Complexity and robustness in hypernetwork models of metabolism

Metabolic reaction data is commonly modelled using a complex network approach, whereby nodes represent the chemical species present within the organism of interest, and connections are formed between those nodes participating in the same chemical reaction. Unfortunately, such an approach provides an inadequate description of the metabolic process in general, as a typical chemical reaction will involve more than two nodes, thus risking over-simplification of the the system of interest in a potentially significant way. In this paper, we employ a complex hypernetwork formalism to investigate the robustness of bacterial metabolic hypernetworks by extending the concept of a percolation process to hypernetworks. Importantly, this provides a novel method for determining the robustness of these systems and thus for quantifying their resilience to random attacks/errors. Moreover, we performed a site percolation analysis on a large cohort of bacterial metabolic networks and found that hypernetworks that evolved in more variable enviro nments displayed increased levels of robustness and topological complexity

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

Attributed Stream Hypergraphs: temporal modeling of node-attributed high-order interactions

Recent advances in network science have resulted in two distinct research directions aimed at augmenting and enhancing representations for complex networks. The first direction, that of high-order modeling, aims to focus on connectivity between sets of nodes rather than pairs, whereas the second one, that of feature-rich augmentation, incorporates into a network all those elements that are driven by information which is external to the structure, like node properties or the flow of time. This paper proposes a novel toolbox, that of Attributed Stream Hypergraphs (ASHs), unifying both high-order and feature-rich elements for representing, mining, and analyzing complex networks. Applied to social network analysis, ASHs can characterize complex social phenomena along topological, dynamic and attributive elements. Experiments on real-world face-to-face and online social media interactions highlight that ASHs can easily allow for the analyses, among others, of high-order groups' homophily, nodes' homophily with respect to the hyperedges in which nodes participate, and time-respecting paths between hyperedges.Comment: Submitted to "Applied Network Science

Hyperlink prediction via local random walks and Jensen-Shannon divergence

Many real-world systems involving higher-order interactions can be modeled by hypergraphs, where vertices represent the systemic units and hyperedges describe the interactions among them. In this paper, we focus on the problem of hyperlink prediction which aims at inferring missing hyperlinks based on observed hyperlinks. We propose three similarity indices for hyperlink prediction based on local random walks and Jensen-Shannon divergence. Numerical experiments show that the proposed indices outperform the state-of-the-art methods on a broad range of datasets.Comment: IoP Latex, 15 pages, 1 figure

A class of models for random hypergraphs

Despite the recently exhibited importance of higher-order interactions for various processes, few flexible (null) models are available. In particular, most studies on hypergraphs focus on a small set of theoretical models. Here, we introduce a class of models for random hypergraphs which displays a similar level of flexibility of complex network models and where the main ingredient is the probability that a node belongs to a hyperedge. When this probability is a constant, we obtain a random hypergraph in the same spirit as the Erdos-Renyi graph. This framework also allows us to introduce different ingredients such as the preferential attachment for hypergraphs, or spatial random hypergraphs. In particular, we show that for the Erdos-Renyi case there is a transition threshold scaling as $1/\sqrt{EN}$ where $N$ is the number of nodes and $E$ the number of hyperedges. We also discuss a random geometric hypergraph which displays a percolation transition for a threshold distance scaling as $r_c^*\sim 1/\sqrt{E}$. For these various models, we provide results for the most interesting measures, and also introduce new ones in the spatial case for characterizing the geometrical properties of hyperedges. These different models might serve as benchmarks useful for analyzing empirical data.Comment: 10 pages, 10 figure

Unravelling the complexity of metabolic networks

Network science provides an invaluable set of tools and techniques for improving our understanding of many important biological processes at the systems level. A network description provides a simplied view of such a system, focusing upon the interactions between a usually large number of similar biological units. At the cellular level, these units are usually interacting genes, proteins or small molecules, resulting in various types of biological networks. Metabolic networks, in particular, play a fundamental role, since they provide the building blocks essential for cellular function, and thus, have recently received a lot of attention. In particular, recent studies have revealed a number of universal topological characteristics, such as a small average path-length, large clustering coecient and a hierarchical modular structure. Relations between structure, function and evolution, however, for even the simplest of organisms is far from understood. In this thesis, we employ network analysis in order to determine important links between an organism's metabolic network structure and the environment under which it evolved. We address this task from two dierent perspectives: (i) a network classication approach; and (ii) a more physiologically realistic modelling approach, namely hypernetwork models. One of the major contributions of this thesis is the development of a novel graph embedding approach, based on low-order network motifs, that compares the structural properties of large numbers of biological networks simultaneously. This method was prototyped on a cohort of 383 bacterial networks, and provides powerful evidence for the role that both environmental variability, and oxygen requirements, play in the forming of these important networked structures. In addition to this, we consider a hypernetwork formalism of metabolism, in an attempt to extend complex network reasoning to this more complicated, yet physiologically more realistic setting. In particular, we extend the concept of network reciprocity to hypernetworks, and again evidence a signicant relationship between bacterial hypernetwork structure and the environment in which these organisms evolved. Moreover, we extend the concept of network percolation to undirected hypernetworks, as a technique for quantifying robustness and fragility within metabolic hypernetworks, and in the process nd yet further evidence of increased topological complexity within organisms inhabiting more uncertain environments. Importantly, many of these relationships are not apparent when considering the standard approach, thus suggesting that a hypernetwork formalism has the potential to reveal biologically relevant information that is beyond the standard network approach