11,054 research outputs found
Complex networks as an emerging property of hierarchical preferential attachment
Real complex systems are not rigidly structured; no clear rules or blueprints
exist for their construction. Yet, amidst their apparent randomness, complex
structural properties universally emerge. We propose that an important class of
complex systems can be modeled as an organization of many embedded levels
(potentially infinite in number), all of them following the same universal
growth principle known as preferential attachment. We give examples of such
hierarchy in real systems, for instance in the pyramid of production entities
of the film industry. More importantly, we show how real complex networks can
be interpreted as a projection of our model, from which their scale
independence, their clustering, their hierarchy, their fractality and their
navigability naturally emerge. Our results suggest that complex networks,
viewed as growing systems, can be quite simple, and that the apparent
complexity of their structure is largely a reflection of their unobserved
hierarchical nature.Comment: 12 pages, 7 figure
Can we avoid high coupling?
It is considered good software design practice to organize source code into modules and to favour within-module connections (cohesion) over between-module connections (coupling), leading to the oft-repeated maxim "low coupling/high cohesion". Prior research into network theory and its application to software systems has found evidence that many important properties in real software systems exhibit approximately scale-free structure, including coupling; researchers have claimed that such scale-free structures are ubiquitous. This implies that high coupling must be unavoidable, statistically speaking, apparently contradicting standard ideas about software structure. We present a model that leads to the simple predictions that approximately scale-free structures ought to arise both for between-module connectivity and overall connectivity, and not as the result of poor design or optimization shortcuts. These predictions are borne out by our large-scale empirical study. Hence we conclude that high coupling is not avoidable--and that this is in fact quite reasonable
On the Stability of Community Detection Algorithms on Longitudinal Citation Data
There are fundamental differences between citation networks and other classes
of graphs. In particular, given that citation networks are directed and
acyclic, methods developed primarily for use with undirected social network
data may face obstacles. This is particularly true for the dynamic development
of community structure in citation networks. Namely, it is neither clear when
it is appropriate to employ existing community detection approaches nor is it
clear how to choose among existing approaches. Using simulated data, we attempt
to clarify the conditions under which one should use existing methods and which
of these algorithms is appropriate in a given context. We hope this paper will
serve as both a useful guidepost and an encouragement to those interested in
the development of more targeted approaches for use with longitudinal citation
data.Comment: 17 pages, 7 figures, presenting at Applications of Social Network
Analysis 2009, ETH Zurich Edit, August 17, 2009: updated abstract, figures,
text clarification
Transitive reduction of citation networks
In many complex networks, the vertices are ordered in time, and edges represent causal connections. We propose methods of analysing such directed acyclic graphs taking into account the constraints of causality and highlighting the causal structure. We illustrate our approach using citation networks formed from academic papers, patents and US Supreme Court verdicts. We show how transitive reduction (TR) reveals fundamental differences in the citation practices of different areas, how it highlights particularly interesting work, and how it can correct for the effect that the age of a document has on its citation count. Finally, we transitively reduce null models of citation networks with similar degree distributions and show the difference in degree distributions after TR to illustrate the lack of causal structure in such models
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