Networks

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Biological Networks ◽  
Generative Models ◽  
The Internet ◽  
Network Data ◽  
Computer Algorithms ◽  
Graph Models ◽  
Random Graph Models ◽  
The Social ◽  
Spectral Algorithms ◽  
Wide Availability

The study of networks, including computer networks, social networks, and biological networks, has attracted enormous interest in recent years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyse network data on an unprecendented scale, and the development of new theoretical tools has allowed us to extract knowledge from networks of many different kinds. The study of networks is broadly interdisciplinary and developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social science. This book brings together the most important breakthroughts in each of these fields and presents them in a unified fashion, highlighting the strong interconnections between work in different areas. Topics covered include the measurement of networks; methods for analysing network data, including methods developed in physics, statistics, and sociology; fundamentals of graph theory; computer algorithms, including spectral algorithms and community detection; mathematical models of networks such as random graph models and generative models; and models of processes taking place on networks.

Why Legislative Networks? Analyzing Legislative Network Formation

2017 ◽  
Vol 7 (3) ◽  
pp. 505-522 ◽  
Author(s):  
Stefan Wojcik
Keyword(s):  
Political Parties ◽  
Network Formation ◽  
Contemporary Literature ◽  
Party Organization ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Personal Traits ◽  
Random Graph Models ◽  
Exponential Random Graph ◽  
The Social

Are the social networks of legislators affected more by their political parties or their personal traits? How does the party organization influence the tendency of members to work collectively on a day-to-day basis? In this paper, I explore the determinants of the relationships of legislators in the Brazilian Chamber of Deputies. I use exponential random graph models to evaluate the relative influence of personal traits versus party influence in generating legislator relationships. Despite a focus on personalism in Brazil, the analysis reveals that the effects of political parties on tie formation are roughly equal to the effects of personal traits, suggesting that networks may make political parties much more cohesive than contemporary literature would lead us to believe.

scholarly journals The performance of permutations and exponential random graph models when analyzing animal networks

2020 ◽  
Vol 31 (5) ◽  
pp. 1266-1276 ◽  
Author(s):  
Julian C Evans ◽  
David N Fisher ◽  
Matthew J Silk
Keyword(s):  
Social Network ◽  
Random Graph ◽  
False Positive ◽  
False Negative ◽  
Error Rates ◽  
Network Data ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Random Graph Models ◽  
Exponential Random Graph

Abstract Social network analysis is a suite of approaches for exploring relational data. Two approaches commonly used to analyze animal social network data are permutation-based tests of significance and exponential random graph models. However, the performance of these approaches when analyzing different types of network data has not been simultaneously evaluated. Here we test both approaches to determine their performance when analyzing a range of biologically realistic simulated animal social networks. We examined the false positive and false negative error rate of an effect of a two-level explanatory variable (e.g., sex) on the number and combined strength of an individual’s network connections. We measured error rates for two types of simulated data collection methods in a range of network structures, and with/without a confounding effect and missing observations. Both methods performed consistently well in networks of dyadic interactions, and worse on networks constructed using observations of individuals in groups. Exponential random graph models had a marginally lower rate of false positives than permutations in most cases. Phenotypic assortativity had a large influence on the false positive rate, and a smaller effect on the false negative rate for both methods in all network types. Aspects of within- and between-group network structure influenced error rates, but not to the same extent. In "grouping event-based" networks, increased sampling effort marginally decreased rates of false negatives, but increased rates of false positives for both analysis methods. These results provide guidelines for biologists analyzing and interpreting their own network data using these methods.

A Weighted Network Modeling Approach for Analyzing Product Competition

2020 ◽  
Author(s):  
Yaxin Cui ◽  
Faez Ahmed ◽  
Zhenghui Sha ◽  
Lijun Wang ◽  
Yan Fu ◽  
...  
Keyword(s):  
Network Theory ◽  
Network Modeling ◽  
Network Models ◽  
Social Aspects ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Random Graph Models ◽  
Exponential Random Graph ◽  
The Social ◽  
Product Competition

Abstract Statistical network models allow us to study the co-evolution between the products and the social aspects of a market system, by modeling these components and their interactions as graphs. In this paper, we study competition between different car models using network theory, with a focus on how product attributes (like fuel economy and price) affect which cars are considered together and which cars are finally bought by customers. Unlike past work, where most systems have been studied with the assumption that relationships between competitors are binary (i.e., whether a relationship exists or not), we allow relationships to take strengths (i.e., how strong a relationship is). Specifically, we use valued Exponential Random Graph Models and show that our approach provides a significant improvement over the baselines in predicting product co-considerations as well as in the validation of market share. This is also the first attempt to study aggregated purchase preference and car competition using valued directed networks.

Cytoscape Plugin for Reconstruction of Structural Random Graph Models of Biological Networks

2018 ◽  
Vol 16 (3) ◽  
pp. 37-50
Author(s):  
N. L. Podkolodnyy ◽  
◽  
D. A. Gavrilov ◽  
N. N. Tverdokhleb ◽  
O. A. Podkolodnaya ◽  
...  
Keyword(s):  
Random Graph ◽  
Biological Networks ◽  
Graph Models ◽  
Random Graph Models

scholarly journals Inferential Network Analysis with Exponential Random Graph Models

2011 ◽  
Vol 19 (1) ◽  
pp. 66-86 ◽  
Author(s):  
Skyler J. Cranmer ◽  
Bruce A. Desmarais
Keyword(s):  
Network Analysis ◽  
Random Graph ◽  
Graph Model ◽  
Network Data ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Random Graph Model ◽  
General Acceptance ◽  
Random Graph Models ◽  
Exponential Random Graph

Methods for descriptive network analysis have reached statistical maturity and general acceptance across the social sciences in recent years. However, methods for statistical inference with network data remain fledgling by comparison. We introduce and evaluate a general model for inference with network data, the Exponential Random Graph Model (ERGM) and several of its recent extensions. The ERGM simultaneously allows both inference on covariates and for arbitrarily complex network structures to be modeled. Our contributions are three-fold: beyond introducing the ERGM and discussing its limitations, we discuss extensions to the model that allow for the analysis of non-binary and longitudinally observed networks and show through applications that network-based inference can improve our understanding of political phenomena.

scholarly journals Diagnosing Multicollinearity in Exponential Random Graph Models

2017 ◽  
Author(s):  
Scott W Duxbury
Keyword(s):  
Random Graph ◽  
Standard Errors ◽  
Exponential Random Graph Models ◽  
Multilevel Regression ◽  
Graph Models ◽  
Network Characteristics ◽  
Random Graph Models ◽  
Exponential Random Graph ◽  
The Social ◽  
Inflation Factor

Exponential random graph models (ERGM) have been widely applied in the social sciences in the past ten years. However, diagnostics for ERGM have lagged behind their use. Collinearity-type problems can emerge without detection when fitting ERGM, skewing coefficients, biasing standard errors, and yielding inconsistent model estimates. This article provides a method to detect multicollinearity in ERGM. It outlines the problem and provides a method to calculate the variance inflation factor from ERGM parameters. It then evaluates the method with a Monte Carlo simulation, fitting 216,000 ERGMs and calculating the variance inflation factors for each model. The distribution of variance inflation factors is analyzed using multilevel regression to determine what network characteristics lend themselves to collinearity-type problems. The relationship between variance inflation factors and unstable standard errors (a standard sign of collinearity) is also examined. The method is shown to effectively detect multicollinearity and guidelines for interpretation are discussed.

The origins of asymmetric ties in friendship networks: From status differential to self-perceived centrality

2015 ◽  
Vol 3 (2) ◽  
pp. 269-292 ◽  
Author(s):  
WEIHUA AN ◽  
WILL R. MCCONNELL
Keyword(s):  
Significant Proportion ◽  
Network Data ◽  
Friendship Networks ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Random Graph Models ◽  
Exponential Random Graph ◽  
Status Characteristics ◽  
General Norm ◽  
Status Differences

AbstractAsymmetric ties make up a significant proportion of ties in friendship networks. But little is known about their origins. Prior research has suggested treating them either as “accidental” (e.g., resulting from constraints in name generators) or “aspirational” (i.e., the attempts of individuals to pursue relationships with higher status peers). In this paper, we show that self-perception can also explain the occurrence of asymmetric ties. We argue that under the general norm of reciprocity, actors with high self-perceived centrality will more likely send out ties to others than their counterparts. Supposing that outgoing ties are similarly reciprocated by peers, then actors with high self-perceived centrality will also entail more asymmetric ties. We test this idea along with the competing arguments using exponential random graph models (ERGMs) on network data collected from over 4,000 students in China. Consistent with previous findings, we find that asymmetric ties reflect status differences, but probably more strongly so for difference in individual status characteristics than difference in social positional status. More importantly, we find that students with high self-perceived centrality are about twice as likely to send asymmetric ties as their peers. Last, we examine the implications of our findings for future network research.

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