scholarly journals Gene divergence and pathway duplication in the metabolic network of yeast and digital organisms

2009 ◽  
Vol 6 (41) ◽  
pp. 1233-1245 ◽  
Author(s):  
P. Gerlee ◽  
T. Lundh ◽  
B. Zhang ◽  
A. R. A. Anderson
Keyword(s):  
Gene Function ◽  
Degree Distribution ◽  
Gene Networks ◽  
Preferential Attachment ◽  
Bipartite Network ◽  
Scale Free ◽  
Evolving Systems ◽  
Digital Organisms ◽  
Free Gene ◽  
Function Network

We have studied the metabolic gene–function network in yeast and digital organisms evolved in the artificial life platform A vida . The gene–function network is a bipartite network in which a link exists between a gene and a function (pathway) if that function depends on that gene, and can also be viewed as a decomposition of the more traditional functional gene networks, where two genes are linked if they share any function. We show that the gene–function network exhibits two distinct degree distributions: the gene degree distribution is scale-free while the pathway distribution is exponential. This is true for both yeast and digital organisms, which suggests that this is a general property of evolving systems, and we propose that the scale-free gene degree distribution is due to pathway duplication, i.e. the development of a new pathway where the original function is still retained. Pathway duplication would serve as preferential attachment for the genes, and the experiments with A vida revealed precisely this; genes involved in many pathways are more likely to increase their connectivity. Measuring the overlap between different pathways, in terms of the genes that constitute them, showed that pathway duplication also is a likely mechanism in yeast evolution. This analysis sheds new light on the evolution of genes and functionality, and suggests that function duplication could be an important mechanism in evolution.

scholarly journals Microarray analysis and scale-free gene networks identify candidate regulators in drought-stressed roots of loblolly pine (P. taeda L.)

BMC Genomics ◽  
2011 ◽  
Vol 12 (1) ◽  
Author(s):  
W Walter Lorenz ◽  
Rob Alba ◽  
Yuan-Sheng Yu ◽  
John M Bordeaux ◽  
Marta Simões ◽  
...  
Keyword(s):  
Microarray Analysis ◽  
Loblolly Pine ◽  
Gene Networks ◽  
Scale Free ◽  
Free Gene

GROWING HIERARCHICAL SCALE-FREE NETWORKS BY MEANS OF NONHIERARCHICAL PROCESSES

2007 ◽  
Vol 17 (07) ◽  
pp. 2447-2452 ◽  
Author(s):  
S. BOCCALETTI ◽  
D.-U. HWANG ◽  
V. LATORA
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Rate Equations ◽  
Scale Free ◽  
Scale Free Networks ◽  
Degree Correlations ◽  
Law Degree ◽  
Hierarchical Scale

We introduce a fully nonhierarchical network growing mechanism, that furthermore does not impose explicit preferential attachment rules. The growing procedure produces a graph featuring power-law degree and clustering distributions, and manifesting slightly disassortative degree-degree correlations. The rigorous rate equations for the evolution of the degree distribution and for the conditional degree-degree probability are derived.

scholarly journals Generation of 2-mode scale-free graphs for link-level internet topology modeling

PLoS ONE ◽  
2020 ◽  
Vol 15 (11) ◽  
pp. e0240100
Author(s):  
Khalid Bakhshaliyev ◽  
Mehmet Hadi Gunes
Keyword(s):  
Power Law ◽  
Degree Distribution ◽  
Autonomous Systems ◽  
Node Degree ◽  
Bipartite Network ◽  
Research Issues ◽  
Scale Free ◽  
Internet Topology ◽  
Scale Free Graphs ◽  
Multi Access

Comprehensive analysis that aims to understand the topology of real-world networks and the development of algorithms that replicate their characteristics has been significant research issues. Although the accuracy of newly developed network protocols or algorithms does not depend on the underlying topology, the performance generally depends on the topology. As a result, network practitioners have concentrated on generating representative synthetic topologies and utilize them to investigate the performance of their design in simulation or emulation environments. Network generators typically represent the Internet topology as a graph composed of point-to-point links. In this study, we discuss the implications of multi-access links on the synthetic network generation and modeling of the networks as bi-partite graphs to represent both subnetworks and routers. We then analyze the characteristics of sampled Internet topology data sets from backbone Autonomous Systems (AS) and observe that in addition to the commonly recognized power-law node degree distribution, the subnetwork size and the router interface distributions often exhibit power-law characteristics. We introduce a SubNetwork Generator (SubNetG) topology generation approach that incorporates the observed measurements to produce bipartite network topologies. In particular, generated topologies capture the 2-mode relation between the layer-2 (i.e., the subnetwork and interface distributions) and the layer-3 (i.e., the degree distribution) that is missing from the current network generators that produce 1-mode graphs. The SubNetG source code and experimental data is available at https://github.com/netml/sonet.

scholarly journals Scale-Free Property for Degrees and Weights in a Preferential Attachment Random Graph Model

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
István Fazekas ◽  
Bettina Porvázsnyik
Keyword(s):  
Asymptotic Behaviour ◽  
Random Graph ◽  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Graph Model ◽  
Random Graph Model ◽  
Scale Free ◽  
Attachment Model ◽  
Law Degree

A random graph evolution mechanism is defined. The evolution studied is a combination of the preferential attachment model and the interaction of four vertices. The asymptotic behaviour of the graph is described. It is proved that the graph exhibits a power law degree distribution; in other words, it is scale-free. It turns out that any exponent in(2,∞)can be achieved. The proofs are based on martingale methods.

scholarly journals Growing Scale-Free Simplices

2020 ◽  
Author(s):  
Kiriil Kovalenko ◽  
Irene Sendina-Nadal ◽  
Nagi Khalil ◽  
Alex Dainak ◽  
Daniil Musatov ◽  
...  
Keyword(s):  
Degree Distribution ◽  
Preferential Attachment ◽  
General Scheme ◽  
Simplicial Complexes ◽  
Generative Models ◽  
Scaling Exponents ◽  
Scale Free ◽  
Pairwise Interactions ◽  
Order Structures ◽  
Insight Into

Abstract The past two decades have seen significant successes in our understanding of networked systems, from the mapping of real-world networks to the establishment of generative models recovering their observed macroscopic patterns. These advances, however, are restricted to pairwise interactions and provide limited insight into higher-order structures. Such multi-component interactions can only be grasped through simplicial complexes, which have recently found applications in social, technological and biological contexts. Here we introduce, study, and characterize a model to grow simplicial complexes of order two, i.e. nodes, links and triangles. Specifically, through a combination of preferential and/or non preferential attachment mechanisms, the model constructs networks with a scale-free degree distribution and an either bounded or scale-free generalized degree distribution. Allowing to analytically control the scaling exponents we arrive at a highly general scheme by which one is able to construct ensembles of synthetic complexes displaying desired statistical properties.

scholarly journals Percolation phase transition in weight-dependent random connection models

2021 ◽  
Vol 53 (4) ◽  
pp. 1090-1114
Author(s):  
Peter Gracar ◽  
Lukas Lüchtrath ◽  
Peter Mörters
Keyword(s):  
Phase Transition ◽  
Poisson Process ◽  
Random Graphs ◽  
Power Law ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Dimensional Space ◽  
Geometric Model ◽  
Scale Free ◽  
Power Law Exponent

AbstractWe investigate spatial random graphs defined on the points of a Poisson process in d-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point is assigned an independent weight. Given the weight and position of the points, we form an edge between any pair of points independently with a probability depending on the two weights of the points and their distance. Preference is given to short edges and connections to vertices with large weights. We characterize the parameter regime where there is a non-trivial percolation phase transition and show that it depends not only on the power-law exponent of the degree distribution but also on a geometric model parameter. We apply this result to characterize robustness of age-based spatial preferential attachment networks.

scholarly journals Detecting different topologies immanent in scale-free networks with the same degree distribution

2019 ◽  
Vol 116 (14) ◽  
pp. 6701-6706 ◽  
Author(s):  
Dimitrios Tsiotas
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Network Topology ◽  
Degree Distribution ◽  
Growth Process ◽  
Preferential Attachment ◽  
Self Similarity ◽  
Scale Free ◽  
Scale Free Networks ◽  
Definition Of

The scale-free (SF) property is a major concept in complex networks, and it is based on the definition that an SF network has a degree distribution that follows a power-law (PL) pattern. This paper highlights that not all networks with a PL degree distribution arise through a Barabási−Albert (BA) preferential attachment growth process, a fact that, although evident from the literature, is often overlooked by many researchers. For this purpose, it is demonstrated, with simulations, that established measures of network topology do not suffice to distinguish between BA networks and other (random-like and lattice-like) SF networks with the same degree distribution. Additionally, it is examined whether an existing self-similarity metric proposed for the definition of the SF property is also capable of distinguishing different SF topologies with the same degree distribution. To contribute to this discrimination, this paper introduces a spectral metric, which is shown to be more capable of distinguishing between different SF topologies with the same degree distribution, in comparison with the existing metrics.

scholarly journals MODELLING COLLABORATION NETWORKS BASED ON NONLINEAR PREFERENTIAL ATTACHMENT

2007 ◽  
Vol 18 (02) ◽  
pp. 297-314 ◽  
Author(s):  
TAO ZHOU ◽  
BING-HONG WANG ◽  
YING-DI JIN ◽  
DA-REN HE ◽  
PEI-PEI ZHANG ◽  
...  
Keyword(s):  
Empirical Data ◽  
Degree Distribution ◽  
Alternative Model ◽  
Free Parameter ◽  
Preferential Attachment ◽  
Average Distance ◽  
Small World ◽  
Clustering Coefficient ◽  
Collaboration Networks ◽  
Scale Free

In this paper, we propose an alternative model for collaboration networks based on nonlinear preferential attachment. Depending on a single free parameter "preferential exponent", this model interpolates between networks with a scale-free and an exponential degree distribution. The degree distribution in the present networks can be roughly classified into four patterns, all of which are observed in empirical data. And this model exhibits small-world effect, which means the corresponding networks are of very short average distance and highly large clustering coefficient. More interesting, we find a peak distribution of act-size from empirical data which has not been emphasized before. Our model can produce the peak act-size distribution naturally that agrees with the empirical data well.

scholarly journals Random complex networks

2014 ◽  
Vol 1 (3) ◽  
pp. 357-367 ◽  
Author(s):  
Michael Small ◽  
Lvlin Hou ◽  
Linjun Zhang
Keyword(s):  
Complex Networks ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Small World ◽  
Node Degree ◽  
Scale Free ◽  
Wide Range ◽  
Random Complex ◽  
Law Degree ◽  
Attachment Process

Abstract Exactly what is meant by a ‘complex’ network is not clear; however, what is clear is that it is something other than a random graph. Complex networks arise in a wide range of real social, technological and physical systems. In all cases, the most basic categorization of these graphs is their node degree distribution. Particular groups of complex networks may exhibit additional interesting features, including the so-called small-world effect or being scale-free. There are many algorithms with which one may generate networks with particular degree distributions (perhaps the most famous of which is preferential attachment). In this paper, we address what it means to randomly choose a network from the class of networks with a particular degree distribution, and in doing so we show that the networks one gets from the preferential attachment process are actually highly pathological. Certain properties (including robustness and fragility) which have been attributed to the (scale-free) degree distribution are actually more intimately related to the preferential attachment growth mechanism. We focus here on scale-free networks with power-law degree sequences—but our methods and results are perfectly generic.

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