Ricci curvature of the Internet topology

Ni, Chien-Chun; Lin, Yu-Chih; Gao, Jie; Gu, Xianfeng; Saucan, Emil

doi:10.1109/infocom.2015.7218668

Cited by 70 publications

(85 citation statements)

References 47 publications

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“…There are several types of curvature notions, among them Ricci curvature is known to be the most useful for analyzing the complex networks [16][17][18][19][20][21][22][23][28][29][30][31][32][33]. Ricci curvature measures deviance of geodesics (shortest path) relative to Euclidean shortest-paths and is related to mass transport or entropy (Wasserstein metrics) [34][35][36].…”

Section: Curvature-based Methods For Complex Networkmentioning

confidence: 99%

“…Application of graph theory have been utilized to study global impact of long term sickle cell disease on brain [9], to diagnose pre-symptomatic Alzheimer's disease [10][11][12], to understand the human brain network [13,14]. Recently, the development of geometry based measures is significantly attracting the focus of researchers to characterize the structural aspect of complex networks [15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

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Integrative Computational Framework for Understanding Metabolic Modulation in Leishmania

Chauhan

Singh

2019

Preprint

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The integration of computational and mathematical approaches is used to provide a key insight into the biological systems. Here, we seek to find detailed and more robust information on Leishmanial metabolic network by performing mathematical characterization in terms of Forman/Forman-Ricci curvature measures combined with flux balance analysis (FBA). The model prototype developed largely depends on its structure and topological components. The correlation of curvature measures with various network statistical properties revealed the structural-functional framework. The analyses helped us to identify the importance of several nodes and detect sub-networks. Our results revealed several key high curvature nodes (metabolites) belonging to common yet crucial metabolic, thus, maintaining the integrity of the network which signifies its robustness. Further analysis revealed the presence of some of these metabolites in redox metabolism of the parasite. MGO, an important node, has highly cytotoxic and mutagenic nature that can irreversibly modify DNA, proteins and enzymes, making them nonfunctional, leading to the formation of AGEs and MGO •-. Being a component in the glyoxalase pathway, we further attempted to study the outcome of the deletion of the key enzyme (GLOI) mainly involved in the neutralization of MGO by utilizing FBA. The model and the objective function both kept as simple as possible, demonstrated an interesting emergent behavior. The nonfunctional GLOI in the model contributed to 'zero' flux which signifies the key role of GLOI as a rate limiting enzyme. This has led to several fold increase production of MGO, thereby, causing an increased level of MGO •generation. Hence, the integrated computational approaches has deciphered GLOI as a potential target both from curvature measures as well as FBA which could further be explored for kinetic modeling by implying various redox-dependent constraints on the model. Designing various in vitro experimental perspectives could churn the therapeutic importance of GLOI.Leishmaniasis, one of the most neglected tropical diseases in the world, is of primary concern due to the increased risk of emerging drug resistance. To design novel drugs and search effective molecular drug targets with therapeutic importance, it is important to decipher the relation among the components responsible for leishmanial parasite survival inside the host cell at the metabolic level. Here, we have attempted to get an insight in the leishmanial metabolic network and predict the importance of key metabolites by applying mathematical characterization in terms of curvature measures and flux balance analysis (FBA). Our results identified several metabolites playing significant role in parasite's redox homeostasis. Among these MGO (methylglyoxal) caught our interest due to its highly toxic and reactive nature of irreversibly modifying DNA and proteins. FBA results helped us to look into the important role of GLOI (Glyoxalase I), the enzyme that catalyses the detoxification of MGO, in the pathway tha...

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Section: Curvature-based Methods For Complex Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Integrative Computational Framework for Understanding Metabolic Modulation in Leishmania

Chauhan

Singh

2019

Preprint

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“…In particular, a network will be flat, i.e., it will have Forman-Ricci curvature equal to zero, if its growth and geodesics dispersion rates will be similar to that of the Euclidean plane. This aspect represents a further motivation for studying the Ricci curvature of networks, since it allows one to distinguish numerically between expander type networks of negative curvature, such as information networks, and small world networks that are, on average, of strictly positive curvature (see also [25]). We will further explore this in a forthcoming article [36].…”

Section: Forman-ricci Curvature On Networkmentioning

confidence: 99%

“…Those mainly build on a combinatorial version introduced by Chow and Luo [40]. However, other discretizations of the flow, with reported applications in network and imaging sciences, are explored in the literature [25,41].…”

Section: Ricci-flow With Forman Curvaturementioning

confidence: 99%

Forman-Ricci Flow for Change Detection in Large Dynamic Data Sets

Weber

Jost

Saucan

2016

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Abstract:We present a viable geometric solution for the detection of dynamic effects in complex networks. Building on Forman's discretization of the classical notion of Ricci curvature, we introduce a novel geometric method to characterize different types of real-world networks with an emphasis on peer-to-peer networks. We study the classical Ricci-flow in a network-theoretic setting and introduce an analytic tool for characterizing dynamic effects. The formalism suggests a computational method for change detection and the identification of fast evolving network regions and yields insights into topological properties and the structure of the underlying data.

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“…It proved to be an easy, yet powerful tool for the exploration of geometric and related analytic properties of graphs and related structures (see, for instance, [25][26][27]). Moreover, Ollivier's Ricci curvature proved itself to represent an excellent tool for the analysis of complex networks, in their various avatars, as communication [28,29], biological [30], economical [31] or transportation [22] networks.…”

mentioning

confidence: 99%