Relevant Cycles in Chemical Reaction Networks

Gleiss, Petra M.; Stadler, Peter F.; Wagner, Andreas; Fell, David

doi:10.1142/s0219525901000140

Cited by 74 publications

(59 citation statements)

References 34 publications

(43 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This type of graph topology has also importance in biological scale-free networks (metabolic networks) [23,24], where the presence of closed cycles enables feedback regulation. As a further example we mention gene co-regulation networks [5].…”

Section: The Web Graph (Wg) As a Scale-free Cyclic Graphmentioning

confidence: 99%

Information super-diffusion on structured networks

Tadić

Thurner

2004

Physica A: Statistical Mechanics and its Applications

107

View full text Add to dashboard Cite

We study diffusion of information packets on several classes of structured networks. Packets diffuse from a randomly chosen node to a specified destination in the network. As local transport rules we consider random diffusion and an improved local search method. Numerical simulations are performed in the regime of stationary workloads away from the jamming transition. We find that graph topology determines the properties of diffusion in a universal way, which is reflected by powerlaws in the transit-time and velocity distributions of packets. With the use of multifractal scaling analysis and arguments of non-extensive statistics we find that these power-laws are compatible with super-diffusive traffic for random diffusion and for improved local search. We are able to quantify the role of network topology on overall transport efficiency. Further, we demonstrate the implications of improved transport rules and discuss the importance of matching (global) topology with (local) transport rules for the optimal function of networks. The presented model should be applicable to a wide range of phenomena ranging from Internet traffic to protein transport along the cytoskeleton in biological cells.

show abstract

Section: The Web Graph (Wg) As a Scale-free Cyclic Graphmentioning

confidence: 99%

Information super-diffusion on structured networks

Tadić

Thurner

2004

Physica A: Statistical Mechanics and its Applications

107

View full text Add to dashboard Cite

show abstract

“…1 for parameter β = 3, corresponding to α = 0.25 in Eqs. (1)(2). For comparison we also simulate the distributions of outgoing and incoming links in the case of fully random directed network.…”

Section: Growth Model and Rank Distributionsmentioning

confidence: 99%

“…Understanding the evolution of complex networks [1][2][3][4][5][6][7][8][9][10][11][12][13] remains a challenging problem of modern statistical physics. Modeling the dynamic structure of these networks has significant practical applications, for instance in the design of search and control algorithms and in predicting emergence of new phenomena in information networks [5].…”

Section: Introductionmentioning

confidence: 99%

“…For instance, the hierarchically connected networks are shown [10] to be robust to large failure rates, however, they are vulnerable to removal of a few 'key nodes'. The inhomogeneous structure of connections has been found in metabolic cycles [1], in various social networks [2], including the science citation network [3], and the Internet [4] and the world-wide Web [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamics of directed graphs: the world-wide Web

Tadić

2001

Physica A: Statistical Mechanics and its Applications

113

139

View full text Add to dashboard Cite

We introduce and simulate a growth model of the world-wide Web based on the dynamics of outgoing links that is motivated by the conduct of the agents in the real Web to update outgoing links (re)directing them towards constantly changing selected nodes. Emergent statistical correlation between the distributions of outgoing and incoming links is a key feature of the dynamics of the Web. The growth phase is characterized by temporal fractal structures which are manifested in the hierarchical organization of links. We obtain quantitative agreement with the recent empirical data in the real Web for the distributions of in-and out-links and for the size of connected component. In a fully grown network of N nodes we study the structure of connected clusters of nodes that are accessible along outgoing links from a randomly selected node. The distributions of size and depth of the connected clusters with a giant component exhibit supercritical behavior. By decreasing the control parameter-average fraction β of updated and added links per time step-towards βc(N ) < 10% the Web can resume a critical structure with no giant component in it. We find a different universality class when the updates of links are not allowed, i.e., for β ≡ 0, corresponding to the network of science citations.

show abstract

“…It is therefore of immediate interest to determine which features are generic properties of large-scale reaction networks and which properties are the consequence of a particular chemistry. For instance, do all large reaction networks exhibit the powerlaw degree distribution that is indicative of small world networks [4,5], as suggested by data reported in [6]? If this hypothesis should prove to be true it immediately raises the question whether there are other significant differences that imply a natural classification of naturally occurring reaction networks.…”

Section: Introductionmentioning

confidence: 99%

A Graph-Based Toy Model of Chemistry

Benkö

Flamm

Stadler

2003

J. Chem. Inf. Comput. Sci.

Self Cite

View full text Add to dashboard Cite

Large scale chemical reaction networks are a ubiquitous phenomenon, from the metabolism of living cells to processes in planetary atmospheres and chemical technology. At least some of these networks exhibit distinctive global features such as the "small world" behavior. The systematic study of such properties, however, suffers from substantial sampling biases in the few networks that are known in detail. A computational model for generating them is therefore required. Here we present a Toy Model that provides a consistent framework in which generic properties of extensive chemical reaction networks can be explored in detail and that at the same time preserves the "look-and-feel" of chemistry: Molecules are represented as labeled graphs, i.e., by their structural formulae; their basic properties are derived by a caricature version of the Extended Hückel MO theory that operates directly on the graphs; chemical reaction mechanisms are implemented as graph rewriting rules acting on the structural formulae; reactivities and selectivities are modeled by a variant of the Frontier Molecular Orbital Theory based on the Extended Hückel scheme. The approach is illustrated for two types of reaction networks: Diels-Alder reactions and the formose reaction implicated in prebiotic sugar synthesis.

show abstract

Relevant Cycles in Chemical Reaction Networks

Cited by 74 publications

References 34 publications

Information super-diffusion on structured networks

Information super-diffusion on structured networks

Dynamics of directed graphs: the world-wide Web

A Graph-Based Toy Model of Chemistry

Contact Info

Product

Resources

About