topological characteristics, including degree distribution, clustering coefficient, network diameter, average path length and degree correlations. We obtain that this network has the small-world property and positive correlation. The network modeling as we present gives a new perspective on networks, and helps to understand better the evolutions of the real-life systems, making it possible to explore the complexity of complex systems.

scholarly journals Factor or Network Model? Predictions From Neural Networks

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Alexander P. Christensen ◽  
Keyword(s):  
Neural Networks ◽  
Network Model ◽  
Latent Variable ◽  
Random Network ◽  
Network Models ◽  
Small World ◽  
Small World Network ◽  
Monte Carlo Simulation Study ◽  
Psychological Phenomena ◽  
The Neural Networks

The nature of associations between variables is important for constructing theory about psychological phenomena. In the last decade, this topic has received renewed interest with the introduction of psychometric network models. In psychology, network models are often contrasted with latent variable (e.g., factor) models. Recent research has shown that differences between the two tend to be more substantive than statistical. One recently developed algorithm called the Loadings Comparison Test (LCT) was developed to predict whether data were generated from a factor or small-world network model. A significant limitation of the current LCT implementation is that it's based on heuristics that were derived from descriptive statistics. In the present study, we used artificial neural networks to replace these heuristics and develop a more robust and generalizable algorithm. We performed a Monte Carlo simulation study that compared neural networks to the original LCT algorithm as well as logistic regression models that were trained on the same data. We found that the neural networks performed as well as or better than both methods for predicting whether data were generated from a factor, small-world network, or random network model. Although the neural networks were trained on small-world networks, we show that they can reliably predict the data-generating model of random networks, demonstrating generalizability beyond the trained data. We echo the call for more formal theories about the relations between variables and discuss the role of the LCT in this process.

scholarly journals Studies on the Decrease Mechanisms of Typical Complex Networks

2021 ◽  
Author(s):  
Yuhu Qiu ◽  
Tianyang Lyu ◽  
Xizhe Zhang ◽  
Ruozhou Wang
Keyword(s):  
Average Length ◽  
Shortest Paths ◽  
Real Life ◽  
Network Models ◽  
Small World ◽  
Clustering Coefficient ◽  
Network Growth ◽  
Scale Free ◽  
Complex Network Models ◽  
High Degree

Network decrease caused by the removal of nodes is an important evolution process that is paralleled with network growth. However, many complex network models usually lacked a sound decrease mechanism. Thus, they failed to capture how to cope with decreases in real life. The paper proposed decrease mechanisms for three typical types of networks, including the ER networks, the WS small-world networks and the BA scale-free networks. The proposed mechanisms maintained their key features in continuous and independent decrease processes, such as the random connections of ER networks, the long-range connections based on nearest-coupled network of WS networks and the tendency connections and the scale-free feature of BA networks. Experimental results showed that these mechanisms also maintained other topology characteristics including the degree distribution, clustering coefficient, average length of shortest-paths and diameter during decreases. Our studies also showed that it was quite difficult to find an efficient decrease mechanism for BA networks to withstand the continuous attacks at the high-degree nodes, because of the unequal status of nodes.

Abstract 17426: Pulmonary Vein Isolation ‘Rewires’ Electrical Communications to Enhance Small-world Network Topology During Atrial Fibrillation

Circulation ◽  
2015 ◽  
Vol 132 (suppl_3) ◽  
Author(s):  
Hiroshi Ashikaga ◽  
Jonathan Chrispin ◽  
Degang Wu ◽  
Joshua Garland
Keyword(s):  
Atrial Fibrillation ◽  
Communication Network ◽  
Mutual Information ◽  
Path Length ◽  
Random Network ◽  
Small World ◽  
Clustering Coefficient ◽  
Small World Network ◽  
Z Score ◽  
Network Properties

Recent evidence suggests that pulmonary vein isolation (PVI) may perturb the electrophysiological substrate for maintenance of atrial fibrillation (AF). Our previous work indicates that information theory metrics can quantify electrical communications during arrhythmia. We hypothesized that PVI ‘rewires’ the electrical communication network during AF such that the topology exhibits higher levels of small-world network properties, with higher clustering coefficient and lower path length, than would be expected by chance. Thirteen consecutive patients (n=6 with prior PVI and n=7 without) underwent AF ablation using a 64-electrode basket catheter in the left atrium. Multielectrode recording was performed during AF for 60 seconds, followed by PVI. Mutual information was calculated from the time series between each pair of electrodes using the Kraskov-Stögbauer-Grassberger estimator. The all-to-all mutual information matrix (64x64; Figure, upper panels) was thresholded by the median and standard deviations of mutual information to build a binary adjacency matrix for electrical communication networks. The properties of small-world network ( swn ; ‘small-world-ness’) were quantified by the ratio of the observed average clustering coefficient to that of a random network over the ratio of the observed average path length to that of a random network. swn was expressed in normal Z standard deviation units. As the binarizing threshold increased, the Z-score of swn decreased (Figure, lower panel). However, the Z-score at each threshold value was consistently higher with prior PVI than those without (p<0.05). In conclusion, electrical communication network during AF with prior PVI is associated with higher levels of small-world network properties than those without. This finding supports the concept that PVI perturbs the underlying substrate. In addition, swn of electrical communication network may be a promising metric to quantify substrate modification.

scholarly journals Foreshocks and short-term hazard assessment of large earthquakes using complex networks: the case of the 2009 L'Aquila earthquake

2016 ◽  
Vol 23 (4) ◽  
pp. 241-256 ◽  
Author(s):  
Eleni Daskalaki ◽  
Konstantinos Spiliotis ◽  
Constantinos Siettos ◽  
Georgios Minadakis ◽  
Gerassimos A. Papadopoulos
Keyword(s):  
Hazard Assessment ◽  
Betweenness Centrality ◽  
Small World ◽  
Clustering Coefficient ◽  
Earthquake Catalog ◽  
Short Term ◽  
2009 L’Aquila Earthquake ◽  
Topological Measures ◽  
Network Properties ◽  
Large Earthquakes

Abstract. The monitoring of statistical network properties could be useful for the short-term hazard assessment of the occurrence of mainshocks in the presence of foreshocks. Using successive connections between events acquired from the earthquake catalog of the Istituto Nazionale di Geofisica e Vulcanologia (INGV) for the case of the L'Aquila (Italy) mainshock (Mw = 6.3) of 6 April 2009, we provide evidence that network measures, both global (average clustering coefficient, small-world index) and local (betweenness centrality) ones, could potentially be exploited for forecasting purposes both in time and space. Our results reveal statistically significant increases in the topological measures and a nucleation of the betweenness centrality around the location of the epicenter about 2 months before the mainshock. The results of the analysis are robust even when considering either large or off-centered the main event space windows.

OPTIMAL INTERCONNECTION OF AD HOC INJECTION NETWORKS

2008 ◽  
Vol 09 (03) ◽  
pp. 277-297 ◽  
Author(s):  
GREGOIRE DANOY ◽  
ENRIQUE ALBA ◽  
PASCAL BOUVRY
Keyword(s):  
Ad Hoc Networks ◽  
Ad Hoc ◽  
Small World ◽  
Access Point ◽  
Clustering Coefficient ◽  
Mobility Patterns ◽  
Characteristic Path Length ◽  
Network Properties ◽  
Hoc Networks ◽  
Topology Control Problem

Multi-hop ad hoc networks allow establishing local groups of communicating devices in a self-organizing way. However, when considering realistic mobility patterns, such networks most often get divided in a set of disjoint partitions. This presence of partitions is an obstacle to communication within these networks. Ad hoc networks are generally composed of devices capable of communicating in a geographical neighborhood for free (e.g. using Wi-Fi or Bluetooth). In most cases a communication infrastructure is available. It can be a set of access point as well as a GSM/UMTS network. The use of such an infrastructure is billed, but it permits to interconnect distant nodes, through what we call “bypass links”. The objective of our work is to optimize the placement of these long-range links. To this end we rely on small-world network properties, which consist in a high clustering coefficient and a low characteristic path length. In this article we investigate the use of three genetic algorithms (generational, steady-state, and cooperative coevolutionary) to optimize three instances of this topology control problem and present initial evidence of their capacity to solve it.

scholarly journals Inferring network properties from time series using transfer entropy and mutual information: Validation of multivariate versus bivariate approaches

2020 ◽  
pp. 1-32
Author(s):  
Leonardo Novelli ◽  
Joseph T. Lizier
Keyword(s):  
Time Series ◽  
Mutual Information ◽  
Network Models ◽  
Small World ◽  
Structural Features ◽  
Transfer Entropy ◽  
Statistical Dependence ◽  
Neural Mass Model ◽  
Mass Model ◽  
Network Properties

Functional and effective networks inferred from time series are at the core of network neuroscience. Interpreting properties of these networks requires inferred network models to reflect key underlying structural features. However, even a few spurious links can severely distort network measures, posing a challenge for functional connectomes. We study the extent to which micro- and macroscopic properties of underlying networks can be inferred by algorithms based on mutual information and bivariate/multivariate transfer entropy. The validation is performed on two macaque connectomes and on synthetic networks with various topologies (regular lattice, small-world, random, scale-free, modular). Simulations are based on a neural mass model and on autoregressive dynamics (employing Gaussian estimators for direct comparison to functional connectivity and Granger causality). We find that multivariate transfer entropy captures key properties of all network structures for longer time series. Bivariate methods can achieve higher recall (sensitivity) for shorter time series but are unable to control false positives (lower specificity) as available data increases. This leads to overestimated clustering, small-world, and rich-club coefficients, underestimated shortest path lengths and hub centrality, and fattened degree distribution tails. Caution should therefore be used when interpreting network properties of functional connectomes obtained via correlation or pairwise statistical dependence measures, rather than more holistic (yet data-hungry) multivariate models.

THE SMALL-WORLD PROPERTY IN NETWORKS GROWING BY ACTIVE EDGES

2011 ◽  
Vol 14 (06) ◽  
pp. 853-869 ◽  
Author(s):  
PHILIPPE J. GIABBANELLI
Keyword(s):  
Growth Mechanism ◽  
Average Distance ◽  
Network Models ◽  
Small World ◽  
Clustering Coefficient ◽  
Small World Networks ◽  
Fractal Approach ◽  
Small World Property ◽  
Complex Network Models ◽  
Similar Growth

In the last three years, we have witnessed an increasing number of complex network models based on a 'fractal' approach, in which parts of the network are repeatedly replaced by a given pattern. Our focus is on models that can be defined by repeatedly adding a pattern network to selected edges, called active edges. We prove that when a pattern network has at least two active edges, then the resulting network has an average distance at most logarithmic in the number of nodes. This suggests that real-world networks based on a similar growth mechanism are likely to have small average distance. We provide an estimate of the clustering coefficient and verify its accuracy using simulations. Using numerous examples of simple patterns, our simulations show various ways to generate small-world networks. Finally, we discuss extensions to our framework encompassing probabilistic patterns and active subnetworks.

scholarly journals Foreshocks and Short-Term Hazard Assessment to Large Earthquakes using Complex Networks: the Case of the 2009 L'Aquila Earthquake

2016 ◽  
Author(s):  
E. Daskalaki ◽  
K. Spiliotis ◽  
C. Siettos ◽  
G. Minadakis ◽  
G. A. Papadopoulos
Keyword(s):  
Hazard Assessment ◽  
Betweenness Centrality ◽  
Small World ◽  
Clustering Coefficient ◽  
Event Space ◽  
Short Term ◽  
2009 L’Aquila Earthquake ◽  
Topological Measures ◽  
Network Properties ◽  
Large Earthquakes

Abstract. The monitoring of statistical network properties could be useful for the short-term hazard assessment of the occurrence of mainshocks in the presence of foreshocks. Using successive connections between events acquired from the earthquake catalogue of INGV for the case of the L'Aquila (Italy) mainshock (Mw = 6.3) of 6th April 2009, we provide evidence that network measures, both global (e.g. average clustering coefficient, small-world index) and local (betweenness centrality), could potentially be exploited for forecasting purposes both in time and space. Our results reveal statistically significant increases of the topological measures and a nucleation of the betweenness centrality around the location of the epicenter about two months before the mainshock. The results of the analysis are robust even when considering either large or off-centered the main event space-windows.

scholarly journals Small-world Structure in Children’s Featured Semantic Networks

2021 ◽  
Vol 7 (4) ◽  
pp. 185-192
Author(s):  
Somayeh Sadat Hashemikamangar ◽  
◽  
Shahriar Gharibzadeh ◽  
Fatemeh Bakouie ◽  
◽  
...  
Keyword(s):  
Developmental Psychology ◽  
Network Models ◽  
Small World ◽  
Semantic Networks ◽  
Clustering Coefficient ◽  
Random Networks ◽  
Dense Networks ◽  
Global Access ◽  
Small World Property ◽  
Feature Norms

Background: Knowing the development pattern of children’s language is applicable in developmental psychology. Network models of language are helpful for the identification of these patterns. Objectives: We examined the small-world properties of featured semantic networks of developing children. Materials & Methods: In this longitudinal study, the featured semantic networks of children aged 18-30 months were obtained using R software version 3.5.2 and the igraph software package. The data of 2000 English (British)-speaking children, half boy and half girls, were gathered from existing databases of MCDI (between 2000 and 2007) and McRae feature norms. The growth pattern of these networks was illustrated by graph measures. Comparing these measures with those of the reference random networks, the small-world structure can be examined. Results: To have a comparison between path length and clustering coefficient of featured semantic networks with those of random networks, we computed the Q quotient. The results showed that the values of the Q quotient at 18, 22, 26, and 30 months of age were all more than 1, which confirms the small-world characteristic of the networks. Conclusion: Featured semantic networks of children exhibited a small-world structure, in which there was a local structure in the form of clusters of words. For global access, some words act as bridges connecting semantically distant clusters. These networks possess small-world property from the early months of age. The small-world structure cannot be seen in the less dense networks built with a higher cut-off threshold.

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