12 research outputs found
Reticula: A temporal network and hypergraph analysis software package
In the last decade, temporal networks and static and temporal hypergraphs
have enabled modelling connectivity and spreading processes in a wide array of
real-world complex systems such as economic transactions, information
spreading, brain activity and disease spreading. In this manuscript, we present
the Reticula C++ library and Python package: A comprehensive suite of tools for
working with real-world and synthetic static and temporal networks and
hypergraphs. This includes various methods of creating synthetic networks and
randomised null models based on real-world data, calculating reachability and
simulating compartmental models on networks. The library is designed
principally on an extensible, cache-friendly representation of networks, with
an aim of easing multi-thread use in the high-performance computing
environment
Weighted temporal event graphs
The times of temporal-network events and their correlations contain
information on the function of the network and they influence dynamical
processes taking place on it. To extract information out of correlated event
times, techniques such as the analysis of temporal motifs have been developed.
We discuss a recently-introduced, more general framework that maps
temporal-network structure into static graphs while retaining information on
time-respecting paths and the time differences between their consequent events.
This framework builds on weighted temporal event graphs: directed, acyclic
graphs (DAGs) that contain a superposition of all temporal paths. We introduce
the reader to the temporal event-graph mapping and associated computational
methods and illustrate its use by applying the framework to temporal-network
percolation
Embedded representations of social interactions
Social interactions have been the focus of social science research for a century, but their study has recently been revolutionized by novel data sources and by methods from computer science, network science, and complex systems science. The study of social interactions is crucial for understanding complex societal behaviours. Social interactions are naturally represented as networks, which have emerged as a unifying mathematical language to understand structural and dynamical aspects of socio-technical systems. Networks are, however, highly dimensional objects, especially when considering the scales of real-world systems and the need to model the temporal dimension. Hence the study of empirical data from social systems is challenging both from a conceptual and a computational standpoint. A possible approach to tackling such a challenge is to use dimensionality reduction techniques that represent network entities in a low-dimensional feature space, preserving some desired properties of the original data. Low-dimensional vector space representations, also known as network embeddings, have been extensively studied, also as a way to feed network data to machine learning algorithms. Network embeddings were initially developed for static networks and then extended to incorporate temporal network data. We focus on dimensionality reduction techniques for time-resolved social interaction data modelled as temporal networks. We introduce a novel embedding technique that models the temporal and structural similarities of events rather than nodes. Using empirical data on social interactions, we show that this representation captures information relevant for the study of dynamical processes unfolding over the network, such as epidemic spreading. We then turn to another large-scale dataset on social interactions: a popular Web-based crowdfunding platform. We show that tensor-based representations of the data and dimensionality reduction techniques such as tensor factorization allow us to uncover the structural and temporal aspects of the system and to relate them to geographic and temporal activity patterns
Mapping temporal-network percolation to weighted, static event graphs
12 pages, 3 figuresMany processes of spreading and diffusion take place on temporal networks, and their outcomes are influenced by correlations in the times of contact. These correlations have a particularly strong influence on processes where the spreading agent has a limited lifetime at nodes: disease spreading (recovery time), diffusion of rumors (lifetime of information), and passenger routing (maximum acceptable time between transfers). Here, we introduce weighted event graphs as a powerful and fast framework for studying connectivity determined by time-respecting paths where the allowed waiting times between contacts have an upper limit. We study percolation on the weighted event graphs and in the underlying temporal networks, with simulated and real-world networks. We show that this type of temporal-network percolation is analogous to directed percolation, and that it can be characterized by multiple order parameters
Mapping temporal-network percolation to weighted, static event graphs
12 pages, 3 figuresMany processes of spreading and diffusion take place on temporal networks, and their outcomes are influenced by correlations in the times of contact. These correlations have a particularly strong influence on processes where the spreading agent has a limited lifetime at nodes: disease spreading (recovery time), diffusion of rumors (lifetime of information), and passenger routing (maximum acceptable time between transfers). Here, we introduce weighted event graphs as a powerful and fast framework for studying connectivity determined by time-respecting paths where the allowed waiting times between contacts have an upper limit. We study percolation on the weighted event graphs and in the underlying temporal networks, with simulated and real-world networks. We show that this type of temporal-network percolation is analogous to directed percolation, and that it can be characterized by multiple order parameters
Mapping temporal-network percolation to weighted, static event graphs
12 pages, 3 figuresMany processes of spreading and diffusion take place on temporal networks, and their outcomes are influenced by correlations in the times of contact. These correlations have a particularly strong influence on processes where the spreading agent has a limited lifetime at nodes: disease spreading (recovery time), diffusion of rumors (lifetime of information), and passenger routing (maximum acceptable time between transfers). Here, we introduce weighted event graphs as a powerful and fast framework for studying connectivity determined by time-respecting paths where the allowed waiting times between contacts have an upper limit. We study percolation on the weighted event graphs and in the underlying temporal networks, with simulated and real-world networks. We show that this type of temporal-network percolation is analogous to directed percolation, and that it can be characterized by multiple order parameters