A Structural Model of Dense Network Formation

Advances in exponential random graph ( p*) models applied to a large social network

Efficient emergency collaboration is essential in modern complex disaster response scenarios. Understanding the key factors that influence the formation and evolution of collaboration relationships is fundamental for establishing effective emergency collaboration networks. Therefore, this study focuses on investigating these factors using Exponential Random Graph Models (ERGM), within the context of extreme weather disasters. The potential influencing factors are summarized as four categories: nature of the organizations, similarity among the response organizations, pre-disaster collaborative experiences, and self-organizing during emergency response. A two-stage Zhengzhou heavy rainstorm disaster (“July” and “August”) was selected as a case study to examine the hypothesis. Firstly, two emergency collaboration networks were constructed based on the same rules with special news reports and related official data. Then, the examinations were conducted respectively based on ERGM to explore the explanatory power of those factors in the formation and evolution of emergency collaboration networks. Further, through a comparative verification analysis, the factors to be examined are divided into three groups according to their performance at different phases. The findings indicate that: (1) Internal and external factors jointly contribute to the formation of emergency collaboration networks, but the endogenous structures can offset some organizational attribute preferences and homogeneity factors. (2) Among the endogenous structural factors, the transitivity effect significantly promotes the formation and expansion of the network, rather than the expansion effect and bridging effect. (3)Collaborating with public sectors, organizations with command and coordination responsibilities, and those possessing information resource endowments can contribute to the improvement of the emergency collaboration efficiency. (4) Pre-disaster collaborative experiences, such as emergency drills and previous crisis experiences, facilitate the evolution and optimization of emergency collaboration networks. The research findings aim to support local governments in establishing a more comprehensive collaboration mechanism for responding to complex disasters.

The ties that belong: Tie formation in preservice teacher identification networks

Understanding the factors of network formation is a fundamental aspect in the study of social dynamics. Online activity provides us with abundance of data that allows us to reconstruct and study social networks. Statistical inference methods are often used to study network formation. Ideally, statistical inference allows the researcher to study the significance of specific factors to the network formation. One popular framework is known as Exponential Random Graph Models (ERGM) which provides principled and statistically sound interpretation of an observed network structure. Network, however, are not always given set in stone. Often times, a network is “reconstructed” by applying some thresholds on the observed data/signals. We show that subtle changes in the thresholding have significant effects on the ERGM results, casting doubts on the interpretability of the model. In this work we present a case study in which different thresholding techniques yield radically different results that lead to contrastive interpretations. Consequently, we revisit the applicability of ERGM to thresholded networks.

Synthetic power grids enable real-world energy system simulations and are crucial for algorithm testing, resilience assessment, and policy formulation. We propose a novel method for the generation of synthetic transmission power grids using exponential random graph (ERG) models. Our two main contributions are (1) the formulation of an ERG model tailored specifically for capturing the topological nuances of power grids and (2) a general procedure for estimating the parameters of such a model conditioned on working with connected graphs. From a modeling perspective, we identify edge counts per bus type and k-triangles as crucial topological characteristics for synthetic power-grid generation. From a technical perspective, we develop a rigorous methodology to estimate the parameters of an ERG constrained to the space of connected graphs. The proposed model is flexible, easy to implement, and successfully captures the desired topological properties of power grids. Published by the American Physical Society 2024

Understanding user-to-User interaction on government microblogs: An exponential random graph model with the homophily and emotional effect

Stable exponential random graph models with non-parametric components for large dense networks

Background: The relationship between policy networks and policy development among local health departments (LHDs) is a growing area of interest to public health practitioners and researchers alike. In this study, we examine policy activity and ties between public health leadership across large urban health departments. Methods: This study uses data from a national profile of local health departments as well as responses from a survey sent to three staff members (local health official, chief of policy, chief science officer) in each of 16 urban health departments in the United States. Network questions related to frequency of contact with health department personnel in other cities. Using exponential random graph models, network density and centrality were examined, as were patterns of communication among those working on several policy areas using exponential random graph models. Results: All 16 LHDs were active in communicating about chronic disease as well as about use of alcohol, tobacco, and other drugs (ATOD). Connectedness was highest among local health officials (density = .55), and slightly lower for chief science officers (d = .33) and chiefs of policy (d = .29). After accounting for organizational characteristics, policy homophily (i.e., when two network members match on a single characteristic) and tenure were the most significant predictors of formation of network ties. Conclusion: Networking across health departments has the potential for accelerating the adoption of public health policies. This study suggests similar policy interests and formation of connections among senior leadership can potentially drive greater connectedness among other staff.

In the study of social processes, the presence of unobserved heterogeneity is a regular concern. It should be particularly worrisome for the statistical analysis of networks, given the complex dependencies that shape network formation combined with the restrictive assumptions of related models. In this paper, we demonstrate the importance of explicitly accounting for unobserved heterogeneity in exponential random graph models (ERGM) with a Monte Carlo analysis and two applications that have played an important role in the networks literature. Overall, these analyses show that failing to account for unobserved heterogeneity can have a significant impact on inferences about network formation. The proposed frailty extension to the ERGM (FERGM) generally outperforms the ERGM in these cases, and does so by relatively large margins. Moreover, our novel multilevel estimation strategy has the advantage of avoiding the problem of degeneration that plagues the standard MCMC-MLE approach.

Exponential random graph models (ERGMs) provide conceptually elegant recipes for generating soft-constrained random graphs. This chapter begins by explaining the theory and describing how to properly specify an ERGM, including demonstrating Lagrange’s method to derive the values of the model parameters that correspond to the desired constraints. Three ERGMs, all with constraints depending linearly on the adjacency matrix, are solved exactly: the targeted total number of links, targeted individual node degrees and targeted number of two-way links in a directed graph. However, when the controlled features become more complicated, ERGMs have a tendency to produce graphs in extreme phases (very dense or very sparse). The two-star model and the Strauss model are worked through in detail using advanced techniques from statistical mechanics in order to analyze the phase transitions. The chapter closes with a discussion of the strengths and weaknesses of ERGMs as null models.

Exponential random graph models (ERGMs) are increasingly applied to observed network data and are central to understanding social structure and network processes. The chapters in this edited volume provide a self-contained, exhaustive account of the theoretical and methodological underpinnings of ERGMs, including models for univariate, multivariate, bipartite, longitudinal and social-influence type ERGMs. Each method is applied in individual case studies illustrating how social science theories may be examined empirically using ERGMs. The authors supply the reader with sufficient detail to specify ERGMs, fit them to data with any of the available software packages and interpret the results.

In this chapter we consider extensive-form games of network formation. The starting point is a coalitional game that describes the profits obtainable by all possible coalitions of players. The players engage in a network-formation process to be able to coordinate their actions and realize the possible gains from cooperation. The network-formation process itself is sequential, i.e., links are formed one at a time and players observe which links are formed as the game progresses. Once a network has been formed, the players bargain over the division of the jointly obtained profits. This bargaining process is not modeled explicitly. Rather, an exogenously given allocation rule is used to describe the payoffs to the players in any of the networks that they can form. Most of the results in this chapter are obtained for network-formation games in which the allocation rule used to determine the players’ payoffs is the Myerson value.

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.

The structure of polymer networks is closely related to the network formation (structure growth) process. A covalent polymer network is a giant macromolecule of dimensions commensurable with the macroscopic dimensions of a given object. Although it can be characterized by a number of average structural parameters, like sol fraction or crosslinking density, its internal structure can be very different1 varying from that of a random loosely crosslinked network of vulcanized rubber to that of very dense networks of some thermosets or ceramers. Also, micronetworks (microgels) or other microscopic precursors (dendritic structures, star- burst polymers, etc.) are formed first and then they grow into a macronetwork with the same or other types of structure growth processes. Vinyl-divinyl copolymerization can serve as an example.2 Therefore, the understanding of structure growth is necessary for understanding the network structure, and the properties of polymer networks can be correlated with their structure. An important role in undestanding of the network structure via the network formation process is played by the network formation theories.

Chapter 6 - An empirical model for strategic network formation