486 research outputs found
Clustering and information in correlation based financial networks
Networks of companies can be constructed by using return correlations. A
crucial issue in this approach is to select the relevant correlations from the
correlation matrix. In order to study this problem, we start from an empty
graph with no edges where the vertices correspond to stocks. Then, one by one,
we insert edges between the vertices according to the rank of their correlation
strength, resulting in a network called asset graph. We study its properties,
such as topologically different growth types, number and size of clusters and
clustering coefficient. These properties, calculated from empirical data, are
compared against those of a random graph. The growth of the graph can be
classified according to the topological role of the newly inserted edge. We
find that the type of growth which is responsible for creating cycles in the
graph sets in much earlier for the empirical asset graph than for the random
graph, and thus reflects the high degree of networking present in the market.
We also find the number of clusters in the random graph to be one order of
magnitude higher than for the asset graph. At a critical threshold, the random
graph undergoes a radical change in topology related to percolation transition
and forms a single giant cluster, a phenomenon which is not observed for the
asset graph. Differences in mean clustering coefficient lead us to conclude
that most information is contained roughly within 10% of the edges.Comment: 11 pages including 14 figures. Uses REVTeX4. To be published in a
special volume of EPJ on network
Dynamic asset trees and Black Monday
The minimum spanning tree, based on the concept of ultrametricity, is
constructed from the correlation matrix of stock returns. The dynamics of this
asset tree can be characterised by its normalised length and the mean
occupation layer, as measured from an appropriately chosen centre called the
`central node'. We show how the tree length shrinks during a stock market
crisis, Black Monday in this case, and how a strong reconfiguration takes
place, resulting in topological shrinking of the tree.Comment: 6 pages, 3 eps figues. Elsevier style. Will appear in Physica A as
part of the Bali conference proceedings, in pres
Dynamic asset trees and portfolio analysis
The minimum spanning tree, based on the concept of ultrametricity, is
constructed from the correlation matrix of stock returns and provides a
meaningful economic taxonomy of the stock market. In order to study the
dynamics of this asset tree we characterize it by its normalized length and by
the mean occupation layer, as measured from an appropriately chosen center. We
show how the tree evolves over time, and how it shrinks particularly strongly
during a stock market crisis. We then demonstrate that the assets of the
optimal Markowitz portfolio lie practically at all times on the outskirts of
the tree. We also show that the normalized tree length and the investment
diversification potential are very strongly correlated.Comment: 9 pages, 3 figures (encapsulated postscript
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
Community Structure in Time-Dependent, Multiscale, and Multiplex Networks
Network science is an interdisciplinary endeavor, with methods and
applications drawn from across the natural, social, and information sciences. A
prominent problem in network science is the algorithmic detection of
tightly-connected groups of nodes known as communities. We developed a
generalized framework of network quality functions that allowed us to study the
community structure of arbitrary multislice networks, which are combinations of
individual networks coupled through links that connect each node in one network
slice to itself in other slices. This framework allows one to study community
structure in a very general setting encompassing networks that evolve over
time, have multiple types of links (multiplexity), and have multiple scales.Comment: 31 pages, 3 figures, 1 table. Includes main text and supporting
material. This is the accepted version of the manuscript (the definitive
version appeared in Science), with typographical corrections included her
Dynamics of market correlations: Taxonomy and portfolio analysis
The time dependence of the recently introduced minimum spanning tree
description of correlations between stocks, called the ``asset tree'' have been
studied to reflect the economic taxonomy. The nodes of the tree are identified
with stocks and the distance between them is a unique function of the
corresponding element of the correlation matrix. By using the concept of a
central vertex, chosen as the most strongly connected node of the tree, an
important characteristic is defined by the mean occupation layer (MOL). During
crashes the strong global correlation in the market manifests itself by a low
value of MOL. The tree seems to have a scale free structure where the scaling
exponent of the degree distribution is different for `business as usual' and
`crash' periods. The basic structure of the tree topology is very robust with
respect to time. We also point out that the diversification aspect of portfolio
optimization results in the fact that the assets of the classic Markowitz
portfolio are always located on the outer leaves of the tree. Technical aspects
like the window size dependence of the investigated quantities are also
discussed.Comment: 13 pages including 12 figures. Uses REVTe
Circadian pattern and burstiness in mobile phone communication
The temporal communication patterns of human individuals are known to be
inhomogeneous or bursty, which is reflected as the heavy tail behavior in the
inter-event time distribution. As the cause of such bursty behavior two main
mechanisms have been suggested: a) Inhomogeneities due to the circadian and
weekly activity patterns and b) inhomogeneities rooted in human task execution
behavior. Here we investigate the roles of these mechanisms by developing and
then applying systematic de-seasoning methods to remove the circadian and
weekly patterns from the time-series of mobile phone communication events of
individuals. We find that the heavy tails in the inter-event time distributions
remain robustly with respect to this procedure, which clearly indicates that
the human task execution based mechanism is a possible cause for the remaining
burstiness in temporal mobile phone communication patterns.Comment: 17 pages, 12 figure
Urban Gravity: a Model for Intercity Telecommunication Flows
We analyze the anonymous communication patterns of 2.5 million customers of a
Belgian mobile phone operator. Grouping customers by billing address, we build
a social network of cities, that consists of communications between 571 cities
in Belgium. We show that inter-city communication intensity is characterized by
a gravity model: the communication intensity between two cities is proportional
to the product of their sizes divided by the square of their distance
Emergence of good conduct, scaling and Zipf laws in human behavioral sequences in an online world
We study behavioral action sequences of players in a massive multiplayer
online game. In their virtual life players use eight basic actions which allow
them to interact with each other. These actions are communication, trade,
establishing or breaking friendships and enmities, attack, and punishment. We
measure the probabilities for these actions conditional on previous taken and
received actions and find a dramatic increase of negative behavior immediately
after receiving negative actions. Similarly, positive behavior is intensified
by receiving positive actions. We observe a tendency towards anti-persistence
in communication sequences. Classifying actions as positive (good) and negative
(bad) allows us to define binary 'world lines' of lives of individuals.
Positive and negative actions are persistent and occur in clusters, indicated
by large scaling exponents alpha~0.87 of the mean square displacement of the
world lines. For all eight action types we find strong signs for high levels of
repetitiveness, especially for negative actions. We partition behavioral
sequences into segments of length n (behavioral `words' and 'motifs') and study
their statistical properties. We find two approximate power laws in the word
ranking distribution, one with an exponent of kappa-1 for the ranks up to 100,
and another with a lower exponent for higher ranks. The Shannon n-tuple
redundancy yields large values and increases in terms of word length, further
underscoring the non-trivial statistical properties of behavioral sequences. On
the collective, societal level the timeseries of particular actions per day can
be understood by a simple mean-reverting log-normal model.Comment: 6 pages, 5 figure
Structure and tie strengths in mobile communication networks
Electronic databases, from phone to emails logs, currently provide detailed
records of human communication patterns, offering novel avenues to map and
explore the structure of social and communication networks. Here we examine the
communication patterns of millions of mobile phone users, allowing us to
simultaneously study the local and the global structure of a society-wide
communication network. We observe a coupling between interaction strengths and
the network's local structure, with the counterintuitive consequence that
social networks are robust to the removal of the strong ties, but fall apart
following a phase transition if the weak ties are removed. We show that this
coupling significantly slows the diffusion process, resulting in dynamic
trapping of information in communities, and find that when it comes to
information diffusion, weak and strong ties are both simultaneously
ineffective.Comment: 30 pages (manuscript + supplementary material), 11 figure
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