121 research outputs found
The Rich-Club Phenomenon In The Internet Topology
We show that the Internet topology at the Autonomous System (AS) level has a
rich--club phenomenon. The rich nodes, which are a small number of nodes with
large numbers of links, are very well connected to each other. The rich--club
is a core tier that we measured using the rich--club connectivity and the
node--node link distribution. We obtained this core tier without any heuristic
assumption between the ASes. The rich--club phenomenon is a simple qualitative
way to differentiate between power law topologies and provides a criterion for
new network models. To show this, we compared the measured rich--club of the AS
graph with networks obtained using the Barab\'asi--Albert (BA) scale--free
network model, the Fitness BA model and the Inet--3.0 model.Comment: To be appeared in the IEEE Communications Letter
Chinese Internet AS-level Topology
We present the first complete measurement of the Chinese Internet topology at
the autonomous systems (AS) level based on traceroute data probed from servers
of major ISPs in mainland China. We show that both the Chinese Internet AS
graph and the global Internet AS graph can be accurately reproduced by the
Positive-Feedback Preference (PFP) model with the same parameters. This result
suggests that the Chinese Internet preserves well the topological
characteristics of the global Internet. This is the first demonstration of the
Internet's topological fractality, or self-similarity, performed at the level
of topology evolution modeling.Comment: This paper is a preprint of a paper submitted to IEE Proceedings on
Communications and is subject to Institution of Engineering and Technology
Copyright. If accepted, the copy of record will be available at IET Digital
Librar
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
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
Characterising Web Site Link Structure
The topological structures of the Internet and the Web have received
considerable attention. However, there has been little research on the
topological properties of individual web sites. In this paper, we consider
whether web sites (as opposed to the entire Web) exhibit structural
similarities. To do so, we exhaustively crawled 18 web sites as diverse as
governmental departments, commercial companies and university departments in
different countries. These web sites consisted of as little as a few thousand
pages to millions of pages. Statistical analysis of these 18 sites revealed
that the internal link structure of the web sites are significantly different
when measured with first and second-order topological properties, i.e.
properties based on the connectivity of an individual or a pairs of nodes.
However, examination of a third-order topological property that consider the
connectivity between three nodes that form a triangle, revealed a strong
correspondence across web sites, suggestive of an invariant. Comparison with
the Web, the AS Internet, and a citation network, showed that this third-order
property is not shared across other types of networks. Nor is the property
exhibited in generative network models such as that of Barabasi and Albert.Comment: To appear at IEEE/WSE0
- …