3,665 research outputs found
Self-organized Emergence of Navigability on Small-World Networks
This paper mainly investigates why small-world networks are navigable and how
to navigate small-world networks. We find that the navigability can naturally
emerge from self-organization in the absence of prior knowledge about
underlying reference frames of networks. Through a process of information
exchange and accumulation on networks, a hidden metric space for navigation on
networks is constructed. Navigation based on distances between vertices in the
hidden metric space can efficiently deliver messages on small-world networks,
in which long range connections play an important role. Numerical simulations
further suggest that high cluster coefficient and low diameter are both
necessary for navigability. These interesting results provide profound insights
into scalable routing on the Internet due to its distributed and localized
requirements.Comment: 3 figure
A Game Theoretic Model for the Formation of Navigable Small-World Networks
Kleinberg proposed a family of small-world networks to ex-plain the navigability of large-scale real-world social net-works. However, the underlying mechanism that drives real networks to be navigable is not yet well understood. In this paper, we present a game theoretic model for the for-mation of navigable small world networks. We model the network formation as a game in which people seek for both high reciprocity and long-distance relationships. We show that the navigable small-world network is a Nash Equilib-rium of the game. Moreover, we prove that the navigable small-world equilibrium tolerates collusions of any size and arbitrary deviations of a large random set of nodes, while non-navigable equilibria do not tolerate small group collu-sions or random perturbations. Our empirical evaluation further demonstrates that the system always converges to the navigable network even when limited or no information about other players ’ strategies is available. Our theoretical and empirical analyses provide important new insight on the connection between distance, reciprocity and navigability in social networks
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
The Navigability of Strong Ties: Small Worlds, Tie Strength and Network Topology
International audienceWe examine data on and models of small world properties and parameters of social networks. Our focus, on tie-strength, multilevel networks and searchability in strong-tie social networks, allows us to extend some of the questions and findings of recent research and the fit of small world models to sociological and anthropological data on human communities. We offer a 'navigability of strong ties' hypothesis about network topologies tested with data from kinship systems, but potentially applicable to corporate cultures and business networks
Extended navigability of small world networks: exact results and new insights
Navigability of networks, that is the ability to find any given destination
vertex starting from any other vertex, is crucial to their usefulness. In 2000
Kleinberg showed that optimal navigability could be achieved in small-world
networks provided that a special recipe was used to establish long range
connections, and that a greedy algorithm, that ensures that the destination
will be reached, is used. Here we provide an exact solution for the asymptotic
behavior of such a greedy algorithm as a function of the system's parameters.
Our solution enables us to show that the original claim that only a very
special construction is optimal can be relaxed depending on further criteria,
such as, for example, cost minimization, that must be satisfied.Comment: Presented at the BCNet Workshop in Barcelona on December 12 2008;
submitted to PR
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
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
Adaptive Dynamics of Realistic Small-World Networks
Continuing in the steps of Jon Kleinberg's and others celebrated work on
decentralized search in small-world networks, we conduct an experimental
analysis of a dynamic algorithm that produces small-world networks. We find
that the algorithm adapts robustly to a wide variety of situations in realistic
geographic networks with synthetic test data and with real world data, even
when vertices are uneven and non-homogeneously distributed.
We investigate the same algorithm in the case where some vertices are more
popular destinations for searches than others, for example obeying power-laws.
We find that the algorithm adapts and adjusts the networks according to the
distributions, leading to improved performance. The ability of the dynamic
process to adapt and create small worlds in such diverse settings suggests a
possible mechanism by which such networks appear in nature
Collective navigation of complex networks: Participatory greedy routing
Many networks are used to transfer information or goods, in other words, they
are navigated. The larger the network, the more difficult it is to navigate
efficiently. Indeed, information routing in the Internet faces serious
scalability problems due to its rapid growth, recently accelerated by the rise
of the Internet of Things. Large networks like the Internet can be navigated
efficiently if nodes, or agents, actively forward information based on hidden
maps underlying these systems. However, in reality most agents will deny to
forward messages, which has a cost, and navigation is impossible. Can we design
appropriate incentives that lead to participation and global navigability?
Here, we present an evolutionary game where agents share the value generated by
successful delivery of information or goods. We show that global navigability
can emerge, but its complete breakdown is possible as well. Furthermore, we
show that the system tends to self-organize into local clusters of agents who
participate in the navigation. This organizational principle can be exploited
to favor the emergence of global navigability in the system.Comment: Supplementary Information and Videos:
https://koljakleineberg.wordpress.com/2016/11/14/collective-navigation-of-complex-networks-participatory-greedy-routing
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