1,241 research outputs found
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
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
On functional module detection in metabolic networks
Functional modules of metabolic networks are essential for understanding the metabolism of an organism as a whole. With the vast amount of experimental data and the construction of complex and large-scale, often genome-wide, models, the computer-aided identification of functional modules becomes more and more important. Since steady states play a key role in biology, many methods have been developed in that context, for example, elementary flux modes, extreme pathways, transition invariants and place invariants. Metabolic networks can be studied also from the point of view of graph theory, and algorithms for graph decomposition have been applied for the identification of functional modules. A prominent and currently intensively discussed field of methods in graph theory addresses the Q-modularity. In this paper, we recall known concepts of module detection based on the steady-state assumption, focusing on transition-invariants (elementary modes) and their computation as minimal solutions of systems of Diophantine equations. We present the Fourier-Motzkin algorithm in detail. Afterwards, we introduce the Q-modularity as an example for a useful non-steady-state method and its application to metabolic networks. To illustrate and discuss the concepts of invariants and Q-modularity, we apply a part of the central carbon metabolism in potato tubers (Solanum tuberosum) as running example. The intention of the paper is to give a compact presentation of known steady-state concepts from a graph-theoretical viewpoint in the context of network decomposition and reduction and to introduce the application of Q-modularity to metabolic Petri net models
AI-driven Hypernetwork of Organic Chemistry: Network Statistics and Applications in Reaction Classification
Rapid discovery of new reactions and molecules in recent years has been
facilitated by the advancements in high throughput screening, accessibility to
a much more complex chemical design space, and the development of accurate
molecular modeling frameworks. A holistic study of the growing chemistry
literature is, therefore, required that focuses on understanding the recent
trends and extrapolating them into possible future trajectories. To this end,
several network theory-based studies have been reported that use a directed
graph representation of chemical reactions. Here, we perform a study based on
representing chemical reactions as hypergraphs where the hyperedges represent
chemical reactions and nodes represent the participating molecules. We use a
standard reactions dataset to construct a hypernetwork and report its
statistics such as degree distributions, average path length, assortativity or
degree correlations, PageRank centrality, and graph-based clusters (or
communities). We also compute each statistic for an equivalent directed graph
representation of reactions to draw parallels and highlight differences between
the two. To demonstrate the AI applicability of hypergraph reaction
representation, we generate dense hypergraph embeddings and use them in the
reaction classification problem. We conclude that the hypernetwork
representation is flexible, preserves reaction context, and uncovers hidden
insights that are otherwise not apparent in a traditional directed graph
representation of chemical reactions
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