Multilayer Networks

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure

An introduction to Graph Data Management

A graph database is a database where the data structures for the schema and/or instances are modeled as a (labeled)(directed) graph or generalizations of it, and where querying is expressed by graph-oriented operations and type constructors. In this article we present the basic notions of graph databases, give an historical overview of its main development, and study the main current systems that implement them

A Relational Hyperlink Analysis of an Online Social Movement

In this paper we propose relational hyperlink analysis (RHA) as a distinct approach for empirical social science research into hyperlink networks on the World Wide Web. We demonstrate this approach, which employs the ideas and techniques of social network analysis (in particular, exponential random graph modeling), in a study of the hyperlinking behaviors of Australian asylum advocacy groups. We show that compared with the commonly-used hyperlink counts regression approach, relational hyperlink analysis can lead to fundamentally different conclusions about the social processes underpinning hyperlinking behavior. In particular, in trying to understand why social ties are formed, counts regressions may over-estimate the role of actor attributes in the formation of hyperlinks when endogenous, purely structural network effects are not taken into account. Our analysis involves an innovative joint use of two software programs: VOSON, for the automated retrieval and processing of considerable quantities of hyperlink data, and LPNet, for the statistical modeling of social network data. Together, VOSON and LPNet enable new and unique research into social networks in the online world, and our paper highlights the importance of complementary research tools for social science research into the web

HYPA: Efficient Detection of Path Anomalies in Time Series Data on Networks

The unsupervised detection of anomalies in time series data has important applications in user behavioral modeling, fraud detection, and cybersecurity. Anomaly detection has, in fact, been extensively studied in categorical sequences. However, we often have access to time series data that represent paths through networks. Examples include transaction sequences in financial networks, click streams of users in networks of cross-referenced documents, or travel itineraries in transportation networks. To reliably detect anomalies, we must account for the fact that such data contain a large number of independent observations of paths constrained by a graph topology. Moreover, the heterogeneity of real systems rules out frequency-based anomaly detection techniques, which do not account for highly skewed edge and degree statistics. To address this problem, we introduce HYPA, a novel framework for the unsupervised detection of anomalies in large corpora of variable-length temporal paths in a graph. HYPA provides an efficient analytical method to detect paths with anomalous frequencies that result from nodes being traversed in unexpected chronological order.Comment: 11 pages with 8 figures and supplementary material. To appear at SIAM Data Mining (SDM 2020

Kaskade: Graph Views for Efficient Graph Analytics

Graphs are an increasingly popular way to model real-world entities and relationships between them, ranging from social networks to data lineage graphs and biological datasets. Queries over these large graphs often involve expensive subgraph traversals and complex analytical computations. These real-world graphs are often substantially more structured than a generic vertex-and-edge model would suggest, but this insight has remained mostly unexplored by existing graph engines for graph query optimization purposes. Therefore, in this work, we focus on leveraging structural properties of graphs and queries to automatically derive materialized graph views that can dramatically speed up query evaluation. We present KASKADE, the first graph query optimization framework to exploit materialized graph views for query optimization purposes. KASKADE employs a novel constraint-based view enumeration technique that mines constraints from query workloads and graph schemas, and injects them during view enumeration to significantly reduce the search space of views to be considered. Moreover, it introduces a graph view size estimator to pick the most beneficial views to materialize given a query set and to select the best query evaluation plan given a set of materialized views. We evaluate its performance over real-world graphs, including the provenance graph that we maintain at Microsoft to enable auditing, service analytics, and advanced system optimizations. Our results show that KASKADE substantially reduces the effective graph size and yields significant performance speedups (up to 50X), in some cases making otherwise intractable queries possible