scholarly journals The evolution of network topology by selective removal

2005 ◽  
Vol 2 (5) ◽  
pp. 533-536 ◽  
Author(s):  
Marcel Salathé ◽  
Robert M May ◽  
Sebastian Bonhoeffer
Keyword(s):  
Network Topology ◽  
Biological Networks ◽  
Preferential Attachment ◽  
Protein Interaction Networks ◽  
Interaction Networks ◽  
Network Growth ◽  
Scale Free ◽  
The Past ◽  
The World ◽  
Growing Networks

The topology of large social, technical and biological networks such as the World Wide Web or protein interaction networks has caught considerable attention in the past few years (reviewed in Newman 2003 ), and analysis of the structure of such networks revealed that many of them can be classified as broad-tailed, scale-free-like networks, since their vertex connectivities follow approximately a power-law. Preferential attachment of new vertices to highly connected vertices is commonly seen as the main mechanism that can generate scale-free connectivity in growing networks ( Watts 2004 ). Here, we propose a new model that can generate broad-tailed networks even in the absence of network growth, by not only adding vertices, but also selectively eliminating vertices with a probability that is inversely related to the sum of their first- and second order connectivity.

scholarly journals RECIPROCITY AND THE EMERGENCE OF POWER LAWS IN SOCIAL NETWORKS

2006 ◽  
Vol 17 (07) ◽  
pp. 1067-1076 ◽  
Author(s):  
MICHAEL SCHNEGG
Keyword(s):  
Social Networks ◽  
Power Laws ◽  
Scaling Exponent ◽  
Policy Makers ◽  
Public Health Programs ◽  
Scale Free ◽  
The Past ◽  
Naturally Occurring ◽  
Growing Networks ◽  
Law Degree

Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the existing network with a probability proportional to its number of links (= degree). Little is known about whether the same principles of local attachment and global properties apply to societies as well. Empirical evidence from six ethnographic case studies shows that complex social networks have significantly lower scaling exponents γ ~ 1 than have been assumed in the past. Apparently humans do not only look for the most prominent players to play with. Moreover cooperation in humans is characterized through reciprocity, the tendency to give to those from whom one has received in the past. Both variables — reciprocity and the scaling exponent — are negatively correlated (r = -0.767, sig = 0.075). If we include this effect in simulations of growing networks, degree distributions emerge that are much closer to those empirically observed. While the proportion of nodes with small degrees decreases drastically as we introduce reciprocity, the scaling exponent is more robust and changes only when a relatively large proportion of attachment decisions follow this rule. If social networks are less scale free than previously assumed this has far reaching implications for policy makers, public health programs and marketing alike.

scholarly journals Topological network alignment uncovers biological function and phylogeny

2010 ◽  
Vol 7 (50) ◽  
pp. 1341-1354 ◽  
Author(s):  
Oleksii Kuchaiev ◽  
Tijana Milenković ◽  
Vesna Memišević ◽  
Wayne Hayes ◽  
Nataša Pržulj
Keyword(s):  
Network Topology ◽  
Biological Networks ◽  
Biological Function ◽  
Protein Interaction Networks ◽  
Phylogenetic Information ◽  
Protein Protein Interaction ◽  
Species Phylogeny ◽  
Topological Network ◽  
Protein Protein Interaction Networks ◽  
Life On Earth

Sequence comparison and alignment has had an enormous impact on our understanding of evolution, biology and disease. Comparison and alignment of biological networks will probably have a similar impact. Existing network alignments use information external to the networks, such as sequence, because no good algorithm for purely topological alignment has yet been devised. In this paper, we present a novel algorithm based solely on network topology, that can be used to align any two networks. We apply it to biological networks to produce by far the most complete topological alignments of biological networks to date. We demonstrate that both species phylogeny and detailed biological function of individual proteins can be extracted from our alignments. Topology-based alignments have the potential to provide a completely new, independent source of phylogenetic information. Our alignment of the protein–protein interaction networks of two very different species—yeast and human—indicate that even distant species share a surprising amount of network topology, suggesting broad similarities in internal cellular wiring across all life on Earth.

Scale-free growing networks imply linear preferential attachment

2001 ◽  
Vol 65 (1) ◽  
Author(s):  
Kasper Astrup Eriksen ◽  
Michael Hörnquist
Keyword(s):  
Preferential Attachment ◽  
Scale Free ◽  
Growing Networks

scholarly journals Refining modules to determine functionally significant clusters in molecular networks

2019 ◽  
Author(s):  
Rama Kaalia ◽  
Jagath C. Rajapakse
Keyword(s):  
Protein Interaction ◽  
Biological Networks ◽  
Protein Interaction Networks ◽  
Interaction Networks ◽  
Molecular Networks ◽  
Resolution Limit ◽  
Protein Protein Interaction ◽  
Functional Coverage ◽  
Topological Modules ◽  
Protein Protein Interaction Networks

AbstractModule detection algorithms relying on modularity maximization suffer from an inherent resolution limit that hinders detection of small topological modules, especially in molecular networks where most biological processes are believed to form small and compact communities. We propose a novel modular refinement approach that helps finding functionally significant modules of molecular networks. The module refinement algorithm improves the quality of topological modules in protein-protein interaction networks by finding biologically functionally significant modules. The algorithm is based on the fact that functional modules in biology do not necessarily represent those corresponding to maximum modularity. Larger modules corresponding to maximal modularity are incrementally re-modularized again under specific constraints so that smaller yet topologically and biologically valid modules are recovered. We show improvement in quality and functional coverage of modules using experiments on synthetic and real protein-protein interaction networks. Results were also compared with six existing methods available for clustering biological networks. In conclusion, the proposed algorithm finds smaller but functionally relevant modules that are undetected by classical quality maximization approaches for modular detection. The refinement procedure helps to detect more functionally enriched modules in protein-protein interaction networks, which are also more coherent with functionally characterised gene sets.

Incorporating Network Topology Improves Prediction of Protein Interaction Networks from Transcriptomic Data

2013 ◽  
pp. 203-221
Author(s):  
Peter E. Larsen ◽  
Frank Collart ◽  
Yang Dai
Keyword(s):  
Experimental Data ◽  
Protein Interaction ◽  
Network Topology ◽  
Biological Networks ◽  
Dimensional Space ◽  
Interaction Networks ◽  
Protein Protein Interactions ◽  
Transcriptomic Data ◽  
Protein Protein Interaction ◽  
Ppi Networks

The reconstruction of protein-protein interaction (PPI) networks from high-throughput experimental data is one of the most challenging problems in bioinformatics. These biological networks have specific topologies defined by the functional and evolutionary relationships between the proteins and the physical limitations imposed on proteins interacting in the three-dimensional space. In this paper, the authors propose a novel approach for the identification of potential protein-protein interactions based on the integration of known PPI network topology and transcriptomic data. The proposed method, Function Restricted Value Neighborhood (FRV-N), was used to reconstruct PPI networks using an experimental data set consisting of 170 yeast microarray profiles. The results of this analysis demonstrate that incorporating knowledge of interactome topology improves the ability of transcriptome analysis to reconstruct interaction networks with a high degree of biological relevance.

Discovery and Existence of Communities in the World Wide Web

2010 ◽  
pp. 436-442
Author(s):  
Antonis Sidiropoulos ◽  
Dimitrios Katsaros ◽  
Yannis Manolopoulos
Keyword(s):  
Social Networks ◽  
Social Network ◽  
World Wide Web ◽  
World Wide ◽  
Sexual Relationships ◽  
Network Growth ◽  
Scale Free ◽  
The World ◽  
Degree Structure ◽  
The Web

The World Wide Web, or simply Web, is a characteristic example of a social network (Newman, 2003; Wasserman & Faust, 1994). Other examples of social networks include the food web network, scientific collaboration networks, sexual relationships networks, metabolic networks, and air transportation networks. Socials networks are usually abstracted as graphs, comprised by vertices, edges (directed or not), and in some cases, with weights on these edges. Social network theory is concerned with properties related to connectivity (degree, structure, centrality), distances (diameter, shortest paths), “resilience” (geodesic edges or vertices, articulation vertices) of these graphs, models of network growth. Social networks have been studied long before the conception of the Web. Pioneering works for the characterization of the Web as a social network and for the study of its basic properties are due to the work of Barabasi and its colleagues (Albert, Jeong & Barabasi, 1999). Later, several studies investigated other aspects like its growth (Bianconi & Barabasi, 2001; Menczer, 2004; Pennock, Flake, Lawrence, Glover, & Giles, 2002; Watts & Strogatz, 1998), its “small-world” nature in that pages can reach other pages with only a small number of links, and its scale-free nature (Adamic & Huberman, 2000; Barabasi & Albert, 1999; Barabasi & Bonabeau, 2003) (i.e., a feature implying that it is dominated by a relatively small number of Web pages that are connected to many others; these pages are called hubs and have a seemingly unlimited number of hyperlinks). Thus, the distribution of Web page linkages follows a power law in that most nodes have just a few hyperlinks and some have a tremendous number of links In that sense, the system has no “scale” (see Figure 1).

Incorporating Network Topology Improves Prediction of Protein Interaction Networks from Transcriptomic Data

2010 ◽  
Vol 1 (3) ◽  
pp. 1-19 ◽  
Author(s):  
Peter E. Larsen ◽  
Frank Collart ◽  
Yang Dai
Keyword(s):  
Experimental Data ◽  
Protein Interaction ◽  
Network Topology ◽  
Protein Interactions ◽  
Biological Networks ◽  
Dimensional Space ◽  
Interaction Networks ◽  
Data Set ◽  
Transcriptomic Data ◽  
Ppi Networks

The reconstruction of protein-protein interaction (PPI) networks from high-throughput experimental data is one of the most challenging problems in bioinformatics. These biological networks have specific topologies defined by the functional and evolutionary relationships between the proteins and the physical limitations imposed on proteins interacting in the three-dimensional space. In this paper, the authors propose a novel approach for the identification of potential protein-protein interactions based on the integration of known PPI network topology and transcriptomic data. The proposed method, Function Restricted Value Neighborhood (FRV-N), was used to reconstruct PPI networks using an experimental data set consisting of 170 yeast microarray profiles. The results of this analysis demonstrate that incorporating knowledge of interactome topology improves the ability of transcriptome analysis to reconstruct interaction networks with a high degree of biological relevance.

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.

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