The generalized 3-connectivity of two kinds of regular networks

2021 ◽  
Author(s):  
Jing Wang
Keyword(s):  
Regular Networks

Joint Distribution of Distances in Large Random Regular Networks

2013 ◽  
Vol 50 (03) ◽  
pp. 861-870 ◽  
Author(s):  
Justin Salez
Keyword(s):  
Joint Distribution ◽  
Marginal Distribution ◽  
Weak Sense ◽  
Regular Graphs ◽  
Random Array ◽  
Point To Point ◽  
Regular Networks ◽  
Different Sources ◽  
Individual Entry

We study the array of point-to-point distances in random regular graphs equipped with exponential edge lengths. We consider the regime where the degree is kept fixed while the number of vertices tends to ∞. The marginal distribution of an individual entry is now well understood, thanks to the work of Bhamidi, van der Hofstad and Hooghiemstra (2010). The purpose of this note is to show that the whole array, suitably recentered, converges in the weak sense to an explicit infinite random array. Our proof consists in analyzing the invasion of the network by several mutually exclusive flows emanating from different sources and propagating simultaneously along the edges.

scholarly journals The Speed of Innovation Diffusion in Social Networks

Econometrica ◽  
2020 ◽  
Vol 88 (2) ◽  
pp. 569-594
Author(s):  
Itai Arieli ◽  
Yakov Babichenko ◽  
Ron Peretz ◽  
H. Peyton Young
Keyword(s):  
Social Networks ◽  
Social Network ◽  
Waiting Time ◽  
Network Topology ◽  
Upper Bound ◽  
Status Quo ◽  
Arbitrary Size ◽  
The Status ◽  
Expected Waiting Time ◽  
Regular Networks

New ways of doing things often get started through the actions of a few innovators, then diffuse rapidly as more and more people come into contact with prior adopters in their social network. Much of the literature focuses on the speed of diffusion as a function of the network topology. In practice, the topology may not be known with any precision, and it is constantly in flux as links are formed and severed. Here, we establish an upper bound on the expected waiting time until a given proportion of the population has adopted that holds independently of the network structure. Kreindler and Young (2014) demonstrated such a bound for regular networks when agents choose between two options: the innovation and the status quo. Our bound holds for directed and undirected networks of arbitrary size and degree distribution, and for multiple competing innovations with different payoffs.

Some new characterizations of metrizable spaces

2010 ◽  
Vol 47 (2) ◽  
pp. 223-229 ◽  
Author(s):  
Rongxin Shen
Keyword(s):  
Metrizable Spaces ◽  
Regular Networks

In this paper, some new metrization theorems about regular networks are obtained, which improve related results in [2], [10], [15], and [20].

Strongly Menger-edge-connectedness and strongly Menger-vertex-connectedness of regular networks

2018 ◽  
Vol 731 ◽  
pp. 50-67 ◽  
Author(s):  
Shengjie He ◽  
Rong-Xia Hao ◽  
Eddie Cheng
Keyword(s):  
Regular Networks

scholarly journals Semantic representation for visual reasoning

2019 ◽  
Vol 277 ◽  
pp. 02006 ◽  
Author(s):  
Xubin Ni ◽  
Lirong Yin ◽  
Xiaobing Chen ◽  
Shan Liu ◽  
Bo Yang ◽  
...  
Keyword(s):  
Neural Networks ◽  
Semantic Representation ◽  
Image Features ◽  
Gram Matrix ◽  
Human Reasoning ◽  
Style Transfer ◽  
Related Information ◽  
Abstract Description ◽  
High Level ◽  
Regular Networks

In the field of visual reasoning, image features are widely used as the input of neural networks to get answers. However, image features are too redundant to learn accurate characterizations for regular networks. While in human reasoning, abstract description is usually constructed to avoid irrelevant details. Inspired by this, a higher-level representation named semantic representation is introduced in this paper to make visual reasoning more efficient. The idea of the Gram matrix used in the neural style transfer research is transferred here to build a relation matrix which enables the related information between objects to be better represented. The model using semantic representation as input outperforms the same model using image features as input which verifies that more accurate results can be obtained through the introduction of high-level semantic representation in the field of visual reasoning.

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