Ordered community structure in networks

Community structure in networks is often a consequence of homophily, or assortative mixing, based on some attribute of the vertices. For example, researchers may be grouped into communities corresponding to their research topic. This is possible if vertex attributes have discrete values, but many networks exhibit assortative mixing by some continuous-valued attribute, such as age or geographical location. In such cases, no discrete communities can be identified. We consider how the notion of community structure can be generalized to networks that are based on continuous-valued attributes: in general, a network may contain discrete communities which are ordered according to their attribute values. We propose a method of generating synthetic ordered networks and investigate the effect of ordered community structure on the spread of infectious diseases. We also show that community detection algorithms fail to recover community structure in ordered networks, and evaluate an alternative method using a layout algorithm to recover the ordering.Comment: This is an extended preprint version that includes an extra example: the college football network as an ordered (spatial) network. Further improvements, not included here, appear in the journal version. Original title changed (from "Ordered and continuous community structure in networks") to match journal versio

Detecting Communities in Networks by Merging Cliques

Many algorithms have been proposed for detecting disjoint communities (relatively densely connected subgraphs) in networks. One popular technique is to optimize modularity, a measure of the quality of a partition in terms of the number of intracommunity and intercommunity edges. Greedy approximate algorithms for maximizing modularity can be very fast and effective. We propose a new algorithm that starts by detecting disjoint cliques and then merges these to optimize modularity. We show that this performs better than other similar algorithms in terms of both modularity and execution speed.Comment: 5 pages, 7 figure

Identifying Communities and Key Vertices by Reconstructing Networks from Samples

Sampling techniques such as Respondent-Driven Sampling (RDS) are widely used in epidemiology to sample "hidden" populations, such that properties of the network can be deduced from the sample. We consider how similar techniques can be designed that allow the discovery of the structure, especially the community structure, of networks. Our method involves collecting samples of a network by random walks and reconstructing the network by probabilistically coalescing vertices, using vertex attributes to determine the probabilities. Even though our method can only approximately reconstruct a part of the original network, it can recover its community structure relatively well. Moreover, it can find the key vertices which, when immunized, can effectively reduce the spread of an infection through the original network.Comment: 15 pages, 17 figure

Finding missing edges in networks based on their community structure

Many edge prediction methods have been proposed, based on various local or global properties of the structure of an incomplete network. Community structure is another significant feature of networks: Vertices in a community are more densely connected than average. It is often true that vertices in the same community have "similar" properties, which suggests that missing edges are more likely to be found within communities than elsewhere. We use this insight to propose a strategy for edge prediction that combines existing edge prediction methods with community detection. We show that this method gives better prediction accuracy than existing edge prediction methods alone.Comment: 7 pages, 6 figure

From the volcano effect to banding: a minimal model for bacterial behavioral transitions near chemoattractant sources

Sharp chemoattractant (CA) gradient variations near food sources may give rise to dramatic behavioral changes of bacteria neighboring these sources. For instance, marine bacteria exhibiting run-reverse motility are known to form distinct bands around patches (large sources) of chemoattractant such as nutrient-soaked beads while run-and-tumble bacteria have been predicted to exhibit a 'volcano effect' (spherical shell-shaped density) around a small (point) source of food. Here we provide the first minimal model of banding for run-reverse bacteria and show that, while banding and the volcano effect may appear superficially similar, they are different physical effects manifested under different source emission rate (and thus effective source size). More specifically, while the volcano effect is known to arise around point sources from a bacterium's temporal differentiation of signal (and corresponding finite integration time), this effect alone is insufficient to account for banding around larger patches as bacteria would otherwise cluster around the patch without forming bands at some fixed radial distance. In particular, our model demonstrates that banding emerges from the interplay of run-reverse motility and saturation of the bacterium's chemoreceptors to CA molecules and our model furthermore predicts that run-reverse bacteria susceptible to banding behavior should also exhibit a volcano effect around sources with smaller emission rates

A determination of the spin-orbit alignment of the anomalously dense planet orbiting HD 149026

We report 35 radial velocity measurements of HD 149026 taken with the Keck Telescope. Of these measurements, 15 were made during the transit of the companion planet HD 149026b, which occurred on 2005 June 25. These velocities provide a high-cadence observation of the Rossiter-McLaughlin effect, the shifting of photospheric line profiles that occurs when a planet occults a portion of the rotating stellar surface. We combine these radial velocities with previously published radial velocity and photometric data sets and derive a composite best-fit model for the star-planet system. This model confirms and improves previously published orbital parameters, including the remarkably small planetary radius, the planetary mass, and the orbital inclination, found to be Rp/RJup = 0.718 ± 0.065, Mp/MJup = 0.352 ± 0.025, and I = 86.1° ± 1.4°, respectively. Together the planetary mass and radius determinations imply a mean planetary density of 1.18(-0.30)(+0.38)g cm(-3). The new data also allow for the determination of the angle between the apparent stellar equator and the orbital plane, which we constrain to be λ = -12° ± 15°