Functional centrality in graphs

In this paper we introduce the functional centrality as a generalization of the subgraph centrality. We propose a general method for characterizing nodes in the graph according to the number of closed walks starting and ending at the node. Closed walks are appropriately weighted according to the topological features that we need to measure

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

Ranking sets of morbidities using hypergraph centrality

Multi-morbidity, the health state of having two or more concurrent chronic conditions, is becoming more common as populations age, but is poorly understood. Identifying and understanding commonly occurring sets of diseases is important to inform clinical decisions to improve patient services and outcomes. Network analysis has been previously used to investigate multi-morbidity, but a classic application only allows for information on binary sets of diseases to contribute to the graph. We propose the use of hypergraphs, which allows for the incorporation of data on people with any number of conditions, and also allows us to obtain a quantitative understanding of the centrality, a measure of how well connected items in the network are to each other, of both single diseases and sets of conditions. Using this framework we illustrate its application with the set of conditions described in the Charlson morbidity index using data extracted from routinely collected population-scale, patient level electronic health records (EHR) for a cohort of adults in Wales, UK. Stroke and diabetes were found to be the most central single conditions. Sets of diseases featuring diabetes; diabetes with Chronic Pulmonary Disease, Renal Disease, Congestive Heart Failure and Cancer were the most central pairs of diseases. We investigated the differences between results obtained from the hypergraph and a classic binary graph and found that the cen-trality of diseases such as paraplegia, which are connected strongly to a single other disease is exaggerated in binary graphs compared to hypergraphs. The measure of centrality is derived from the weighting metrics calculated for disease sets and further investigation is needed to better understand the effect of the metric used in identifying the clinical significance and ranked centrality of grouped diseases. These initial results indicate that hypergraphs can be used as a valuable tool for analysing previously poorly understood relationships and in-formation available in EHR data

Predicting Multi-actor collaborations using Hypergraphs

Social networks are now ubiquitous and most of them contain interactions involving multiple actors (groups) like author collaborations, teams or emails in an organizations, etc. Hypergraphs are natural structures to effectively capture multi-actor interactions which conventional dyadic graphs fail to capture. In this work the problem of predicting collaborations is addressed while modeling the collaboration network as a hypergraph network. The problem of predicting future multi-actor collaboration is mapped to hyperedge prediction problem. Given that the higher order edge prediction is an inherently hard problem, in this work we restrict to the task of predicting edges (collaborations) that have already been observed in past. In this work, we propose a novel use of hyperincidence temporal tensors to capture time varying hypergraphs and provides a tensor decomposition based prediction algorithm. We quantitatively compare the performance of the hypergraphs based approach with the conventional dyadic graph based approach. Our hypothesis that hypergraphs preserve the information that simple graphs destroy is corroborated by experiments using author collaboration network from the DBLP dataset. Our results demonstrate the strength of hypergraph based approach to predict higher order collaborations (size>4) which is very difficult using dyadic graph based approach. Moreover, while predicting collaborations of size>2 hypergraphs in most cases provide better results with an average increase of approx. 45% in F-Score for different sizes = {3,4,5,6,7}