How people interact in evolving online affiliation networks

The study of human interactions is of central importance for understanding the behavior of individuals, groups, and societies. Here, we observe the formation and evolution of networks by monitoring the addition of all new links, and we analyze quantitatively the tendencies used to create ties in these evolving online affiliation networks. We show that an accurate estimation of these probabilistic tendencies can be achieved only by following the time evolution of the network. Inferences about the reason for the existence of links using statistical analysis of network snapshots must therefore be made with great caution. Here, we start by characterizing every single link when the tie was established in the network. This information allows us to describe the probabilistic tendencies of tie formation and extract meaningful sociological conclusions. We also find significant differences in behavioral traits in the social tendencies among individuals according to their degree of activity, gender, age, popularity, and other attributes. For instance, in the particular data sets analyzed here, we find that women reciprocate connections 3 times as much as men and that this difference increases with age. Men tend to connect with the most popular people more often than women do, across all ages. On the other hand, triangular tie tendencies are similar, independent of gender, and show an increase with age. These results require further validation in other social settings. Our findings can be useful to build models of realistic social network structures and to discover the underlying laws that govern establishment of ties in evolving social networks

Anisotropic thermally activated diffusion in percolation systems

We present a study of static and frequency-dependent diffusion with anisotropic thermally activated transition rates in a two-dimensional bond percolation system. The approach accounts for temperature effects on diffusion coefficients in disordered anisotropic systems. Static diffusion shows an Arrhenius behavior for low temperatures with an activation energy given by the highest energy barrier of the system. From the frequency-dependent diffusion coefficients we calculate a characteristic frequency $\omega_{c}\sim 1/t_{c}$, related to the time $t_c$ needed to overcome a characteristic barrier. We find that $\omega_c$ follows an Arrhenius behavior with different activation energies in each direction.Comment: 5 pages, 4 figure

Scaling of mean first-passage time as efficiency measure of nodes sending information on scale-free Koch networks

A lot of previous work showed that the sectional mean first-passage time (SMFPT), i.e., the average of mean first-passage time (MFPT) for random walks to a given hub node (node with maximum degree) averaged over all starting points in scale-free small-world networks exhibits a sublinear or linear dependence on network order $N$ (number of nodes), which indicates that hub nodes are very efficient in receiving information if one looks upon the random walker as an information messenger. Thus far, the efficiency of a hub node sending information on scale-free small-world networks has not been addressed yet. In this paper, we study random walks on the class of Koch networks with scale-free behavior and small-world effect. We derive some basic properties for random walks on the Koch network family, based on which we calculate analytically the partial mean first-passage time (PMFPT) defined as the average of MFPTs from a hub node to all other nodes, excluding the hub itself. The obtained closed-form expression displays that in large networks the PMFPT grows with network order as $N \ln N$, which is larger than the linear scaling of SMFPT to the hub from other nodes. On the other hand, we also address the case with the information sender distributed uniformly among the Koch networks, and derive analytically the entire mean first-passage time (EMFPT), namely, the average of MFPTs between all couples of nodes, the leading scaling of which is identical to that of PMFPT. From the obtained results, we present that although hub nodes are more efficient for receiving information than other nodes, they display a qualitatively similar speed for sending information as non-hub nodes. Moreover, we show that the location of information sender has little effect on the transmission efficiency. The present findings are helpful for better understanding random walks performed on scale-free small-world networks.Comment: Definitive version published in European Physical Journal

Mean first-passage time for random walks on undirected networks

In this paper, by using two different techniques we derive an explicit formula for the mean first-passage time (MFPT) between any pair of nodes on a general undirected network, which is expressed in terms of eigenvalues and eigenvectors of an associated matrix similar to the transition matrix. We then apply the formula to derive a lower bound for the MFPT to arrive at a given node with the starting point chosen from the stationary distribution over the set of nodes. We show that for a correlated scale-free network of size $N$ with a degree distribution $P(d)\sim d^{-\gamma}$, the scaling of the lower bound is $N^{1-1/\gamma}$. Also, we provide a simple derivation for an eigentime identity. Our work leads to a comprehensive understanding of recent results about random walks on complex networks, especially on scale-free networks.Comment: 7 pages, no figures; definitive version published in European Physical Journal

MetroNet: A Metropolitan Simulation Model Based on Commuting Processes

Part 3: Short PapersInternational audienceThe aim of this work is to identify a set of fundamental rules that govern the interactions within urban systems at the metropolitan scale. For that, we developed an USM (Urban Simulation Model) specifically designed to study the evolution and dynamics of systems of cities. Our model is innovative in its structure: it is a superposition of cellular automata and agent based modeling approaches (that are essentially spatial analyses) and a complex network approach (that is essentially a topological analysis). This implies that in our model, the local activities and interaction of agents give rise to the global urban structure and network that in turn affects the agents’ cognition, behavior, movement and action in the city and so on in circular causality. The model simulates commuting patterns of agents within a metropolis. The agents in our model represent workers who look for working places, the nodes represent urban employment centers, and the links represent commuters. Our results address three issues: the first suggests that the perception of urban boundaries plays a significant role in the metropolitan evolution in terms of network topology. This means that the existence of business centers, located in proximity to each other (but belonging to different municipalities) may lead to the emergence of new centers at the metropolis scale. The second issue concerns urban segregation; our results suggest that the location preferences of the agents regarding proximity to similar/different agents have a major affect not only on the urban morphology but also on the topology of the urban network. The third and last issue concerns the size distributions of agents in our model; these distributions correspond to all types of homogenous distributions observed in real system of cities

SDSS J211852.96−073227.5: The first non-local, interacting, late-type intermediate Seyfert galaxy with relativistic jets

It has been often suggested that a tangible relation exists between relativistic jets in active galactic nuclei (AGN) and the morphology of their host galaxies. In particular, relativistic jets may commonly be related to merging events. Here we present for the first time a detailed spectroscopic and morphological analysis of a Seyfert galaxy, SDSS J211852.96−073227.5, at z = 0.26. This source has previously been classified as a gamma-ray emitting narrow-line Seyfert 1 galaxy. We re-observed it with the 6.5 m Clay Telescope and these new, high-quality spectroscopic data have revealed that it is actually an intermediate-type Seyfert galaxy. Furthermore, the results of modelling the Ks-band near-infrared images obtained with the 6.5 m Baade Telescope indicate that the AGN is hosted by a late-type galaxy in an interacting system, strengthening the suggested connection between galaxy interactions and relativistic jets

Controlling self-organized criticality in complex networks

A control scheme to reduce the size of avalanches of the Bak-Tang-Wiesenfeld model on complex networks is proposed. Three network types are considered: those proposed by Erdős-Renyi, Goh-Kahng-Kim, and a real network representing the main connections of the electrical power grid of the western United States. The control scheme is based on the idea of triggering avalanches in the highest degree nodes that are near to become critical. We show that this strategy works in the sense that the dissipation of mass occurs most locally avoiding larger avalanches. We also compare this strategy with a random strategy where the nodes are chosen randomly. Although the random control has some ability to reduce the probability of large avalanches, its performance is much worse than the one based on the choice of the highest degree nodes. Finally, we argue that the ability of the proposed control scheme is related to its ability to reduce the concentration of mass on the network. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010