469 research outputs found
On the Analysis of a Label Propagation Algorithm for Community Detection
This paper initiates formal analysis of a simple, distributed algorithm for
community detection on networks. We analyze an algorithm that we call
\textsc{Max-LPA}, both in terms of its convergence time and in terms of the
"quality" of the communities detected. \textsc{Max-LPA} is an instance of a
class of community detection algorithms called \textit{label propagation}
algorithms. As far as we know, most analysis of label propagation algorithms
thus far has been empirical in nature and in this paper we seek a theoretical
understanding of label propagation algorithms. In our main result, we define a
clustered version of \er random graphs with clusters where
the probability , of an edge connecting nodes within a cluster is
higher than , the probability of an edge connecting nodes in distinct
clusters. We show that even with fairly general restrictions on and
( for any , , where is the number of nodes), \textsc{Max-LPA} detects the
clusters in just two rounds. Based on this and on empirical
results, we conjecture that \textsc{Max-LPA} can correctly and quickly identify
communities on clustered \er graphs even when the clusters are much sparser,
i.e., with for some .Comment: 17 pages. Submitted to ICDCN 201
Dynamical decoherence of a qubit coupled to a quantum dot or the SYK black hole
We study the dynamical decoherence of a qubit weakly coupled to a two-body
random interaction model (TBRIM) describing a quantum dot of interacting
fermions or the Sachdev-Ye-Kitaev (SYK) black hole model. We determine the
rates of qubit relaxation and dephasing for regimes of dynamical thermalization
of the quantum dot or of quantum chaos in the SYK model. These rates are found
to correspond to the Fermi golden rule and quantum Zeno regimes depending on
the qubit-fermion coupling strength. An unusual regime is found where these
rates are practically independent of TBRIM parameters. We push forward an
analogy between TBRIM and quantum small-world networks with an explosive
spreading over exponentially large number of states in a finite time being
similar to six degrees of separation in small-world social networks. We find
that the SYK model has approximately two-three degrees of separation.Comment: 17 pages, 15 pdf-figure
Identification of Peer Effects through Social Networks
We provide new results regarding the identification of peer effects. We consider an extended version of the linear-in-means model where each individual has his own specific reference group. Interactions are thus structured through a social network. We assume that correlated unobservables are either absent, or treated as fixed effects at the component level. In both cases, we provide easy-to-check necessary and sufficient conditions for identification. We show that endogenous and exogenous effects are generally identified under network interaction, although identification may fail for some particular structures. Monte Carlo simulations provide an analysis of the effects of some crucial characteristics of a network (i.e., density, intransitivity) on the estimates of social effects. Our approach generalizes a number of previous results due to Manski (1993), Moffitt (2001), and Lee (2006).Social networks, Peer effects, identification, reflection problem
Effort and synergies in network formation
The aim of this paper is to understand the interactions between productive effort and the
creation of synergies that are the sources of technological collaboration agreements,
agglomeration, social stratification, etc. We model this interaction in a way that allows
us to characterize how agents devote resources to both activities. This permits a fullfledged
equilibrium/welfare analysis of network formation with endogenous investment
efforts and to derive unambiguous comparative statics results. In spite of its parsimony
that ensures tractability, the model retains enough richness to replicate a (relatively)
broad range of empirical regularities displayed by social and economic networks, and is
directly estimable to recover is structural parameters
Universality in protein residue networks
Residue networks representing 595 nonhomologous proteins are studied. These networks exhibit universal topological characteristics as they belong to the topological class of modular networks formed by several highly interconnected clusters separated by topological cavities. There are some networks which tend to deviate from this universality. These networks represent small-size proteins having less than 200 residues. We explain such differences in terms of the domain structure of these proteins. On the other hand, we find that the topological cavities characterizing proteins residue networks match very well with protein binding sites. We then investigate the effect of the cutoff value used in building the residue network. For small cutoff values, less than 5Ă
, the cavities found are very large corresponding almost to the whole protein surface. On the contrary, for large cutoff value, more than 10.0 Ă
, only very large cavities are detected and the networks look very homogeneous. These findings are useful for practical purposes as well as for identifying "protein-like" complex networks. Finally, we show that the main topological class of residue networks is not reproduced by random networks growing according to Erdös-Rényi model or the preferential attachment method of Barabåsi-Albert. However, the Watts-Strogatz (WS) model reproduces very well the topological class as well as other topological properties of residue network. We propose here a more biologically appealing modification of the WS model to describe residue networks
Assortative mixing in close-packed spatial networks
Background
In recent years, there is aroused interest in expressing complex systems as networks of interacting nodes. Using descriptors from graph theory, it has been possible to classify many diverse systems derived from social and physical sciences alike. In particular, folded proteins as examples of self-assembled complex molecules have also been investigated intensely using these tools. However, we need to develop additional measures to classify different systems, in order to dissect the underlying hierarchy.
Methodology and Principal Findings
In this study, a general analytical relation for the dependence of nearest neighbor degree correlations on degree is derived. Dependence of local clustering on degree is shown to be the sole determining factor of assortative versus disassortative mixing in networks. The characteristics of networks constructed from spatial atomic/molecular systems exemplified by self-organized residue networks built from folded protein structures and block copolymers, atomic clusters and well-compressed polymeric melts are studied. Distributions of statistical properties of the networks are presented. For these densely-packed systems, assortative mixing in the network construction is found to apply, and conditions are derived for a simple linear dependence.
Conclusions
Our analyses (i) reveal patterns that are common to close-packed clusters of atoms/molecules, (ii) identify the type of surface effects prominent in different close-packed systems, and (iii) associate fingerprints that may be used to classify networks with varying types of correlations
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