Analysis of spatial networks from bipartite projections using the R backbone package

Abstract

Spatial networks can be difficult to measure. Bipartite projections offer a potential solution by indirectly inferring a network from data that is easier to collect. They are now used in many subfields of geography, and are among the most common ways to measure the world city network, where intercity links are inferred from firm co-location patterns. However, spatial bipartite projections are difficult to analyze because the links in these networks are weighted, and larger weights do not necessarily indicate stronger or more important connections. Methods for extracting the backbone of bipartite projections offer a solution by using statistical models for identifying the links that have statistically significant weights. In this paper, we introduce the open-source backbone R package, which implements several backbone models, and demonstrate its key features by using it to measure a world city network.

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

“…We focus on a bipartite network with right-tailed degree distributions because they are common in many empirical unipartite 43 and bipartite networks. 5,6,22 This synthetic bipartite network could represent a legislative body composed of 200 legislators casting votes on 1000 bills, where any given legislator had a 10% chance of voting in favor of any given bill. The right-tailed degree distributions capture the fact that most legislators vote in favor of only a few bills, and that most bills receive the support of only a few legislators, which is typical of legislative bodies.…”

“…The Globalization and World Cities (GaWC) dataset has been widely-used in this context, and takes the form of a bipartite network recording the presence or absence of 100 firms (artifacts) in 196 cities (agents) in the year 2000. 2,22 In this bipartite network, the agent degrees are right-tailed because most cities contain only a few firms, while a few cities (e.g., New York) contain many. Likewise, the artifact degrees are also right tailed because most firms maintain locations in only a few cities, while a few firms (e.g., KPMG) maintain locations in many.…”

“…Agent and artifact degree distributions are a key feature of a bipartite network, and are known to have implications for bipartite projections. 9,21,22 The FDSM is particularly appealing because it allows decisions about the significance of edges in a projection Most write some papers, but a few are prolific (most departments).…”

Connection Characteristics and Hierarchical Structure of China’s Urban Network‐Based on the Communications Technology Service Industry

“…ey found that the top-down method from the perspective of large-scale advanced production and service industry firms is more suitable to identify the world city network, while the bottom-up method that focuses on important enterprise companies in a specific region is a more suitable model to study regional urban networks. Neal et al [5] proposed a bipartite projection to identify enterprise or city contacts more accurately, given that "strong connection does not necessarily mean great power." Regarding the research content, network hierarchy, and node centrality, studying the factors that influence network formation and the impact of network embedding on other networks remains part of the basic research material of urban networks [6][7][8].…”