258 research outputs found
Exact analytical solution of average path length for Apollonian networks
The exact formula for the average path length of Apollonian networks is
found. With the help of recursion relations derived from the self-similar
structure, we obtain the exact solution of average path length, ,
for Apollonian networks. In contrast to the well-known numerical result
[Phys. Rev. Lett. \textbf{94}, 018702
(2005)], our rigorous solution shows that the average path length grows
logarithmically as in the infinite limit of network
size . The extensive numerical calculations completely agree with our
closed-form solution.Comment: 8 pages, 4 figure
Impact of a Microbial-Enhanced Oil Recovery Field Trial on Microbial Communities in a Low-Temperature Heavy Oil Reservoir
Part-Whole Relational Few-Shot 3D Point Cloud Semantic Segmentation
The author wishes to extend sincere appreciation to Professor Lin Shi for the generous provision of equipment support, which significantly aided in the successful completion of this research. Furthermore, the author expresses gratitude to Associate Professor Ning Li and Teacher Wei Guan for their invaluable academic guidance and unwavering support. Their expertise and advice played a crucial role in shaping the direction and quality of this research.Peer reviewe
Maximal planar scale-free Sierpinski networks with small-world effect and power-law strength-degree correlation
Many real networks share three generic properties: they are scale-free,
display a small-world effect, and show a power-law strength-degree correlation.
In this paper, we propose a type of deterministically growing networks called
Sierpinski networks, which are induced by the famous Sierpinski fractals and
constructed in a simple iterative way. We derive analytical expressions for
degree distribution, strength distribution, clustering coefficient, and
strength-degree correlation, which agree well with the characterizations of
various real-life networks. Moreover, we show that the introduced Sierpinski
networks are maximal planar graphs.Comment: 6 pages, 5 figures, accepted by EP
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