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Comprehending complex systems by simplifying and highlighting important dynamical patterns requires modeling and mapping higher-order network flows. However, complex systems come in many forms and demand a range of representations,…
To better understand the flows of ideas or information through social and biological systems, researchers develop maps that reveal important patterns in network flows. In practice, network flow models have implied memoryless first-order…
Complex systems made of interacting elements are commonly abstracted as networks, in which nodes are associated with dynamic state variables, whose evolution is driven by interactions mediated by the edges. Markov processes have been the…
Random walks on networks is the standard tool for modelling spreading processes in social and biological systems. This first-order Markov approach is used in conventional community detection, ranking, and spreading analysis although it…
Hypergraphs offer an explicit formalism to describe multibody interactions in complex systems. To connect dynamics and function in systems with these higher-order interactions, network scientists have generalised random-walk models to…
Many networks in nature, society and technology are characterized by a mesoscopic level of organization, with groups of nodes forming tightly connected units, called communities or modules, that are only weakly linked to each other.…
To better understand the overlapping modular organization of large networks with respect to flow, here we introduce the map equation for overlapping modules. In this information-theoretic framework, we use the correspondence between…
To comprehend the multipartite organization of large-scale biological and social systems, we introduce a new information theoretic approach that reveals community structure in weighted and directed networks. The method decomposes a network…
Networks are a powerful tool to model the structure and dynamics of complex systems across scales. Direct connections between system components are often represented as edges, while paths and walks capture indirect interactions. This…
Mapping network flows provides insight into the organization of networks, but even though many real-networks are bipartite, no method for mapping flows takes advantage of the bipartite structure. What do we miss by discarding this…
Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. In this work we propose a principled framework to model the organization of…
Detection of overlapping communities in complex networks has motivated recent research in the relevant fields. Aiming this problem, we propose a Markov dynamics based algorithm, called UEOC, which means, 'unfold and extract overlapping…
A network community-based reduced-order model is developed to capture key interactions amongst coherent structures in high-dimensional unsteady vortical flows. The present approach is data-inspired and founded on network-theoretic…
Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the…
A fundamental problem in the analysis of network data is the detection of network communities, groups of densely interconnected nodes, which may be overlapping or disjoint. Here we describe a method for finding overlapping communities based…
Networks have become a key approach to understanding systems of interacting objects, unifying the study of diverse phenomena including biological organisms and human society. One crucial step when studying the structure and dynamics of…
Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to…
Unveiling the community structure of networks is a powerful methodology to comprehend interconnected systems across the social and natural sciences. To identify different types of functional modules in interaction data aggregated in a…
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…
As research into community finding in social networks progresses, there is a need for algorithms capable of detecting overlapping community structure. Many algorithms have been proposed in recent years that are capable of assigning each…