Mapping higher-order network flows in memory and multilayer networks with Infomap

@article{Edler2017MappingHN,
  title={Mapping higher-order network flows in memory and multilayer networks with Infomap},
  author={Daniel Edler and Ludvig Bohlin and Martin Rosvall},
  journal={ArXiv},
  year={2017},
  volume={abs/1706.04792}
}
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 ... 

Figures and Tables from this paper

Toward higher-order network models
Complex systems play an essential role in our daily lives. These systems consist of many connected components that interact with each other. Consider, for example, society with billions of collabor
From networks to optimal higher-order models of complex systems
Rich data are revealing that complex dependencies between the nodes of a network may not be captured by models based on pairwise interactions. Higher-order network models go beyond these limitations,
Understanding Complex Systems: From Networks to Optimal Higher-Order Models
TLDR
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.
Predicting Influential Higher-Order Patterns in Temporal Network Data
TLDR
Eight centrality measures based on MOGen, a multi-order generative model that accounts for all paths up to a maximum distance but disregards paths at higher distances are proposed, showing strong evidence supporting the hypothesis that network models, which capture only direct interactions, are likely to misidentify inential nodes in complex networks.
Mapping flows on hypergraphs
TLDR
Unipartite, bipartite and multilayer network representations of hypergraph flows are derived and how they and the underlying random-walk model change the number, size, depth, and overlap of identified multilevel communities are explored to help researchers choose the appropriate modelling approach when mapping flows on hypergraphs.
Mapping flows on sparse networks with missing links.
TLDR
Results in both synthetic and real-world networks show that the Bayesian estimate of the map equation provides a principled approach to revealing significant structures in undersampled networks.
Representing Big Data as Networks: New Methods and Insights
TLDR
This dissertation proposes theHigher-order network, which is a critical piece for representing higher-order interaction data; it introduces a scalable algorithm for building the network, and visualization tools for interactive exploration, and presents broad applications of the higher- order network in the real-world.
A dynamical perspective to community detection in ecological networks
TLDR
Infomap is an established community-detection method that maps flows on networks into modules based on random walks that has strong potential to provide new insights into the organisation of ecological networks, that are more relevant to the system/question at hand, compared to methods that ignore dynamics.
Mapping Flows in Bipartite Networks
TLDR
The community landscape of bipartite real-world networks from no node- type information to full node-type information is explored and it is found that using node types at a higher rate generally leads to deeper community hierarchies and a higher resolution.
Identifying flow modules in ecological networks using Infomap
TLDR
Infomap is a flexible tool that can identify modules in virtually any type of ecological network and is particularly useful for directed, weighted and multilayer networks and it is illustrated how Infomap works on all these network types.
...
...

References

SHOWING 1-10 OF 37 REFERENCES
Identifying modular flows on multilayer networks reveals highly overlapping organization in social systems
TLDR
To comprehend interconnected systems across the social and natural sciences, researchers have developed many powerful methods to identify functional modules, and for example, with interaction data agregation, these methods have become increasingly important.
Maps of sparse Markov chains efficiently reveal community structure in network flows with memory
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 mod
Representing higher-order dependencies in networks
TLDR
The higher-order network (HON) representation is proposed, including accuracy, scalability, and direct compatibility with the existing suite of network analysis methods, and it is illustrated how HON can be applied to a broad variety of tasks, such as random walking, clustering, and ranking.
Betweenness Preference: Quantifying Correlations in the Topological Dynamics of Temporal Networks
TLDR
It is shown that betweenness preference is present in empirical temporal network data and that it influences the length of the shortest time-respecting paths, and it is argued that neglecting betweenness preferences leads to wrong conclusions about dynamical processes on temporal networks.
Mathematical Formulation of Multilayer Networks
TLDR
This paper introduces a tensorial framework to study multilayer networks, and discusses the generalization of several important network descriptors and dynamical processes—including degree centrality, clustering coefficients, eigenvectorcentrality, modularity, von Neumann entropy, and diffusion—for this framework.
The architecture of complex weighted networks.
TLDR
This work studies the scientific collaboration network and the world-wide air-transportation network, which are representative examples of social and large infrastructure systems, respectively, and defines appropriate metrics combining weighted and topological observables that enable it to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices.
Memory in network flows and its effects on spreading dynamics and community detection.
TLDR
It is suggested that accounting for higher-order memory in network flows can help to better understand how real systems are organized and function.
Maps of random walks on complex networks reveal community structure
TLDR
An information theoretic approach is introduced that reveals community structure in weighted and directed networks of large-scale biological and social systems and reveals a directional pattern of citation from the applied fields to the basic sciences.
...
...