154 research outputs found
Fitness-dependent topological properties of the World Trade Web
Among the proposed network models, the hidden variable (or good get richer)
one is particularly interesting, even if an explicit empirical test of its
hypotheses has not yet been performed on a real network. Here we provide the
first empirical test of this mechanism on the world trade web, the network
defined by the trade relationships between world countries. We find that the
power-law distributed gross domestic product can be successfully identified
with the hidden variable (or fitness) determining the topology of the world
trade web: all previously studied properties up to third-order correlation
structure (degree distribution, degree correlations and hierarchy) are found to
be in excellent agreement with the predictions of the model. The choice of the
connection probability is such that all realizations of the network with the
same degree sequence are equiprobable.Comment: 4 Pages, 4 Figures. Final version accepted for publication on
Physical Review Letter
Patterns of link reciprocity in directed networks
We address the problem of link reciprocity, the non-random presence of two
mutual links between pairs of vertices. We propose a new measure of reciprocity
that allows the ordering of networks according to their actual degree of
correlation between mutual links. We find that real networks are always either
correlated or anticorrelated, and that networks of the same type (economic,
social, cellular, financial, ecological, etc.) display similar values of the
reciprocity. The observed patterns are not reproduced by current models. This
leads us to introduce a more general framework where mutual links occur with a
conditional connection probability. In some of the studied networks we discuss
the form of the conditional connection probability and the size dependence of
the reciprocity.Comment: Final version accepted for publication on Physical Review Letter
A microscopic study of the fitness-dependent topology of the world trade network
Previous studies have suggested that the world-trade network belongs to the class of static hidden variable models. In this article we investigate the microscopic structure of the world trade network, that is the hidden variable correlation matrix of the network. The hidden variable is defined as a rank ordering of gross domestic products. This choice significantly reduces the noise in the statistical analysis found in previous studies. The hidden variable correlation matrix, that expresses the probability that a trade relationship between two countries of given fitness exists, suggests an attachment kernel that at least partially favours trading pairs or dissimilar fitness rather than the purely multiplicative one found previously. Additionally, we provide an in-depth look at the data source and reveal that first-order results, such as the degree distribution, exhibit significant qualitative differences depending on the data provider. Furthermore, we shed light on the intertemporal activity of international trade and point out that fluctuations occur mostly between countries with strong dissimilarities of fitness and connectivity
Emergence of weight-topology correlations in complex scale-free networks
Different weighted scale-free networks show weights-topology correlations
indicated by the non linear scaling of the node strength with node
connectivity. In this paper we show that networks with and without
weight-topology correlations can emerge from the same simple growth dynamics of
the node connectivities and of the link weights. A weighted fitness network is
introduced in which both nodes and links are assigned intrinsic fitness. This
model can show a local dependence of the weight-topology correlations and can
undergo a phase transition to a state in which the network is dominated by few
links which acquire a finite fraction of the total weight of the network.Comment: (4 pages,3 figures
Null Models of Economic Networks: The Case of the World Trade Web
In all empirical-network studies, the observed properties of economic
networks are informative only if compared with a well-defined null model that
can quantitatively predict the behavior of such properties in constrained
graphs. However, predictions of the available null-model methods can be derived
analytically only under assumptions (e.g., sparseness of the network) that are
unrealistic for most economic networks like the World Trade Web (WTW). In this
paper we study the evolution of the WTW using a recently-proposed family of
null network models. The method allows to analytically obtain the expected
value of any network statistic across the ensemble of networks that preserve on
average some local properties, and are otherwise fully random. We compare
expected and observed properties of the WTW in the period 1950-2000, when
either the expected number of trade partners or total country trade is kept
fixed and equal to observed quantities. We show that, in the binary WTW,
node-degree sequences are sufficient to explain higher-order network properties
such as disassortativity and clustering-degree correlation, especially in the
last part of the sample. Conversely, in the weighted WTW, the observed sequence
of total country imports and exports are not sufficient to predict higher-order
patterns of the WTW. We discuss some important implications of these findings
for international-trade models.Comment: 39 pages, 46 figures, 2 table
A complementary view on the growth of directory trees
Trees are a special sub-class of networks with unique properties, such as the
level distribution which has often been overlooked. We analyse a general tree
growth model proposed by Klemm {\em et. al.} (2005) to explain the growth of
user-generated directory structures in computers. The model has a single
parameter which interpolates between preferential attachment and random
growth. Our analysis results in three contributions: First, we propose a more
efficient estimation method for based on the degree distribution, which is
one specific representation of the model. Next, we introduce the concept of a
level distribution and analytically solve the model for this representation.
This allows for an alternative and independent measure of . We argue that,
to capture real growth processes, the estimations from the degree and the
level distributions should coincide. Thus, we finally apply both
representations to validate the model with synthetically generated tree
structures, as well as with collected data of user directories. In the case of
real directory structures, we show that measured from the level
distribution are incompatible with measured from the degree distribution.
In contrast to this, we find perfect agreement in the case of simulated data.
Thus, we conclude that the model is an incomplete description of the growth of
real directory structures as it fails to reproduce the level distribution. This
insight can be generalised to point out the importance of the level
distribution for modeling tree growth.Comment: 16 pages, 7 figure
The International-Trade Network: Gravity Equations and Topological Properties
This paper begins to explore the determinants of the topological properties
of the international - trade network (ITN). We fit bilateral-trade flows using
a standard gravity equation to build a "residual" ITN where trade-link weights
are depurated from geographical distance, size, border effects, trade
agreements, and so on. We then compare the topological properties of the
original and residual ITNs. We find that the residual ITN displays, unlike the
original one, marked signatures of a complex system, and is characterized by a
very different topological architecture. Whereas the original ITN is
geographically clustered and organized around a few large-sized hubs, the
residual ITN displays many small-sized but trade-oriented countries that,
independently of their geographical position, either play the role of local
hubs or attract large and rich countries in relatively complex
trade-interaction patterns
A Self-organized model for network evolution
Here we provide a detailed analysis, along with some extensions and additonal
investigations, of a recently proposed self-organised model for the evolution
of complex networks. Vertices of the network are characterised by a fitness
variable evolving through an extremal dynamics process, as in the Bak-Sneppen
model representing a prototype of Self-Organized Criticality. The network
topology is in turn shaped by the fitness variable itself, as in the fitness
network model. The system self-organizes to a nontrivial state, characterized
by a power-law decay of dynamical and topological quantities above a critical
threshold. The interplay between topology and dynamics in the system is the key
ingredient leading to an unexpected behaviour of these quantities
The International Trade Network: weighted network analysis and modelling
Tools of the theory of critical phenomena, namely the scaling analysis and
universality, are argued to be applicable to large complex web-like network
structures. Using a detailed analysis of the real data of the International
Trade Network we argue that the scaled link weight distribution has an
approximate log-normal distribution which remains robust over a period of 53
years. Another universal feature is observed in the power-law growth of the
trade strength with gross domestic product, the exponent being similar for all
countries. Using the 'rich-club' coefficient measure of the weighted networks
it has been shown that the size of the rich-club controlling half of the
world's trade is actually shrinking. While the gravity law is known to describe
well the social interactions in the static networks of population migration,
international trade, etc, here for the first time we studied a non-conservative
dynamical model based on the gravity law which excellently reproduced many
empirical features of the ITN.Comment: 5 pages, 5 figure
An explanatory model for food-web structure and evolution
Food webs are networks describing who is eating whom in an ecological
community. By now it is clear that many aspects of food-web structure are
reproducible across diverse habitats, yet little is known about the driving
force behind this structure. Evolutionary and population dynamical mechanisms
have been considered. We propose a model for the evolutionary dynamics of
food-web topology and show that it accurately reproduces observed food-web
characteristic in the steady state. It is based on the observation that most
consumers are larger than their resource species and the hypothesis that
speciation and extinction rates decrease with increasing body mass. Results
give strong support to the evolutionary hypothesis.Comment: 16 pages, 3 figure
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