A Multi-Scale Analysis of 27,000 Urban Street Networks: Every US City, Town, Urbanized Area, and Zillow Neighborhood

OpenStreetMap offers a valuable source of worldwide geospatial data useful to urban researchers. This study uses the OSMnx software to automatically download and analyze 27,000 US street networks from OpenStreetMap at metropolitan, municipal, and neighborhood scales - namely, every US city and town, census urbanized area, and Zillow-defined neighborhood. It presents empirical findings on US urban form and street network characteristics, emphasizing measures relevant to graph theory, transportation, urban design, and morphology such as structure, connectedness, density, centrality, and resilience. In the past, street network data acquisition and processing have been challenging and ad hoc. This study illustrates the use of OSMnx and OpenStreetMap to consistently conduct street network analysis with extremely large sample sizes, with clearly defined network definitions and extents for reproducibility, and using nonplanar, directed graphs. These street networks and measures data have been shared in a public repository for other researchers to use

On average connectivity of the strong product of graphs

The average connectivity κ(G) of a graph G is the average, over all pairs of vertices, of the maximum number of internally disjoint paths connecting these vertices. The connectivity κ(G) can be seen as the minimum, over all pairs of vertices, of the maximum number of internally disjoint paths connecting these vertices. The connectivity and the average connectivity are upper bounded by the minimum degree δ(G) and the average degree d(G) of G, respectively. In this paper the average connectivity of the strong product G1 G2 of two connected graphs G1 and G2 is studied. A sharp lower bound for this parameter is obtained. As a consequence, we prove that κ(G1 G2) = d(G1 G2) if κ(Gi) = d(Gi), i = 1, 2. Also we deduce that κ(G1 G2) = δ(G1 G2) if κ(Gi) = δ(Gi), i = 1, 2.Ministerio de Educación y Ciencia MTM2011-28800-C02-02Generalitat de Cataluña 1298 SGR200

Spin models on random graphs with controlled topologies beyond degree constraints

We study Ising spin models on finitely connected random interaction graphs which are drawn from an ensemble in which not only the degree distribution $p(k)$ can be chosen arbitrarily, but which allows for further fine-tuning of the topology via preferential attachment of edges on the basis of an arbitrary function Q(k,k') of the degrees of the vertices involved. We solve these models using finite connectivity equilibrium replica theory, within the replica symmetric ansatz. In our ensemble of graphs, phase diagrams of the spin system are found to depend no longer only on the chosen degree distribution, but also on the choice made for Q(k,k'). The increased ability to control interaction topology in solvable models beyond prescribing only the degree distribution of the interaction graph enables a more accurate modeling of real-world interacting particle systems by spin systems on suitably defined random graphs.Comment: 21 pages, 4 figures, submitted to J Phys

The free-linking task: a graph-inspired method for generating non-disjoint similarity data with food products

"Free sorting", in which subjects are asked to sort a set of items into groups of "most similar" items, is increasingly popular as a technique for profiling sets of foods. However, free sorting implies an unrealistic model of sample similarity: that similarity is purely binary (is/is not similar) and that similarity is fully transitive (similarities {A, B} and {B, C} imply {A, C}). This paper proposes a new method of rapid similarity testing -- the "free-linking" task -- that solves both problems: in free linking, subjects draw a similarity graph in which they connect pairs of samples with a line if they are similar, according to the subject s individual criteria. This simple task provides a more realistic model of similarity which allows degrees of similarity through the graph distance metric and does not require transitive similarity. In two pilot studies with spice blends (10 samples, 58 subjects) and chocolate bars (10 samples, 63 subjects), free linking and free sorting are evaluated and compared using DISTATIS, RVb, and the graph parameters degree, transitivity, and connectivity; subjects also indicated their preferences and ease-of-use for the tasks. In both studies, the first two dimensions of the DISTATIS consensus were highly comparable across tasks; however, free linking provided more discrimination in dimensions three and four. RVb stability was equivalent for the two methods. Graph statistics indicated that free linking had greater discrimination power: on average subjects made similarity groupings with lower degree, lower transitivity, and higher connectivity for free linking in both studies. However, subjects did overall find free sorting easier and liked it more, indicating a higher cognitive difficulty of free linking. The free-linking task, therefore, provides more robust, realistic similarity maps at the cost of higher panelist effort, and should prove a valuable alternative for rapid sensory assessment of product sets.Agencia Estatal de Investigació

The Average Lower Connectivity of Graphs

For a vertex v of a graph G, the lower connectivity, denoted by sv(G), is the smallest number of vertices that contains v and those vertices whose deletion from G produces a disconnected or a trivial graph. The average lower connectivity denoted by κav(G) is the value (∑v∈VGsvG)/VG. It is shown that this parameter can be used to measure the vulnerability of networks. This paper contains results on bounds for the average lower connectivity and obtains the average lower connectivity of some graphs