15,870 research outputs found
Random Networks with given Rich-club Coefficient
In complex networks it is common to model a network or generate a surrogate
network based on the conservation of the network's degree distribution. We
provide an alternative network model based on the conservation of connection
density within a set of nodes. This density is measure by the rich-club
coefficient. We present a method to generate surrogates networks with a given
rich-club coefficient. We show that by choosing a suitable local linking term,
the generated random networks can reproduce the degree distribution and the
mixing pattern of real networks. The method is easy to implement and produces
good models of real networks.Comment: revised version, new figure
The Information Coded in the Yeast Response Elements Accounts for Most of the Topological Properties of Its Transcriptional Regulation Network
The regulation of gene expression in a cell relies to a major extent on transcription factors, proteins which recognize and bind the DNA at specific binding sites (response elements) within promoter regions associated with each gene. We present an information theoretic approach to modeling transcriptional regulatory networks, in terms of a simple “sequence-matching” rule and the statistics of the occurrence of binding sequences of given specificity in random promoter regions. The crucial biological input is the distribution of the amount of information coded in these cognate response elements and the length distribution of the promoter regions. We provide an analysis of the transcriptional regulatory network of yeast Saccharomyces cerevisiae, which we extract from the available databases, with respect to the degree distributions, clustering coefficient, degree correlations, rich-club coefficient and the k-core structure. We find that these topological features are in remarkable agreement with those predicted by our model, on the basis of the amount of information coded in the interaction between the transcription factors and response elements
Detecting rich-club ordering in complex networks
Uncovering the hidden regularities and organizational principles of networks
arising in physical systems ranging from the molecular level to the scale of
large communication infrastructures is the key issue for the understanding of
their fabric and dynamical properties [1-5]. The ``rich-club'' phenomenon
refers to the tendency of nodes with high centrality, the dominant elements of
the system, to form tightly interconnected communities and it is one of the
crucial properties accounting for the formation of dominant communities in both
computer and social sciences [4-8]. Here we provide the analytical expression
and the correct null models which allow for a quantitative discussion of the
rich-club phenomenon. The presented analysis enables the measurement of the
rich-club ordering and its relation with the function and dynamics of networks
in examples drawn from the biological, social and technological domains.Comment: 1 table, 3 figure
Structural constraints in complex networks
We present a link rewiring mechanism to produce surrogates of a network where
both the degree distribution and the rich--club connectivity are preserved. We
consider three real networks, the AS--Internet, the protein interaction and the
scientific collaboration. We show that for a given degree distribution, the
rich--club connectivity is sensitive to the degree--degree correlation, and on
the other hand the degree--degree correlation is constrained by the rich--club
connectivity. In particular, in the case of the Internet, the assortative
coefficient is always negative and a minor change in its value can reverse the
network's rich--club structure completely; while fixing the degree distribution
and the rich--club connectivity restricts the assortative coefficient to such a
narrow range, that a reasonable model of the Internet can be produced by
considering mainly the degree distribution and the rich--club connectivity. We
also comment on the suitability of using the maximal random network as a null
model to assess the rich--club connectivity in real networks.Comment: To appear in New Journal of Physics (www.njp.org
On the influence of topological characteristics on robustness of complex networks
In this paper, we explore the relationship between the topological
characteristics of a complex network and its robustness to sustained targeted
attacks. Using synthesised scale-free, small-world and random networks, we look
at a number of network measures, including assortativity, modularity, average
path length, clustering coefficient, rich club profiles and scale-free exponent
(where applicable) of a network, and how each of these influence the robustness
of a network under targeted attacks. We use an established robustness
coefficient to measure topological robustness, and consider sustained targeted
attacks by order of node degree. With respect to scale-free networks, we show
that assortativity, modularity and average path length have a positive
correlation with network robustness, whereas clustering coefficient has a
negative correlation. We did not find any correlation between scale-free
exponent and robustness, or rich-club profiles and robustness. The robustness
of small-world networks on the other hand, show substantial positive
correlations with assortativity, modularity, clustering coefficient and average
path length. In comparison, the robustness of Erdos-Renyi random networks did
not have any significant correlation with any of the network properties
considered. A significant observation is that high clustering decreases
topological robustness in scale-free networks, yet it increases topological
robustness in small-world networks. Our results highlight the importance of
topological characteristics in influencing network robustness, and illustrate
design strategies network designers can use to increase the robustness of
scale-free and small-world networks under sustained targeted attacks
Rich-club and page-club coefficients for directed graphs
Rich-club and page-club coefficients and their null models are introduced for
directed graphs. Null models allow for a quantitative discussion of the
rich-club and page-club phenomena. These coefficients are computed for four
directed real-world networks: Arxiv High Energy Physics paper citation network,
Web network (released from Google), Citation network among US Patents, and
Email network from a EU research institution. The results show a high
correlation between rich-club and page-club ordering. For journal paper
citation network, we identify both rich-club and page-club ordering, showing
that {}"elite" papers are cited by other {}"elite" papers. Google web network
shows partial rich-club and page-club ordering up to some point and then a
narrow declining of the corresponding normalized coefficients, indicating the
lack of rich-club ordering and the lack of page-club ordering, i.e. high
in-degree (PageRank) pages purposely avoid sharing links with other high
in-degree (PageRank) pages. For UC patents citation network, we identify
page-club and rich-club ordering providing a conclusion that {}"elite" patents
are cited by other {}"elite" patents. Finally, for e-mail communication network
we show lack of both rich-club and page-club ordering. We construct an example
of synthetic network showing page-club ordering and the lack of rich-club
ordering.Comment: 18 pages, 6 figure
Rich-club vs rich-multipolarization phenomena in weighted networks
Large scale hierarchies characterize complex networks in different domains.
Elements at their top, usually the most central or influential, may show
multipolarization or tend to club forming tightly interconnected communities.
The rich-club phenomenon quantified this tendency based on unweighted network
representations. Here, we define this metric for weighted networks and discuss
the appropriate normalization which preserves nodes' strengths and discounts
structural strength-strength correlations if present. We find that in some real
networks the results given by the weighted rich-club coefficient can be in
sharp contrast to the ones in the unweighted approach. We also discuss that the
scanning of the weighted subgraphs formed by the high-strength hubs is able to
unveil features contrary to the average: the formation of local alliances in
rich-multipolarized environments, or a lack of cohesion even in the presence of
rich-club ordering. Beyond structure, this analysis matters for understanding
correctly functionalities and dynamical processes relying on hub
interconnectedness.Comment: 12 pages, 2 figure
Statistical significance of rich-club phenomena in complex networks
We propose that the rich-club phenomena in complex networks should be defined
in the spirit of bootstrapping, in which a null model is adopted to assess the
statistical significance of the rich-club detected. Our method can be served as
a definition of rich-club phenomenon and is applied to analyzing three real
networks and three model networks. The results improve significantly compared
with previously reported results. We report a dilemma with an exceptional
example, showing that there does not exist an omnipotent definition for the
rich-club phenomenon.Comment: 3 Revtex pages + 5 figure
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