Extracting the multiscale backbone of complex weighted networks

A large number of complex systems find a natural abstraction in the form of weighted networks whose nodes represent the elements of the system and the weighted edges identify the presence of an interaction and its relative strength. In recent years, the study of an increasing number of large scale networks has highlighted the statistical heterogeneity of their interaction pattern, with degree and weight distributions which vary over many orders of magnitude. These features, along with the large number of elements and links, make the extraction of the truly relevant connections forming the network's backbone a very challenging problem. More specifically, coarse-graining approaches and filtering techniques are at struggle with the multiscale nature of large scale systems. Here we define a filtering method that offers a practical procedure to extract the relevant connection backbone in complex multiscale networks, preserving the edges that represent statistical significant deviations with respect to a null model for the local assignment of weights to edges. An important aspect of the method is that it does not belittle small-scale interactions and operates at all scales defined by the weight distribution. We apply our method to real world network instances and compare the obtained results with alternative backbone extraction techniques

Robustness and modular structure in networks

Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives [1, 2]. A critical property of a network is its resilience to random breakdown and failure [3-6], typically studied as a percolation problem [7-9] or by modeling cascading failures [10-12]. Many complex systems, from power grids and the Internet to the brain and society [13-15], can be modeled using modular networks comprised of small, densely connected groups of nodes [16, 17]. These modules often overlap, with network elements belonging to multiple modules [18, 19]. Yet existing work on robustness has not considered the role of overlapping, modular structure. Here we study the robustness of these systems to the failure of elements. We show analytically and empirically that it is possible for the modules themselves to become uncoupled or non-overlapping well before the network disintegrates. If overlapping modular organization plays a role in overall functionality, networks may be far more vulnerable than predicted by conventional percolation theory.Comment: 14 pages, 9 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

Information filtering in complex weighted networks

Many systems in nature, society and technology can be described as networks, where the vertices are the system's elements and edges between vertices indicate the interactions between the corresponding elements. Edges may be weighted if the interaction strength is measurable. However, the full network information is often redundant because tools and techniques from network analysis do not work or become very inefficient if the network is too dense and some weights may just reflect measurement errors, and shall be discarded. Moreover, since weight distributions in many complex weighted networks are broad, most of the weight is concentrated among a small fraction of all edges. It is then crucial to properly detect relevant edges. Simple thresholding would leave only the largest weights, disrupting the multiscale structure of the system, which is at the basis of the structure of complex networks, and ought to be kept. In this paper we propose a weight filtering technique based on a global null model (GloSS filter), keeping both the weight distribution and the full topological structure of the network. The method correctly quantifies the statistical significance of weights assigned independently to the edges from a given distribution. Applications to real networks reveal that the GloSS filter is indeed able to identify relevantconnections between vertices.Comment: 9 pages, 7 figures, 1 Table. The GloSS filter is implemented in a freely downloadable software (http://filrad.homelinux.org/resources

Nonparametric Sparsification of Complex Multiscale Networks

Many real-world networks tend to be very dense. Particular examples of interest arise in the construction of networks that represent pairwise similarities between objects. In these cases, the networks under consideration are weighted, generally with positive weights between any two nodes. Visualization and analysis of such networks, especially when the number of nodes is large, can pose significant challenges which are often met by reducing the edge set. Any effective “sparsification” must retain and reflect the important structure in the network. A common method is to simply apply a hard threshold, keeping only those edges whose weight exceeds some predetermined value. A more principled approach is to extract the multiscale “backbone” of a network by retaining statistically significant edges through hypothesis testing on a specific null model, or by appropriately transforming the original weight matrix before applying some sort of threshold. Unfortunately, approaches such as these can fail to capture multiscale structure in which there can be small but locally statistically significant similarity between nodes. In this paper, we introduce a new method for backbone extraction that does not rely on any particular null model, but instead uses the empirical distribution of similarity weight to determine and then retain statistically significant edges. We show that our method adapts to the heterogeneity of local edge weight distributions in several paradigmatic real world networks, and in doing so retains their multiscale structure with relatively insignificant additional computational costs. We anticipate that this simple approach will be of great use in the analysis of massive, highly connected weighted networks