scholarly journals Polytopes from Subgraph Statistics

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Alexander Engström ◽  
Patrik Norén
Keyword(s):  
Exponential Random Graph Models ◽  
Schur Polynomials ◽  
Graph Models ◽  
Selberg Integral ◽  
General Picture ◽  
Cyclic Polytopes ◽  
Random Graph Models ◽  
Exponential Random Graph ◽  
Nous Trouvons ◽  
International Audience

International audience We study polytopes that are convex hulls of vectors of subgraph densities. Many graph theoretical questions can be expressed in terms of these polytopes, and statisticians use them to understand exponential random graph models. Relations among their Ehrhart polynomials are described, their duals are applied to certify that polynomials are non-negative, and we find some of their faces. For the general picture we inscribe cyclic polytopes in them and calculate volumes. From the volume calculations we conjecture that a variation of the Selberg integral indexed by Schur polynomials has a combinatorial formula. We inscribe polynomially parametrized sets, called curvy zonotopes, in the polytopes and show that they approximate the polytopes arbitrarily close. Nous étudions les polytopes qui sont les enveloppes convexes des vecteurs des densités de sous-graphe. Beaucop de questions théoriques de graphe peuvent être exprimées en termes de ces polytopes, et les statisticiens les utilisent pour comprendre les modèles de graphes aléatoires exponentielles Des relations parmi leurs polynômes d'Ehrhart sont décrites leurs duals sont appliqués pour certifier que les polynômes sont non négatifs, et nous trouvons certaines de leurs faces. Pour la description générale nous inscrivons les polytopes cycliques dans eux et calculons les volumes. D'après les calculs de volume, nous conjecturons qu'une variation de l'intégrale de Selberg indexés par des polynômes de Schur a une formule combinatoire. Nous inscrivons polynomialement les ensembles paramétrisés appelés ``curvy zonotopes'' dans les polytopes et montrons qu'ils sont arbitrairement proches de polytopes.

scholarly journals Exponential random graph models for little networks

2021 ◽  
Vol 64 ◽  
pp. 225-238
Author(s):  
George G. Vega Yon ◽  
Andrew Slaughter ◽  
Kayla de la Haye
Keyword(s):  
Random Graph ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Random Graph Models ◽  
Exponential Random Graph

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.

Following the Leader: The Evolving Network of Charter School Giving

2019 ◽  
Vol 121 (10) ◽  
pp. 1-32
Author(s):  
David Diehl ◽  
Robert A. Marx
Keyword(s):  
Charter Schools ◽  
Charter School ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Random Graph Models ◽  
Exponential Random Graph ◽  
Disproportionate Number ◽  
Charter Management Organizations ◽  
Foundation Type ◽  
Over Time

Background/Context Research on the patterns of philanthropic funding of charter schools has largely focused on the behavior of major foundations. This work has documented how the once diffuse giving by these major foundations has become increasingly concentrated on a small number of jurisdictional challengers in the form of charter schools, charter management organizations, and intermediary organizations. Purpose The current study examines whether this convergence in giving has spread to the entire network of foundations giving to charter-school-related organizations. We do so by extending current work and focus on the broader institutional field that includes the interactions between major foundations, smaller foundations, and grantees over time. Moreover, we look to see, if such a field-wide convergence is present, whether there is evidence consistent with the institutional process of isomorphism in which low-status foundations match the giving strategy of higher status ones. Research Design We test for these dynamics using exponential random graph models (ERGMs), a hypothesis-testing framework for network analysis. More specifically, we analyze the funding ties among 809 foundations that gave grants to California charter schools and charter-school-related organizations between 2003 and 2014, as available through the Foundation Directory Online. We constructed multiyear windows to examine funding ties between foundations and recipients, using organizational characteristics, such as foundation type, foundation year, professionalization, foundation size, organizational type, and location, and endogenous features of the network as independent variables. Findings Results indicate centralization of giving over time, as larger and newer foundations began practicing more targeted giving and the most connected recipients were involved in a disproportionate number of funding ties. We also found evidence consistent with institutionalization, as foundations with professional staffs played a larger role in giving, and smaller foundations increasingly engaged in behavior similar to their larger peers over time. Finally, we found evidence for the consistent effect of propinquity: We observe co-funding and co-receiving ties between foundations and grantees in geographical proximity to each other. Conclusions This work examines the network dynamics of charter school philanthropic giving and provides evidence for the centralization and institutionalization of the field. In turn, this may create inequity in funding for charter schools because it may be more difficult for smaller or less ideologically popular organizations to penetrate the field. Policy makers should be aware of these forces and should take them into account when making budgetary and funding decisions.

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.

scholarly journals Bayesian exponential random graph models with nodal random effects

2016 ◽  
Vol 46 ◽  
pp. 11-28 ◽  
Author(s):  
S. Thiemichen ◽  
N. Friel ◽  
A. Caimo ◽  
G. Kauermann
Keyword(s):  
Random Effects ◽  
Random Graph ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Random Graph Models ◽  
Exponential Random Graph
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