37,558 research outputs found
Optimal scales in weighted networks
The analysis of networks characterized by links with heterogeneous intensity
or weight suffers from two long-standing problems of arbitrariness. On one
hand, the definitions of topological properties introduced for binary graphs
can be generalized in non-unique ways to weighted networks. On the other hand,
even when a definition is given, there is no natural choice of the (optimal)
scale of link intensities (e.g. the money unit in economic networks). Here we
show that these two seemingly independent problems can be regarded as
intimately related, and propose a common solution to both. Using a formalism
that we recently proposed in order to map a weighted network to an ensemble of
binary graphs, we introduce an information-theoretic approach leading to the
least biased generalization of binary properties to weighted networks, and at
the same time fixing the optimal scale of link intensities. We illustrate our
method on various social and economic networks.Comment: Accepted for presentation at SocInfo 2013, Kyoto, 25-27 November 2013
(http://www.socinfo2013.org
Variations on the Theme of Conning in Mathematical Economics
The mathematization of economics is almost exclusively in terms of the mathematics of real analysis which, in turn, is founded on set theory (and the axiom of choice) and orthodox mathematical logic. In this paper I try to point out that this kind of mathematization is replete with economic infelicities. The attempt to extract these infelicities is in terms of three main examples: dynamics, policy and rational expectations and learning. The focus is on the role and reliance on standard xed point theorems in orthodox mathematical economics
Analytical maximum-likelihood method to detect patterns in real networks
In order to detect patterns in real networks, randomized graph ensembles that
preserve only part of the topology of an observed network are systematically
used as fundamental null models. However, their generation is still
problematic. The existing approaches are either computationally demanding and
beyond analytic control, or analytically accessible but highly approximate.
Here we propose a solution to this long-standing problem by introducing an
exact and fast method that allows to obtain expectation values and standard
deviations of any topological property analytically, for any binary, weighted,
directed or undirected network. Remarkably, the time required to obtain the
expectation value of any property is as short as that required to compute the
same property on the single original network. Our method reveals that the null
behavior of various correlation properties is different from what previously
believed, and highly sensitive to the particular network considered. Moreover,
our approach shows that important structural properties (such as the modularity
used in community detection problems) are currently based on incorrect
expressions, and provides the exact quantities that should replace them.Comment: 26 pages, 10 figure
Complex Networks and Symmetry I: A Review
In this review we establish various connections between complex networks and
symmetry. While special types of symmetries (e.g., automorphisms) are studied
in detail within discrete mathematics for particular classes of deterministic
graphs, the analysis of more general symmetries in real complex networks is far
less developed. We argue that real networks, as any entity characterized by
imperfections or errors, necessarily require a stochastic notion of invariance.
We therefore propose a definition of stochastic symmetry based on graph
ensembles and use it to review the main results of network theory from an
unusual perspective. The results discussed here and in a companion paper show
that stochastic symmetry highlights the most informative topological properties
of real networks, even in noisy situations unaccessible to exact techniques.Comment: Final accepted versio
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