By Giuseppe Mangioni, Filippo Simini, Stephen Miles Uzzo, Dashun Wang
Elucidating the spatial and temporal dynamics of the way issues attach has turn into some of the most vital components of study within the twenty first century. community technological know-how now pervades approximately each technology area, leading to new discoveries in a bunch of dynamic social and ordinary structures, together with: how neurons attach and converse within the mind, how details percolates inside and between social networks, the evolution of technological know-how examine via co-authorship networks, the unfold of epidemics and lots of different complicated phenomena.
Over the earlier decade, advances in computational energy have positioned the instruments of community research within the fingers of accelerating numbers of scientists, allowing extra explorations of our international than ever sooner than attainable. info technology, social sciences, structures biology, ecosystems ecology, neuroscience and physics all take advantage of this circulation, which mixes graph thought with info sciences to enhance and validate theories concerning the international round us.
This publication brings jointly state of the art examine from the community technological know-how box and contains varied and interdisciplinary subject matters equivalent to: modeling the constitution of city platforms, habit in social networks, schooling and studying, facts community structure, constitution and dynamics of agencies, crime and terrorism, in addition to community topology, modularity and group detection.
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Comparison of Percentage Error value for various methods. The dataset name, motif size, and the number of samples (in parenthesis) are given in figure sub-title. 1 Error Comparison We compare the error percentage (PE) of various topologies using SRW- RW, MHRW, and FANMOD algorithms on all the datasets for different size values (p). , for these topologies, the zG (g) value in Equation 3 is the highest among all the topologies. For this experiment, we fixed the number of samples to 10000 for all of the experiments except for the experiment of Ca-AstroPh dataset, where we use 40000 samples.
Random graphs with arbitrary degree distributions and their applications. Physical Review E 64(2), 026118 (2001) 19. : Robustness of network measures to link errors. Physical Review E 88(6), 062812 (2013) 20. : Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52(3), 1059–1069 (2010) 36 S. Tsugawa and H. Ohsaki 21. : Emergence of fractals in social networks: Analysis of community structure and interaction locality. In: Proceedings of the 38th Annual IEEE International Computers, Software, and Applications Conference (COMPSAC 2014), pp.
Also note that, FANMOD runs only for subgraph size up to 8. MHRW SRW-rw FANMOD 50 40 30 20 10 0 10 22 16 Iteration (103) (a) Sample size vs Runtime 28 RunTime (s) for 10000 iteration 60 RunTime (s) SRW-rw MHRW FANMOD 5 70 10 4 10 103 102 101 100 6 7 8 Subgraph Size 9 10 (b) Subgraph Size vs Runtime Fig. 5. 3 Convergence Comparison In this experiment, we study the convergence using the negative log (KL) metric by varying the number of samples. e. with an increasing number of samples FANMOD does not converge to the true concentration.