11 research outputs found
Scaling in public transport networks
We analyse the statistical properties of public transport networks. These
networks are defined by a set of public transport routes (bus lines) and the
stations serviced by these. For larger networks these appear to possess a
scale-free structure, as it is demonstrated e.g. by the Zipf law distribution
of the number of routes servicing a given station or for the distribution of
the number of stations which can be visited from the chosen one without
changing the means of transport. Moreover, a rather particular feature of the
public transport network is that many routes service common subsets of
stations. We discuss the possibility of new scaling laws that govern intrinsic
features of such subsets.Comment: 9 pages, 4 figure
Public transport networks: empirical analysis and modeling
We use complex network concepts to analyze statistical properties of urban
public transport networks (PTN). To this end, we present a comprehensive survey
of the statistical properties of PTNs based on the data of fourteen cities of
so far unexplored network size. Especially helpful in our analysis are
different network representations. Within a comprehensive approach we calculate
PTN characteristics in all of these representations and perform a comparative
analysis. The standard network characteristics obtained in this way often
correspond to features that are of practical importance to a passenger using
public traffic in a given city. Specific features are addressed that are unique
to PTNs and networks with similar transport functions (such as networks of
neurons, cables, pipes, vessels embedded in 2D or 3D space). Based on the
empirical survey, we propose a model that albeit being simple enough is capable
of reproducing many of the identified PTN properties. A central ingredient of
this model is a growth dynamics in terms of routes represented by self-avoiding
walks.Comment: 19 pages, 23 figure
Entropic equation of state and scaling functions near the critical point in scale-free networks
We analyze the entropic equation of state for a many-particle interacting
system in a scale-free network. The analysis is performed in terms of scaling
functions which are of fundamental interest in the theory of critical phenomena
and have previously been theoretically and experimentally explored in the
context of various magnetic, fluid, and superconducting systems in two and
three dimensions. Here, we obtain general scaling functions for the entropy,
the constant-field heat capacity, and the isothermal magnetocaloric coefficient
near the critical point in scale-free networks, where the node-degree
distribution exponent appears to be a global variable and plays a
crucial role, similar to the dimensionality for systems on lattices. This
extends the principle of universality to systems on scale-free networks and
allows quantification of the impact of fluctuations in the network structure on
critical behavior.Comment: 8 pages, 4 figure
Critical phenomena on scale-free networks: logarithmic corrections and scaling functions
In this paper, we address the logarithmic corrections to the leading power
laws that govern thermodynamic quantities as a second-order phase transition
point is approached. For phase transitions of spin systems on d-dimensional
lattices, such corrections appear at some marginal values of the order
parameter or space dimension. We present new scaling relations for these
exponents. We also consider a spin system on a scale-free network which
exhibits logarithmic corrections due to the specific network properties. To
this end, we analyze the phase behavior of a model with coupled order
parameters on a scale-free network and extract leading and logarithmic
correction-to-scaling exponents that determine its field- and temperature
behavior. Although both non-trivial sets of exponents emerge from the
correlations in the network structure rather than from the spin fluctuations
they fulfil the respective thermodynamic scaling relations. For the scale-free
networks the logarithmic corrections appear at marginal values of the node
degree distribution exponent. In addition we calculate scaling functions, which
also exhibit nontrivial dependence on intrinsic network properties.Comment: 15 pages, 4 figure
Network Harness: Metropolis Public Transport
We analyze the public transport networks (PTNs) of a number of major cities
of the world. While the primary network topology is defined by a set of routes
each servicing an ordered series of given stations, a number of different
neighborhood relations may be defined both for the routes and the stations. The
networks defined in this way display distinguishing properties, the most
striking being that often several routes proceed in parallel for a sequence of
stations. Other networks with real-world links like cables or neurons embedded
in two or three dimensions often show the same feature - we use the car
engineering term "harness" for such networks. Geographical data for the routes
reveal surprising self-avoiding walk (SAW) properties. We propose and simulate
an evolutionary model of PTNs based on effectively interacting SAWs that
reproduces the key features.Comment: 5 pages, 4 figure
Universal Properties of Mythological Networks
As in statistical physics, the concept of universality plays an important,
albeit qualitative, role in the field of comparative mythology. Here we apply
statistical mechanical tools to analyse the networks underlying three iconic
mythological narratives with a view to identifying common and distinguishing
quantitative features. Of the three narratives, an Anglo-Saxon and a Greek text
are mostly believed by antiquarians to be partly historically based while the
third, an Irish epic, is often considered to be fictional. Here we show that
network analysis is able to discriminate real from imaginary social networks
and place mythological narratives on the spectrum between them. Moreover, the
perceived artificiality of the Irish narrative can be traced back to anomalous
features associated with six characters. Considering these as amalgams of
several entities or proxies, renders the plausibility of the Irish text
comparable to the others from a network-theoretic point of view.Comment: 6 pages, 3 figures, 2 tables. Updated to incorporate corrections from
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