1,808 research outputs found
Navigability is a Robust Property
The Small World phenomenon has inspired researchers across a number of
fields. A breakthrough in its understanding was made by Kleinberg who
introduced Rank Based Augmentation (RBA): add to each vertex independently an
arc to a random destination selected from a carefully crafted probability
distribution. Kleinberg proved that RBA makes many networks navigable, i.e., it
allows greedy routing to successfully deliver messages between any two vertices
in a polylogarithmic number of steps. We prove that navigability is an inherent
property of many random networks, arising without coordination, or even
independence assumptions
Navigating Networks with Limited Information
We study navigation with limited information in networks and demonstrate that
many real-world networks have a structure which can be described as favoring
communication at short distance at the cost of constraining communication at
long distance. This feature, which is robust and more evident with limited than
with complete information, reflects both topological and possibly functional
design characteristics. For example, the characteristics of the networks
studied derived from a city and from the Internet are manifested through
modular network designs. We also observe that directed navigation in typical
networks requires remarkably little information on the level of individual
nodes. By studying navigation, or specific signaling, we take a complementary
approach to the common studies of information transfer devoted to broadcasting
of information in studies of virus spreading and the like.Comment: 6 pages, 6 figures. For associated Java applet, see
http://cmol.nbi.dk/models/bit/bit.htm
Improving Reachability and Navigability in Recommender Systems
In this paper, we investigate recommender systems from a network perspective
and investigate recommendation networks, where nodes are items (e.g., movies)
and edges are constructed from top-N recommendations (e.g., related movies). In
particular, we focus on evaluating the reachability and navigability of
recommendation networks and investigate the following questions: (i) How well
do recommendation networks support navigation and exploratory search? (ii) What
is the influence of parameters, in particular different recommendation
algorithms and the number of recommendations shown, on reachability and
navigability? and (iii) How can reachability and navigability be improved in
these networks? We tackle these questions by first evaluating the reachability
of recommendation networks by investigating their structural properties.
Second, we evaluate navigability by simulating three different models of
information seeking scenarios. We find that with standard algorithms,
recommender systems are not well suited to navigation and exploration and
propose methods to modify recommendations to improve this. Our work extends
from one-click-based evaluations of recommender systems towards multi-click
analysis (i.e., sequences of dependent clicks) and presents a general,
comprehensive approach to evaluating navigability of arbitrary recommendation
networks
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
Navigability of temporal networks in hyperbolic space
Information routing is one of the main tasks in many complex networks with a
communication function. Maps produced by embedding the networks in hyperbolic
space can assist this task enabling the implementation of efficient navigation
strategies. However, only static maps have been considered so far, while
navigation in more realistic situations, where the network structure may vary
in time, remain largely unexplored. Here, we analyze the navigability of real
networks by using greedy routing in hyperbolic space, where the nodes are
subject to a stochastic activation-inactivation dynamics. We find that such
dynamics enhances navigability with respect to the static case. Interestingly,
there exists an optimal intermediate activation value, which ensures the best
trade-off between the increase in the number of successful paths and a limited
growth of their length. Contrary to expectations, the enhanced navigability is
robust even when the most connected nodes inactivate with very high
probability. Finally, our results indicate that some real networks are
ultranavigable and remain highly navigable even if the network structure is
extremely unsteady. These findings have important implications for the design
and evaluation of efficient routing protocols that account for the temporal
nature of real complex networks.Comment: 10 pages, 4 figures. Includes Supplemental Informatio
Hyperbolic Geometry of Complex Networks
We develop a geometric framework to study the structure and function of
complex networks. We assume that hyperbolic geometry underlies these networks,
and we show that with this assumption, heterogeneous degree distributions and
strong clustering in complex networks emerge naturally as simple reflections of
the negative curvature and metric property of the underlying hyperbolic
geometry. Conversely, we show that if a network has some metric structure, and
if the network degree distribution is heterogeneous, then the network has an
effective hyperbolic geometry underneath. We then establish a mapping between
our geometric framework and statistical mechanics of complex networks. This
mapping interprets edges in a network as non-interacting fermions whose
energies are hyperbolic distances between nodes, while the auxiliary fields
coupled to edges are linear functions of these energies or distances. The
geometric network ensemble subsumes the standard configuration model and
classical random graphs as two limiting cases with degenerate geometric
structures. Finally, we show that targeted transport processes without global
topology knowledge, made possible by our geometric framework, are maximally
efficient, according to all efficiency measures, in networks with strongest
heterogeneity and clustering, and that this efficiency is remarkably robust
with respect to even catastrophic disturbances and damages to the network
structure
Just Around the Riverbed: Reconciling Navigability Rules in North Carolina
Entrenched in the common law, North Carolina\u27s public trust doctrine applies to waterways and their underlying riverbeds-protecting them from misuse and adverse possession-so long as the waterways are navigable in fact. In North Carolina v. Alcoa Power Generating, Inc., the United States Court of Appeals for the Fourth Circuit veered away from the North Carolina common law rules governing navigability and instead applied the more stringent federal test. The differences between the current North Carolina common law and federal navigability tests for waterways illustrate the state\u27s sovereign interests, and why the Fourth Circuit erred in applying the federal regime. This Comment explores the present and future ramifications of the Alcoa decision on public trust jurisprudence in North Carolina and other original states.
Public trust doctrine cases implicate unique choice of law considerations. By disregarding common law precedent dating back to the American Revolution, the Fourth Circuit\u27s decision disrupts the delicate balance of federalism between state and federal courts. The present consequences of the Fourth Circuit\u27s decision include public policy concerns and clouded land titles in North Carolina. The future ramifications include an expansion of federal question jurisdiction and an upheaval of common law navigability rules in the original thirteen states
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