74 research outputs found
Measuring Significance of Community Structure in Complex Networks
Many complex systems can be represented as networks and separating a network
into communities could simplify the functional analysis considerably. Recently,
many approaches have been proposed for finding communities, but none of them
can evaluate the communities found are significant or trivial definitely. In
this paper, we propose an index to evaluate the significance of communities in
networks. The index is based on comparing the similarity between the original
community structure in network and the community structure of the network after
perturbed, and is defined by integrating all the similarities. Many artificial
networks and real-world networks are tested. The results show that the index is
independent from the size of network and the number of communities. Moreover,
we find the clear communities always exist in social networks, but don't find
significative communities in proteins interaction networks and metabolic
networks.Comment: 6 pages, 4 figures, 1 tabl
On Counting Triangles through Edge Sampling in Large Dynamic Graphs
Traditional frameworks for dynamic graphs have relied on processing only the
stream of edges added into or deleted from an evolving graph, but not any
additional related information such as the degrees or neighbor lists of nodes
incident to the edges. In this paper, we propose a new edge sampling framework
for big-graph analytics in dynamic graphs which enhances the traditional model
by enabling the use of additional related information. To demonstrate the
advantages of this framework, we present a new sampling algorithm, called Edge
Sample and Discard (ESD). It generates an unbiased estimate of the total number
of triangles, which can be continuously updated in response to both edge
additions and deletions. We provide a comparative analysis of the performance
of ESD against two current state-of-the-art algorithms in terms of accuracy and
complexity. The results of the experiments performed on real graphs show that,
with the help of the neighborhood information of the sampled edges, the
accuracy achieved by our algorithm is substantially better. We also
characterize the impact of properties of the graph on the performance of our
algorithm by testing on several Barabasi-Albert graphs.Comment: A short version of this article appeared in Proceedings of the 2017
IEEE/ACM International Conference on Advances in Social Networks Analysis and
Mining (ASONAM 2017
Flip dynamics in octagonal rhombus tiling sets
We investigate the properties of classical single flip dynamics in sets of
two-dimensional random rhombus tilings. Single flips are local moves involving
3 tiles which sample the tiling sets {\em via} Monte Carlo Markov chains. We
determine the ergodic times of these dynamical systems (at infinite
temperature): they grow with the system size like ;
these dynamics are rapidly mixing. We use an inherent symmetry of tiling sets
and a powerful tool from probability theory, the coupling technique. We also
point out the interesting occurrence of Gumbel distributions.Comment: 5 Revtex pages, 4 figures; definitive versio
Efficient Triangle Counting in Large Graphs via Degree-based Vertex Partitioning
The number of triangles is a computationally expensive graph statistic which
is frequently used in complex network analysis (e.g., transitivity ratio), in
various random graph models (e.g., exponential random graph model) and in
important real world applications such as spam detection, uncovering of the
hidden thematic structure of the Web and link recommendation. Counting
triangles in graphs with millions and billions of edges requires algorithms
which run fast, use small amount of space, provide accurate estimates of the
number of triangles and preferably are parallelizable.
In this paper we present an efficient triangle counting algorithm which can
be adapted to the semistreaming model. The key idea of our algorithm is to
combine the sampling algorithm of Tsourakakis et al. and the partitioning of
the set of vertices into a high degree and a low degree subset respectively as
in the Alon, Yuster and Zwick work treating each set appropriately. We obtain a
running time
and an approximation (multiplicative error), where is the number
of vertices, the number of edges and the maximum number of
triangles an edge is contained.
Furthermore, we show how this algorithm can be adapted to the semistreaming
model with space usage and a constant number of passes (three) over the graph
stream. We apply our methods in various networks with several millions of edges
and we obtain excellent results. Finally, we propose a random projection based
method for triangle counting and provide a sufficient condition to obtain an
estimate with low variance.Comment: 1) 12 pages 2) To appear in the 7th Workshop on Algorithms and Models
for the Web Graph (WAW 2010
Correlations in Bipartite Collaboration Networks
Collaboration networks are studied as an example of growing bipartite
networks. These have been previously observed to have structure such as
positive correlations between nearest-neighbour degrees. However, a detailed
understanding of the origin of this phenomenon and the growth dynamics is
lacking. Both of these are analyzed empirically and simulated using various
models. A new one is presented, incorporating empirically necessary ingredients
such as bipartiteness and sublinear preferential attachment. This, and a
recently proposed model of team assembly both agree roughly with some empirical
observations and fail in several others.Comment: 13 pages, 17 figures, 2 table, submitted to JSTAT; manuscript
reorganized, figures and a table adde
Worldwide food recall patterns over an eleven month period: A country perspective.
<p>Abstract</p> <p>Background</p> <p>Following the World Health Organization Forum in November 2007, the Beijing Declaration recognized the importance of food safety along with the rights of all individuals to a safe and adequate diet. The aim of this study is to retrospectively analyze the patterns in food alert and recall by countries to identify the principal hazard generators and gatekeepers of food safety in the eleven months leading up to the Declaration.</p> <p>Methods</p> <p>The food recall data set was collected by the Laboratory of the Government Chemist (LGC, UK) over the period from January to November 2007. Statistics were computed with the focus reporting patterns by the 117 countries. The complexity of the recorded interrelations was depicted as a network constructed from structural properties contained in the data. The analysed network properties included degrees, weighted degrees, modularity and <it>k</it>-core decomposition. Network analyses of the reports, based on 'country making report' (<it>detector</it>) and 'country reported on' (<it>transgressor</it>), revealed that the network is organized around a dominant core.</p> <p>Results</p> <p>Ten countries were reported for sixty per cent of all faulty products marketed, with the top 5 countries having received between 100 to 281 reports. Further analysis of the dominant core revealed that out of the top five transgressors three made no reports (in the order China > Turkey > Iran). The top ten detectors account for three quarters of reports with three > 300 (Italy: 406, Germany: 340, United Kingdom: 322).</p> <p>Conclusion</p> <p>Of the 117 countries studied, the vast majority of food reports are made by 10 countries, with EU countries predominating. The majority of the faulty foodstuffs originate in ten countries with four major producers making no reports. This pattern is very distant from that proposed by the Beijing Declaration which urges all countries to take responsibility for the provision of safe and adequate diets for their nationals.</p
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