247 research outputs found
Triadic motifs and dyadic self-organization in the World Trade Network
In self-organizing networks, topology and dynamics coevolve in a continuous
feedback, without exogenous driving. The World Trade Network (WTN) is one of
the few empirically well documented examples of self-organizing networks: its
topology strongly depends on the GDP of world countries, which in turn depends
on the structure of trade. Therefore, understanding which are the key
topological properties of the WTN that deviate from randomness provides direct
empirical information about the structural effects of self-organization. Here,
using an analytical pattern-detection method that we have recently proposed, we
study the occurrence of triadic "motifs" (subgraphs of three vertices) in the
WTN between 1950 and 2000. We find that, unlike other properties, motifs are
not explained by only the in- and out-degree sequences. By contrast, they are
completely explained if also the numbers of reciprocal edges are taken into
account. This implies that the self-organization process underlying the
evolution of the WTN is almost completely encoded into the dyadic structure,
which strongly depends on reciprocity.Comment: 12 pages, 3 figures; Best Paper Award at the 6th International
Conference on Self-Organizing Systems, Delft, The Netherlands, 15-16/03/201
Experimental evidence for the interplay between individual wealth and transaction network
We conduct a market experiment with human agents in order to explore the
structure of transaction networks and to study the dynamics of wealth
accumulation. The experiment is carried out on our platform for 97 days with
2,095 effective participants and 16,936 times of transactions. From these data,
the hybrid distribution (log-normal bulk and power-law tail) in the wealth is
observed and we demonstrate that the transaction networks in our market are
always scale-free and disassortative even for those with the size of the order
of few hundred. We further discover that the individual wealth is correlated
with its degree by a power-law function which allows us to relate the exponent
of the transaction network degree distribution to the Pareto index in wealth
distribution.Comment: 6 pages, 7 figure
An ensemble approach to the analysis of weighted networks
We present a new approach to the calculation of measures in weighted
networks, based on the translation of a weighted network into an ensemble of
edges. This leads to a straightforward generalization of any measure defined on
unweighted networks, such as the average degree of the nearest neighbours, the
clustering coefficient, the `betweenness', the distance between two nodes and
the diameter of a network. All these measures are well established for
unweighted networks but have hitherto proven difficult to define for weighted
networks. Further to introducing this approach we demonstrate its advantages by
applying the clustering coefficient constructed in this way to two real-world
weighted networks.Comment: 4 pages 3 figure
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
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
Applying weighted network measures to microarray distance matrices
In recent work we presented a new approach to the analysis of weighted
networks, by providing a straightforward generalization of any network measure
defined on unweighted networks. This approach is based on the translation of a
weighted network into an ensemble of edges, and is particularly suited to the
analysis of fully connected weighted networks. Here we apply our method to
several such networks including distance matrices, and show that the clustering
coefficient, constructed by using the ensemble approach, provides meaningful
insights into the systems studied. In the particular case of two data sets from
microarray experiments the clustering coefficient identifies a number of
biologically significant genes, outperforming existing identification
approaches.Comment: Accepted for publication in J. Phys.
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
Multirelational Organization of Large-scale Social Networks in an Online World
The capacity to collect fingerprints of individuals in online media has
revolutionized the way researchers explore human society. Social systems can be
seen as a non-linear superposition of a multitude of complex social networks,
where nodes represent individuals and links capture a variety of different
social relations. Much emphasis has been put on the network topology of social
interactions, however, the multi-dimensional nature of these interactions has
largely been ignored in empirical studies, mostly because of lack of data.
Here, for the first time, we analyze a complete, multi-relational, large social
network of a society consisting of the 300,000 odd players of a massive
multiplayer online game. We extract networks of six different types of
one-to-one interactions between the players. Three of them carry a positive
connotation (friendship, communication, trade), three a negative (enmity, armed
aggression, punishment). We first analyze these types of networks as separate
entities and find that negative interactions differ from positive interactions
by their lower reciprocity, weaker clustering and fatter-tail degree
distribution. We then proceed to explore how the inter-dependence of different
network types determines the organization of the social system. In particular
we study correlations and overlap between different types of links and
demonstrate the tendency of individuals to play different roles in different
networks. As a demonstration of the power of the approach we present the first
empirical large-scale verification of the long-standing structural balance
theory, by focusing on the specific multiplex network of friendship and enmity
relations.Comment: 7 pages, 5 figures, accepted for publication in PNA
Self-organized network evolution coupled to extremal dynamics
The interplay between topology and dynamics in complex networks is a
fundamental but widely unexplored problem. Here, we study this phenomenon on a
prototype model in which the network is shaped by a dynamical variable. We
couple the dynamics of the Bak-Sneppen evolution model with the rules of the
so-called fitness network model for establishing the topology of a network;
each vertex is assigned a fitness, and the vertex with minimum fitness and its
neighbours are updated in each iteration. At the same time, the links between
the updated vertices and all other vertices are drawn anew with a
fitness-dependent connection probability. We show analytically and numerically
that the system self-organizes to a non-trivial state that differs from what is
obtained when the two processes are decoupled. A power-law decay of dynamical
and topological quantities above a threshold emerges spontaneously, as well as
a feedback between different dynamical regimes and the underlying correlation
and percolation properties of the network.Comment: Accepted version. Supplementary information at
http://www.nature.com/nphys/journal/v3/n11/suppinfo/nphys729_S1.htm
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
- …