Pathlength scaling in graphs with incomplete navigational information

  title={Pathlength scaling in graphs with incomplete navigational information},
  author={Sang Hoon Lee and Petter Holme},
4 Citations

Figures from this paper

Geometric properties of graph layouts optimized for greedy navigation
This work uses a recently developed user-centric navigation protocol to explore spatial layouts of complex networks that are optimal for navigation and discusses the spatial statistical properties of the optimized layouts for better navigability and its implication.
Exploring maps with greedy navigators
This work presents a simple greedy spatial navigation strategy as a probe to explore spatial networks, and suggests that the centralities measures have to be modified to incorporate the navigators' behavior, and presents the intriguing effect of navigator' greediness where removing some edges may actually enhance the routing efficiency.
Decentralized Routing on Spatial Networks with Stochastic Edge Weights
A decentralized routing algorithm is developed that provides en route guidance for travelers on a spatial network with stochastic edge weights without the need to rely on global knowledge about the network.
Does following optimized routes for single cars improve car routing?
It is found that, above a critical car density, the transport improves in all strategies if the time that the vehicles persist in trying to follow a particular strategy when a route is blocked, namely, the mean flux increases, the individual travel times decrease, and the fluctuations of density in the streets decrease.


Navigating networks with limited information.
It is demonstrated 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, and that directed navigation in typical networks requires remarkably little information on the level of individual nodes.
Random graphs with arbitrary degree distributions and their applications.
It is demonstrated that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.
Accuracy and scaling phenomena in Internet mapping.
It is found that in order to accurately estimate alpha, one must use a number of sources which grows linearly in the mean degree of the underlying graph, and comment on the accuracy of the published values of alpha for the Internet.
Navigating ultrasmall worlds in ultrashort time.
It is shown that random scale-free networks are ultrasmall worlds that can be navigated in ultrashort time, implying that the peculiar structure of complex networks ensures that the lack of global topological awareness has asymptotically no impact on the length of communication paths.
Searching in small-world networks.
Through an analytical model, the search time scales as N(1/D(D+1) for small-world networks, where N is the number of nodes and D is the dimension of the underlying lattice, which is shown to be in agreement with numerical simulations.
Searchability of networks.
The searchability at the node level opens the possibility for a generalized hierarchy measure that captures both the hierarchy in the usual terms of trees as in military structures, and the intrinsic hierarchical nature of topological hierarchies for scale-free networks as in the Internet.
Scale-free networks are ultrasmall.
It is shown, using analytical arguments, that scale-free networks with 2<lambda<3 have a much smaller diameter, behaving as d approximately ln(ln(N), which is the lowest possible diameter.
Tomography of scale-free networks and shortest path trees.
This paper finds that the distance distribution of all nodes from a specific network node consists of two regimes, and shows analytically that the nodes degree distribution at each layer exhibits a power-law tail with an exponential cutoff.
Random walks on complex networks.
The random walk centrality C is introduced, which is the ratio between its coordination number and a characteristic relaxation time, and it is shown that it determines essentially the mean first-passage time (MFPT) between two nodes.
Entropy of network ensembles.
  • G. Bianconi
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
The structural entropy is defined and evaluated, i.e., the entropy of the ensembles of undirected uncorrelated simple networks with given degree sequence, and a solution to the paradox is proposed by proving that scale-free degree distributions are the most likely degree distribution with the corresponding value of the structural entropy.