Understanding the large-scale structural network formed by neurons is a major challenge in system neuroscience. A detailed connectivity map covering the entire brain would therefore be of great value. Based on diffusion MRI, we propose an efficient methodology to generate large, comprehensive and individual white matter connectional datasets of the living or dead, human or animal brain. This non-invasive tool enables us to study the basic and potentially complex network properties of the entire brain. For two human subjects we find that their individual brain networks have an exponential node degree distribution and that their global organization is in the form of a small world.

Abstract-With more than 250 million active users [1], Facebook (FB) is currently one of the most important online social networks. Our goal in this paper is to obtain a representative (unbiased) sample of Facebook users by crawling its social graph. In this quest, we consider and implement several candidate techniques. Two approaches that are found to perform well are the Metropolis-Hasting random walk (MHRW) and a re-weighted random walk (RWRW). Both have pros and cons, which we demonstrate through a comparison to each other as well as to the "ground-truth" (UNI -obtained through true uniform sampling of FB userIDs). In contrast, the traditional Breadth-First-Search (BFS) and Random Walk (RW) perform quite poorly, producing substantially biased results. In addition to offline performance assessment, we introduce online formal convergence diagnostics to assess sample quality during the data collection process. We show how these can be used to effectively determine when a random walk sample is of adequate size and quality for subsequent use (i.e., when it is safe to cease sampling). Using these methods, we collect the first, to the best of our knowledge, unbiased sample of Facebook. Finally, we use one of our representative datasets, collected through MHRW, to characterize several key properties of Facebook.

Many complex networks are only a part of larger systems, where a number of coexisting topologies interact and depend on each other. We introduce a layered model to facilitate the description and analysis of such systems. As an example of its application, we study the load distribution in three transportation systems, where the lower layer is the physical infrastructure and the upper layer represents the traffic flows. This layered view allows us to capture the fundamental differences between the real load and commonly used load estimators, which explains why these estimators fail to approximate the real load. DOI: 10.1103/PhysRevLett.96.138701 PACS numbers: 89.75.Hc, 89.20.Hh, 89.40.Bb, 89.75.Fb In recent years, studies of biological, social, infrastructure, or technological networks have drawn a substantial amount of attention in the physics community. Although these networks are usually considered as distinct objects, they are often a part of larger complex systems, where a number of coexisting topologies interact and depend on each other. For instance, the topologies of the Internet at the IP layer [1], of the World Wide Web (WWW) [2], or of the networks formed by peer to peer (P2P) applications [3], although studied separately, are closely related: Each WWW or P2P link virtually connects two IP nodes. These two IP nodes are usually distant in the underlying IP topology, and the virtual connection is realized as a path found by IP routers. In other words, the graph formed by an application is mapped on the underlying IP network. Moreover, the IP links are in turn mapped on the physical layer [4] that consists of a mesh of optical fibers usually buried in the ground along roads, rails, or power lines. The resulting topologies at the three layers are very different from each other.Another important class of real-life systems is transportation networks. Graphs derived from the physical infrastructure of such networks were analyzed on the examples of a power grid [5], a railway network [6], road networks [7], or urban mass transportation systems [8]. This approach often gives a valuable insight into the studied topology, but it ignores the real-life traffic pattern. Interestingly, the networks of traffic flows were studied separately, for instance, the flows of people within a city [9] and commuting traffic flows between different cities [10]. These studies, in turn, neglect the underlying physical topology. A comprehensive view of the system often requires one to analyze both layers (physical and traffic) together. Only in some particular cases is one layer sufficient. This is the case, e.g., in airport networks [11], where all traffic flows are one-hop long and the full knowledge of the traffic pattern is introduced into the physical graph by setting the edge weights equal to the amount of traffic they carry. However, in the presence of traffic flows longer than one hop, a weighted physical graph is not sufficient.

Abstract-Our goal in this paper is to develop a practical framework for obtaining a uniform sample of users in an online social network (OSN) by crawling its social graph. Such a sample allows to estimate any user property and some topological properties as well. To this end, first, we consider and compare several candidate crawling techniques. Two approaches that can produce approximately uniform samples are the MetropolisHasting random walk (MHRW) and a re-weighted random walk (RWRW). Both have pros and cons, which we demonstrate through a comparison to each other as well as to the "ground truth." In contrast, using Breadth-First-Search (BFS) or an unadjusted Random Walk (RW) leads to substantially biased results. Second, and in addition to offline performance assessment, we introduce online formal convergence diagnostics to assess sample quality during the data collection process. We show how these diagnostics can be used to effectively determine when a random walk sample is of adequate size and quality. Third, as a case study, we apply the above methods to Facebook and we collect the first, to the best of our knowledge, representative sample of Facebook users. We make it publicly available and employ it to characterize several key properties of Facebook.

The knowledge of real-life traffic pattern is crucial for good understanding and analysis of transportation systems. This data is quite rare. In this paper we propose an algorithm for extracting both the real physical topology and the network of traffic flows from timetables of public mass transportation systems. We apply this algorithm to timetables of three large transportation networks. This enables us to make a systematic comparison between three different approaches to construct a graph representation of a transportation network; the resulting graphs are fundamentally different. We also find that the real-life traffic pattern is very heterogenous, both in space and traffic flow intensities.