2,384 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
Self-organized criticality in the Kardar-Parisi-Zhang-equation
Kardar-Parisi-Zhang interface depinning with quenched noise is studied in an
ensemble that leads to self-organized criticality in the quenched
Edwards-Wilkinson (QEW) universality class and related sandpile models. An
interface is pinned at the boundaries, and a slowly increasing external drive
is added to compensate for the pinning. The ensuing interface behavior
describes the integrated toppling activity history of a QKPZ cellular
automaton. The avalanche picture consists of several phases depending on the
relative importance of the terms in the interface equation. The SOC state is
more complicated than in the QEW case and it is not related to the properties
of the bulk depinning transition.Comment: 5 pages, 3 figures; accepted for publication in Europhysics Letter
Limited resolution and multiresolution methods in complex network community detection
Detecting community structure in real-world networks is a challenging
problem. Recently, it has been shown that the resolution of methods based on
optimizing a modularity measure or a corresponding energy is limited;
communities with sizes below some threshold remain unresolved. One possibility
to go around this problem is to vary the threshold by using a tuning parameter,
and investigate the community structure at variable resolutions. Here, we
analyze the resolution limit and multiresolution behavior for two different
methods: a q-state Potts method proposed by Reichard and Bornholdt, and a
recent multiresolution method by Arenas, Fernandez, and Gomez. These methods
are studied analytically, and applied to three test networks using simulated
annealing.Comment: 6 pages, 2 figures.Minor changes from previous version, shortened a
couple of page
Election results and the Sznajd model on Barabasi network
The network of Barabasi and Albert, a preferential growth model where a new
node is linked to the old ones with a probability proportional to their
connectivity, is applied to Brazilian election results. The application of the
Sznajd rule, that only agreeing pairs of people can convince their neighbours,
gives a vote distribution in good agreement with reality.Comment: 7 pages including two figures, for Eur. Phys. J.
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
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