14 research outputs found
Percolation in the classical blockmodel
Classical blockmodel is known as the simplest among models of networks with
community structure. The model can be also seen as an extremely simply example
of interconnected networks. For this reason, it is surprising that the
percolation transition in the classical blockmodel has not been examined so
far, although the phenomenon has been studied in a variety of much more
complicated models of interconnected and multiplex networks. In this paper we
derive the self-consistent equation for the size the global percolation cluster
in the classical blockmodel. We also find the condition for percolation
threshold which characterizes the emergence of the giant component. We show
that the discussed percolation phenomenon may cause unexpected problems in a
simple optimization process of the multilevel network construction. Numerical
simulations confirm the correctness of our theoretical derivations.Comment: 7 pages, 6 figure
Predicting Missing Links via Local Information
Missing link prediction of networks is of both theoretical interest and
practical significance in modern science. In this paper, we empirically
investigate a simple framework of link prediction on the basis of node
similarity. We compare nine well-known local similarity measures on six real
networks. The results indicate that the simplest measure, namely common
neighbors, has the best overall performance, and the Adamic-Adar index performs
the second best. A new similarity measure, motivated by the resource allocation
process taking place on networks, is proposed and shown to have higher
prediction accuracy than common neighbors. It is found that many links are
assigned same scores if only the information of the nearest neighbors is used.
We therefore design another new measure exploited information of the next
nearest neighbors, which can remarkably enhance the prediction accuracy.Comment: For International Workshop: "The Physics Approach To Risk:
Agent-Based Models and Networks", http://intern.sg.ethz.ch/cost-p10
Urban road networks -- Spatial networks with universal geometric features? A case study on Germany's largest cities
Urban road networks have distinct geometric properties that are partially
determined by their (quasi-) two-dimensional structure. In this work, we study
these properties for 20 of the largest German cities. We find that the
small-scale geometry of all examined road networks is extremely similar. The
object-size distributions of road segments and the resulting cellular
structures are characterised by heavy tails. As a specific feature, a large
degree of rectangularity is observed in all networks, with link angle
distributions approximately described by stretched exponential functions. We
present a rigorous statistical analysis of the main geometric characteristics
and discuss their mutual interrelationships. Our results demonstrate the
fundamental importance of cost-efficiency constraints for in time evolution of
urban road networks.Comment: 16 pages; 8 figure
Opinion formation models on a gradient
10.1371/journal.pone.0114088PLoS ONE912e114088complete
A greedy-navigator approach to navigable city plans
We use a set of four theoretical navigability indices for street maps to investigate the shape of the resulting street networks, if they are grown by optimizing these indices. The indices compare the performance of simulated navigators (having a partial information about the surroundings, like humans in many real situations) to the performance of optimally navigating individuals. We show that our simple greedy shortcut construction strategy generates the emerging structures that are different from real road network, but not inconceivable. The resulting city plans, for all navigation indices, share common qualitative properties such as the tendency for triangular blocks to appear, while the more quantitative features, such as degree distributions and clustering, are characteristically different depending on the type of metrics and routing strategies. We show that it is the type of metrics used which determines the overall shapes characterized by structural heterogeneity, but the routing schemes contribute to more subtle details of locality, which is more emphasized in case of unrestricted connections when the edge crossing is allowed
User-centric time-distance representation of road networks
This paper presents a new algorithm for computing timedistance
transformations of a road network based on modified multidimensional
scaling. The algorithm is designed to perform on a realworld
road network, and provides alternative visualisations for travel
time cognition and route planning. Several extensions are explored, including
user-centric and route-centric road map transformations. Our
implementation of the algorithm can be applied to any locality where
travel time road network data is available. Here, it is illustrated on road
network data for a rural region in Ireland. Limitations of the proposed
algorithm are examined, and potential solutions are discussed