Temporal similarity metrics for latent network reconstruction: The role of time-lag decay

When investigating the spreading of a piece of information or the diffusion of an innovation, we often lack information on the underlying propagation network. Reconstructing the hidden propagation paths based on the observed diffusion process is a challenging problem which has recently attracted attention from diverse research fields. To address this reconstruction problem, based on static similarity metrics commonly used in the link prediction literature, we introduce new node-node temporal similarity metrics. The new metrics take as input the time-series of multiple independent spreading processes, based on the hypothesis that two nodes are more likely to be connected if they were often infected at similar points in time. This hypothesis is implemented by introducing a time-lag function which penalizes distant infection times. We find that the choice of this time-lag strongly affects the metrics' reconstruction accuracy, depending on the network's clustering coefficient and we provide an extensive comparative analysis of static and temporal similarity metrics for network reconstruction. Our findings shed new light on the notion of similarity between pairs of nodes in complex networks

Multiplexity versus correlation: the role of local constraints in real multiplexes

Several real-world systems can be represented as multi-layer complex networks, i.e. in terms of a superposition of various graphs, each related to a different mode of connection between nodes. Hence, the definition of proper mathematical quantities aiming at capturing the level of complexity of those systems is required. Various attempts have been made to measure the empirical dependencies between the layers of a multiplex, for both binary and weighted networks. In the simplest case, such dependencies are measured via correlation-based metrics: we show that this is equivalent to the use of completely homogeneous benchmarks specifying only global constraints, such as the total number of links in each layer. However, these approaches do not take into account the heterogeneity in the degree and strength distributions, which are instead a fundamental feature of real-world multiplexes. In this work, we compare the observed dependencies between layers with the expected values obtained from reference models that appropriately control for the observed heterogeneity in the degree and strength distributions. This leads to novel multiplexity measures that we test on different datasets, i.e. the International Trade Network (ITN) and the European Airport Network (EAN). Our findings confirm that the use of homogeneous benchmarks can lead to misleading results, and furthermore highlight the important role played by the distribution of hubs across layers.Comment: 32 pages, 6 figure

Fast Community Identification by Hierarchical Growth

A new method for community identification is proposed which is founded on the analysis of successive neighborhoods, reached through hierarchical growth from a starting vertex, and on the definition of communities as a subgraph whose number of inner connections is larger than outer connections. In order to determine the precision and speed of the method, it is compared with one of the most popular community identification approaches, namely Girvan and Newman's algorithm. Although the hierarchical growth method is not as precise as Girvan and Newman's method, it is potentially faster than most community finding algorithms.Comment: 6 pages, 5 figure

Traveling Trends: Social Butterflies or Frequent Fliers?

Trending topics are the online conversations that grab collective attention on social media. They are continually changing and often reflect exogenous events that happen in the real world. Trends are localized in space and time as they are driven by activity in specific geographic areas that act as sources of traffic and information flow. Taken independently, trends and geography have been discussed in recent literature on online social media; although, so far, little has been done to characterize the relation between trends and geography. Here we investigate more than eleven thousand topics that trended on Twitter in 63 main US locations during a period of 50 days in 2013. This data allows us to study the origins and pathways of trends, how they compete for popularity at the local level to emerge as winners at the country level, and what dynamics underlie their production and consumption in different geographic areas. We identify two main classes of trending topics: those that surface locally, coinciding with three different geographic clusters (East coast, Midwest and Southwest); and those that emerge globally from several metropolitan areas, coinciding with the major air traffic hubs of the country. These hubs act as trendsetters, generating topics that eventually trend at the country level, and driving the conversation across the country. This poses an intriguing conjecture, drawing a parallel between the spread of information and diseases: Do trends travel faster by airplane than over the Internet?Comment: Proceedings of the first ACM conference on Online social networks, pp. 213-222, 201

Network Effects, Congestion Externalities, and Air Traffic Delays: Or Why All Delays Are Not Evil

We examine two factors that might explain the extent of air traffic delays in the United States: network benefits due to hubbing and congestion externalities. Airline hubs enable passengers to cross-connect to many destinations, thus creating network benefits that increase in the number of markets served from the hub. Delays are the equilibrium outcome of a hub airline equating high marginal benefits from hubbing with the marginal cost of delays. Congestion externalities are created when airlines do not consider that adding flights may lead to increased delays for other air carriers. In this case, delays represent a market failure. Using data on all domestic flights by major US carriers from 1988-2000, we find that delays are increasing in hubbing activity at an airport and decreasing in market concentration but the hubbing effect dominates empirically. In addition, most delays due to hubbing actually accrue to the hub carrier, primarily because the hub carrier clusters its flights in short spans of time in order to maximize passenger interconnections. Non hub flights at hub airports operate with minimal additional travel time by avoiding the congested peak connecting times of the hub carrier. These results suggest that an optimal congestion tax would have a relatively small impact on air traffic delays since hub carriers already internalize most of the costs of hubbing and a tax that did not take the network benefits of hubbing into account could reduce social welfare.

A survey on Human Mobility and its applications

Human Mobility has attracted attentions from different fields of studies such as epidemic modeling, traffic engineering, traffic prediction and urban planning. In this survey we review major characteristics of human mobility studies including from trajectory-based studies to studies using graph and network theory. In trajectory-based studies statistical measures such as jump length distribution and radius of gyration are analyzed in order to investigate how people move in their daily life, and if it is possible to model this individual movements and make prediction based on them. Using graph in mobility studies, helps to investigate the dynamic behavior of the system, such as diffusion and flow in the network and makes it easier to estimate how much one part of the network influences another by using metrics like centrality measures. We aim to study population flow in transportation networks using mobility data to derive models and patterns, and to develop new applications in predicting phenomena such as congestion. Human Mobility studies with the new generation of mobility data provided by cellular phone networks, arise new challenges such as data storing, data representation, data analysis and computation complexity. A comparative review of different data types used in current tools and applications of Human Mobility studies leads us to new approaches for dealing with mentioned challenges