arXiv subjects

Zachary P. Neal

Publications and source records attributed to Zachary P. Neal.

9 recordsLinked to original sources

arXiv2024

A stopping rule for randomly sampling bipartite networks with fixed degree sequences

Statistical analysis of bipartite networks frequently requires randomly sampling from the set of all bipartite networks with the same degree sequence as an observed network. Trade algorithms offer an efficient way to generate samples of bipartite networks by incrementally `trading' the positions of some of their edges. However, it is difficult to know how many such trades are required to ensure that the sample is random. I propose a stopping rule that focuses on the distance between sampled networks and the observed network, and stops performing trades when this distribution stabilizes. Analyses demonstrate that, for over 650 different degree sequences, using this stopping rule ensures a random sample with a high probability, and that it is practical for use in empirical applications.

math.NA↗

arXiv2024

When can networks be inferred from observed groups?

Collecting network data directly from network members can be challenging. One alternative involves inferring a network from observed groups, for example, inferring a network of scientific collaboration from researchers' observed paper authorships. In this paper, I explore when an unobserved undirected network of interest can accurately be inferred from observed groups. The analysis uses simulations to experimentally manipulate the structure of the unobserved network to be inferred, the number of groups observed, the extent to which the observed groups correspond to cliques in the unobserved network, and the method used to draw inferences. I find that when a small number of groups are observed, an unobserved network can be accurately inferred using a simple unweighted two-mode projection, provided that each group's membership closely corresponds to a clique in the unobserved network. In contrast, when a large number of groups are observed, an unobserved network can be accurately inferred using a statistical backbone extraction model, even if the groups' memberships are mostly random. These findings offer guidance for researchers seeking to indirectly measure a network of interest using observations of groups.

cs.SI↗

arXiv2024

Stochastic Degree Sequence Model with Edge Constraints (SDSM-EC) for Backbone Extraction

It is common to use the projection of a bipartite network to measure a unipartite network of interest. For example, scientific collaboration networks are often measured using a co-authorship network, which is the projection of a bipartite author-paper network. Caution is required when interpreting the edge weights that appear in such projections. However, backbone models offer a solution by providing a formal statistical method for evaluating when an edge in a projection is statistically significantly strong. In this paper, we propose an extension to the existing Stochastic Degree Sequence Model (SDSM) that allows the null model to include edge constraints (EC) such as prohibited edges. We demonstrate the new SDSM-EC in toy data and empirical data on young children's' play interactions, illustrating how it correctly omits noisy edges from the backbone.

cs.SI↗

arXiv2022

fastball: A fast algorithm to sample bipartite graphs with fixed degree sequences

Many applications require randomly sampling bipartite graphs with fixed degrees, or randomly sampling incidence matrices with fixed row and column sums. Although several sampling algorithms exist, the ``curveball'' algorithm is the most efficient with an asymptotic time complexity of O(n log n), and has been proven to sample uniformly at random. In this paper, we introduce the ``fastball'' algorithm, which adopts a similar approach but has an asymptotic time complexity of O(n). We show that a C++ implementation of fastball randomly samples large bipartite graphs with fixed degrees faster than curveball, and illustrate the value of this faster algorithm in the context of the fixed degree sequence model for backbone extraction.

cs.DS↗

arXiv2022

The duality of networks and groups: Models to generate two-mode networks from one-mode networks

Focus theory describes how shared memberships, social statuses, beliefs, and places can facilitate the formation of social ties, while two-mode projections provide a method for transforming two-mode data on individuals' memberships in groups into a one-mode network of their possible social ties. In this paper, I explore the opposite process: how social ties can facilitate the formation of groups, and how a two-mode network can be generated from a one-mode network. Drawing on theories of team formation, club joining, and organization recruitment, I propose three models that describe how such groups might emerge from the relationships in a social network. I show that these models can be used to generate two-mode networks that have characteristics commonly observed in empirical two-mode social networks, and that they encode features of the one-mode networks from which they were generated. I conclude by discussing these models' limitations, and future directions for theory and methods concerning group formation.

cs.SI↗

arXiv2022

Identifying hidden coalitions in the US House of Representatives by optimally partitioning signed networks based on generalized balance

In network science, identifying optimal partitions of a signed network into internally cohesive and mutually divisive clusters based on generalized balance theory is computationally challenging. We reformulate and generalize two binary linear programming models that tackle this challenge, demonstrating their practicality by applying them them to partition networks of collaboration in the US House of Representatives. These models guarantee a globally optimal network partition and can be practically applied to signed networks containing up to 30,000 edges. In the US House context, we find that a three-cluster partition is better than a conventional two-cluster partition, where the otherwise hidden third coalition is composed of highly effective legislators who are ideologically aligned with the majority party.

cs.SI↗

arXiv2022

backbone: An R package to extract network backbones

Networks are useful for representing phenomena in a broad range of domains. Although their ability to represent complexity can be a virtue, it is sometimes useful to focus on a simplified network that contains only the most important edges: the backbone. This paper introduces and demonstrates the `backbone' package for R, which implements methods for extracting the backbone from weighted networks, weighted bipartite projections, and unweighted networks. For each type of network, fully replicable code is presented first for small toy examples, then for complete empirical examples using transportation, political, and social networks. The paper also demonstrates the implications of several issues of statistical inference that arise in backbone extraction. It concludes by briefly reviewing existing applications of backbone extraction using the `backbone' package, and future directions for research on network backbone extraction.

cs.SI↗

arXiv2021

Comparing Alternatives to the Fixed Degree Sequence Model for Extracting the Backbone of Bipartite Projections

Projections of bipartite or two-mode networks capture co-occurrences, and are used in diverse fields (e.g., ecology, economics, bibliometrics, politics) to represent unipartite networks. A key challenge in analyzing such networks is determining whether an observed number of co-occurrences between two nodes is significant, and therefore whether an edge exists between them. One approach, the fixed degree sequence model (FDSM), evaluates the significance of an edge's weight by comparison to a null model in which the degree sequences of the original bipartite network are fixed. Although the FDSM is an intuitive null model, it is computationally expensive because it requires Monte Carlo simulation to estimate each edge's $p$-value, and therefore is impractical for large projections. In this paper, we explore four potential alternatives to FDSM: fixed fill model (FFM), fixed row model (FRM), fixed column model (FCM), and stochastic degree sequence model (SDSM). We compare these models to FDSM in terms of accuracy, speed, statistical power, similarity, and ability to recover known communities. We find that the computationally-fast SDSM offers a statistically conservative but close approximation of the computationally-impractical FDSM under a wide range of conditions, and that it correctly recovers a known community structure even when the signal is weak. Therefore, although each backbone model may have particular applications, we recommend SDSM for extracting the backbone of bipartite projections when FDSM is impractical.

cs.SI↗

arXiv2013

Navigating the massive world of reddit: Using backbone networks to map user interests in social media

In the massive online worlds of social media, users frequently rely on organizing themselves around specific topics of interest to find and engage with like-minded people. However, navigating these massive worlds and finding topics of specific interest often proves difficult because the worlds are mostly organized haphazardly, leaving users to find relevant interests by word of mouth or using a basic search feature. Here, we report on a method using the backbone of a network to create a map of the primary topics of interest in any social network. To demonstrate the method, we build an interest map for the social news web site reddit and show how such a map could be used to navigate a social media world. Moreover, we analyze the network properties of the reddit social network and find that it has a scale-free, small-world, and modular community structure, much like other online social networks such as Facebook and Twitter. We suggest that the integration of interest maps into popular social media platforms will assist users in organizing themselves into more specific interest groups, which will help alleviate the overcrowding effect often observed in large online communities.

cs.SI↗