A survey of statistical network models

Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference

Understanding Complex Systems: From Networks to Optimal Higher-Order Models

To better understand the structure and function of complex systems, researchers often represent direct interactions between components in complex systems with networks, assuming that indirect influence between distant components can be modelled by paths. Such network models assume that actual paths are memoryless. That is, the way a path continues as it passes through a node does not depend on where it came from. Recent studies of data on actual paths in complex systems question this assumption and instead indicate that memory in paths does have considerable impact on central methods in network science. A growing research community working with so-called higher-order network models addresses this issue, seeking to take advantage of information that conventional network representations disregard. Here we summarise the progress in this area and outline remaining challenges calling for more research.Comment: 8 pages, 4 figure

Unfolding the Multi-layered Structure of the French Mediascape

Unfolding the Multi-layered Structure of the French Mediascap

Detecting Cohesive and 2-mode Communities in Directed and Undirected Networks

Networks are a general language for representing relational information among objects. An effective way to model, reason about, and summarize networks, is to discover sets of nodes with common connectivity patterns. Such sets are commonly referred to as network communities. Research on network community detection has predominantly focused on identifying communities of densely connected nodes in undirected networks. In this paper we develop a novel overlapping community detection method that scales to networks of millions of nodes and edges and advances research along two dimensions: the connectivity structure of communities, and the use of edge directedness for community detection. First, we extend traditional definitions of network communities by building on the observation that nodes can be densely interlinked in two different ways: In cohesive communities nodes link to each other, while in 2-mode communities nodes link in a bipartite fashion, where links predominate between the two partitions rather than inside them. Our method successfully detects both 2-mode as well as cohesive communities, that may also overlap or be hierarchically nested. Second, while most existing community detection methods treat directed edges as though they were undirected, our method accounts for edge directions and is able to identify novel and meaningful community structures in both directed and undirected networks, using data from social, biological, and ecological domains.Comment: Published in the proceedings of WSDM '1

Footprints of information foragers: Behaviour semantics of visual exploration

Social navigation exploits the knowledge and experience of peer users of information resources. A wide variety of visual–spatial approaches become increasingly popular as a means to optimize information access as well as to foster and sustain a virtual community among geographically distributed users. An information landscape is among the most appealing design options of representing and communicating the essence of distributed information resources to users. A fundamental and challenging issue is how an information landscape can be designed such that it will not only preserve the essence of the underlying information structure, but also accommodate the diversity of individual users. The majority of research in social navigation has been focusing on how to extract useful information from what is in common between users' profiles, their interests and preferences. In this article, we explore the role of modelling sequential behaviour patterns of users in augmenting social navigation in thematic landscapes. In particular, we compare and analyse the trails of individual users in thematic spaces along with their cognitive ability measures. We are interested in whether such trails can provide useful guidance for social navigation if they are embedded in a visual–spatial environment. Furthermore, we are interested in whether such information can help users to learn from each other, for example, from the ones who have been successful in retrieving documents. In this article, we first describe how users' trails in sessions of an experimental study of visual information retrieval can be characterized by Hidden Markov Models. Trails of users with the most successful retrieval performance are used to estimate parameters of such models. Optimal virtual trails generated from the models are visualized and animated as if they were actual trails of individual users in order to highlight behavioural patterns that may foster social navigation. The findings of the research will provide direct input to the design of social navigation systems as well as to enrich theories of social navigation in a wider context. These findings will lead to the further development and consolidation of a tightly coupled paradigm of spatial, semantic and social navigation

Mapping change in large networks

Change is a fundamental ingredient of interaction patterns in biology, technology, the economy, and science itself: Interactions within and between organisms change; transportation patterns by air, land, and sea all change; the global financial flow changes; and the frontiers of scientific research change. Networks and clustering methods have become important tools to comprehend instances of these large-scale structures, but without methods to distinguish between real trends and noisy data, these approaches are not useful for studying how networks change. Only if we can assign significance to the partitioning of single networks can we distinguish meaningful structural changes from random fluctuations. Here we show that bootstrap resampling accompanied by significance clustering provides a solution to this problem. To connect changing structures with the changing function of networks, we highlight and summarize the significant structural changes with alluvial diagrams and realize de Solla Price's vision of mapping change in science: studying the citation pattern between about 7000 scientific journals over the past decade, we find that neuroscience has transformed from an interdisciplinary specialty to a mature and stand-alone discipline.Comment: 10 pages, 4 figure