Local Search in Unstructured Networks

We review a number of message-passing algorithms that can be used to search through power-law networks. Most of these algorithms are meant to be improvements for peer-to-peer file sharing systems, and some may also shed some light on how unstructured social networks with certain topologies might function relatively efficiently with local information. Like the networks that they are designed for, these algorithms are completely decentralized, and they exploit the power-law link distribution in the node degree. We demonstrate that some of these search algorithms can work well on real Gnutella networks, scale sub-linearly with the number of nodes, and may help reduce the network search traffic that tends to cripple such networks.Comment: v2 includes minor revisions: corrections to Fig. 8's caption and references. 23 pages, 10 figures, a review of local search strategies in unstructured networks, a contribution to `Handbook of Graphs and Networks: From the Genome to the Internet', eds. S. Bornholdt and H.G. Schuster (Wiley-VCH, Berlin, 2002), to be publishe

Assortative mixing in networks

A network is said to show assortative mixing if the nodes in the network that have many connections tend to be connected to other nodes with many connections. We define a measure of assortative mixing for networks and use it to show that social networks are often assortatively mixed, but that technological and biological networks tend to be disassortative. We propose a model of an assortative network, which we study both analytically and numerically. Within the framework of this model we find that assortative networks tend to percolate more easily than their disassortative counterparts and that they are also more robust to vertex removal.Comment: 5 pages, 1 table, 1 figur

Ranking and clustering of nodes in networks with smart teleportation

Random teleportation is a necessary evil for ranking and clustering directed networks based on random walks. Teleportation enables ergodic solutions, but the solutions must necessarily depend on the exact implementation and parametrization of the teleportation. For example, in the commonly used PageRank algorithm, the teleportation rate must trade off a heavily biased solution with a uniform solution. Here we show that teleportation to links rather than nodes enables a much smoother trade-off and effectively more robust results. We also show that, by not recording the teleportation steps of the random walker, we can further reduce the effect of teleportation with dramatic effects on clustering.Comment: 10 pages, 7 figure

Stochastic blockmodels and community structure in networks

Stochastic blockmodels have been proposed as a tool for detecting community structure in networks as well as for generating synthetic networks for use as benchmarks. Most blockmodels, however, ignore variation in vertex degree, making them unsuitable for applications to real-world networks, which typically display broad degree distributions that can significantly distort the results. Here we demonstrate how the generalization of blockmodels to incorporate this missing element leads to an improved objective function for community detection in complex networks. We also propose a heuristic algorithm for community detection using this objective function or its non-degree-corrected counterpart and show that the degree-corrected version dramatically outperforms the uncorrected one in both real-world and synthetic networks.Comment: 11 pages, 3 figure

Coexistence of opposite opinions in a network with communities

The Majority Rule is applied to a topology that consists of two coupled random networks, thereby mimicking the modular structure observed in social networks. We calculate analytically the asymptotic behaviour of the model and derive a phase diagram that depends on the frequency of random opinion flips and on the inter-connectivity between the two communities. It is shown that three regimes may take place: a disordered regime, where no collective phenomena takes place; a symmetric regime, where the nodes in both communities reach the same average opinion; an asymmetric regime, where the nodes in each community reach an opposite average opinion. The transition from the asymmetric regime to the symmetric regime is shown to be discontinuous.Comment: 14 pages, 4 figure

Power-law distributions in empirical data

Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution -- the part of the distribution representing large but rare events -- and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out.Comment: 43 pages, 11 figures, 7 tables, 4 appendices; code available at http://www.santafe.edu/~aaronc/powerlaws

Mapping the Urban Lead Exposome: A Detailed Analysis of Soil Metal Concentrations at the Household Scale Using Citizen Science

An ambitious citizen science effort in the city of Indianapolis (IN, USA) led to the collection and analysis of a large number of samples at the property scale, facilitating the analysis of differences in soil metal concentrations as a function of property location (i.e., dripline, yard, and street) and location within the city. This effort indicated that dripline soils had substantially higher values of lead and zinc than other soil locations on a given property, and this pattern was heightened in properties nearer the urban core. Soil lead values typically exceeded the levels deemed safe for children’s play areas in the United States (<400 ppm), and almost always exceeded safe gardening guidelines (<200 ppm). As a whole, this study identified locations within properties and cities that exhibited the highest exposure risk to children, and also exhibited the power of citizen science to produce data at a spatial scale (i.e., within a property boundary), which is usually impossible to feasibly collect in a typical research study

Organizational Chart Inference

Nowadays, to facilitate the communication and cooperation among employees, a new family of online social networks has been adopted in many companies, which are called the "enterprise social networks" (ESNs). ESNs can provide employees with various professional services to help them deal with daily work issues. Meanwhile, employees in companies are usually organized into different hierarchies according to the relative ranks of their positions. The company internal management structure can be outlined with the organizational chart visually, which is normally confidential to the public out of the privacy and security concerns. In this paper, we want to study the IOC (Inference of Organizational Chart) problem to identify company internal organizational chart based on the heterogeneous online ESN launched in it. IOC is very challenging to address as, to guarantee smooth operations, the internal organizational charts of companies need to meet certain structural requirements (about its depth and width). To solve the IOC problem, a novel unsupervised method Create (ChArT REcovEr) is proposed in this paper, which consists of 3 steps: (1) social stratification of ESN users into different social classes, (2) supervision link inference from managers to subordinates, and (3) consecutive social classes matching to prune the redundant supervision links. Extensive experiments conducted on real-world online ESN dataset demonstrate that Create can perform very well in addressing the IOC problem.Comment: 10 pages, 9 figures, 1 table. The paper is accepted by KDD 201

Diffusive Capture Process on Complex Networks

We study the dynamical properties of a diffusing lamb captured by a diffusing lion on the complex networks with various sizes of $N$. We find that the life time $of a lamb scales as \sim N$ and the survival probability $S(N\to \infty,t)$ becomes finite on scale-free networks with degree exponent $\gamma>3$. However, $S(N,t)$ for $\gamma<3$ has a long-living tail on tree-structured scale-free networks and decays exponentially on looped scale-free networks. It suggests that the second moment of degree distribution $is the relevant factor for the dynamical properties in diffusive capture process. We numerically find that the normalized number of capture events at a node with degree$k$,$n(k)$, decreases as$n(k)\sim k^{-\sigma}$. When$\gamma<3$,$n(k)$still increases anomalously for$k\approx k_{max}$. We analytically show that$n(k)$satisfies the relation$n(k)\sim k^2P(k)$and the total number of capture events$N_{tot}$is proportional to$, which causes the $\gamma$ dependent behavior of $S(N,t)$ and $.Comment: 9 pages, 6 figure