Geomedia: Networked Cities and the Future of Public Space

Written by Scott McQuir

Disentangling agglomeration and network externalities : a conceptual typology

Agglomeration and network externalities are fuzzy concepts. When different meanings are (un)intentionally juxtaposed in analyses of the agglomeration/network externalities-menagerie, researchers may reach inaccurate conclusions about how they interlock. Both externality types can be analytically combined, but only when one adopts a coherent approach to their conceptualization and operationalization, to which end we provide a combinatorial typology. We illustrate the typology by applying a state-of-the-art bipartite network projection detailing the presence of globalized producer services firms in cities in 2012. This leads to two one-mode graphs that can be validly interpreted as topological renderings of agglomeration and network externalities

Mixing time for uniform sampling of bipartite graphs with fixed degrees using the trade algorithm

Uniform sampling of bipartite graphs and hypergraphs with given degree sequences is necessary for building null models to statistically evaluate their topology. Because these graphs can be represented as binary matrices, the problem is equivalent to uniformly sampling $r \times c$ binary matrices with fixed row and column sums. The trade algorithm, which includes both the curveball and fastball implementations, is the state-of-the-art for performing such sampling. Its mixing time is currently unknown, although $5r$ is currently used as a heuristic. In this paper we propose a new distribution-based approach that not only provides an estimation of the mixing time, but also actually returns a sample of matrices that are guaranteed (within a user-chosen error tolerance) to be uniformly randomly sampled. In numerical experiments on matrices that vary by size, fill, and row and column sum distributions, we find that the upper bound on mixing time is at least $10r$, and that it increases as a function of both $c$ and the fraction of cells containing a 1

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

Inferring social networks from observed groups

Collecting social network data directly from network members can be challenging. One alternative involves inferring a social network from individuals' memberships in observed groups, such as teams or clubs. Through a series of simulations, I explore when we can expect such inferences to be accurate. I find that an unobserved network can be inferred with high accuracy under a range of circumstances. In particular, I find that social networks inferred from observed groups are more accurate when (1) the unobserved network has a small world structure, (2) the groups are generated by a shuffling or agglomerative process, (3) a large number of groups are observed, and (4) the observed groups' compositions are tightly coupled to the unobserved network's structure. These findings offer guidance for researchers seeking to indirectly measure a social network of interest through observations of groups

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

backbone: An R Package for extracting the backbone of bipartite projections

Bipartite projections are used in a wide range of network contexts including politics (bill co-sponsorship), genetics (gene co-expression), economics (executive board co-membership), and innovation (patent co-authorship). However, because bipartite projections are always weighted graphs, which are inherently challenging to analyze and visualize, it is often useful to examine the 'backbone', an unweighted subgraph containing only the most significant edges. In this paper, we introduce the R package backbone for extracting the backbone of weighted bipartite projections, and use bill sponsorship data from the 114th session of the United States Senate to demonstrate its functionality