Robustness of network coherence in asymmetric unicyclic graphs

2021 ◽  
Author(s):  
Jing Chen ◽  
Ting Jing ◽  
Weigang Sun
Keyword(s):  
Network Size ◽  
Unicyclic Graph ◽  
Symmetric Graph ◽  
Laplacian Spectrum ◽  
Unicyclic Graphs ◽  
Closed Form Solutions ◽  
Asymmetric Structures ◽  
Network Parameters ◽  
Asymmetric Graph ◽  
Better Than

In this paper, we propose a family of unicyclic graphs to study robustness of network coherence quantified by the Laplacian spectrum, which measures the extent of consensus under the noise. We adjust the network parameters to change the structural asymmetries with an aim of studying their effects on the coherence. Using the graph’s structures and matrix theories, we obtain closed-form solutions of the network coherence regarding network parameters and network size. We further show that the coherence of the asymmetric graph is higher than the corresponding symmetric graph and also compare the consensus behaviors for the graphs with different asymmetric structures. It displays that the coherence of the unicyclic graph with one hub is better than the graph with two hubs. Finally, we investigate the effect of degree of hub nodes on the coherence and find that bigger difference of degrees leads to better coherence.

scholarly journals Forecast of Waterway Cargo Turnover Volume Based on Genetic Algorithm to Optimize Neural Network Parameters

2021 ◽  
Vol 2083 (3) ◽  
pp. 032010
Author(s):  
Rong Ma
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Bp Neural Network ◽  
Forecast Model ◽  
Network Parameters ◽  
The Neural Network ◽  
Target Effect ◽  
The Empirical Analysis ◽  
Better Than

Abstract The traditional BP neural network is difficult to achieve the target effect in the prediction of waterway cargo turnover. In order to improve the accuracy of waterway cargo turnover forecast, a waterway cargo turnover forecast model was created based on genetic algorithm to optimize neural network parameters. The genetic algorithm overcomes the trap that the general iterative method easily falls into, that is, the “endless loop” phenomenon that occurs when the local minimum is small, and the calculation time is small, and the robustness is high. Using genetic algorithm optimized BP neural network to predict waterway cargo turnover, and the empirical analysis of the waterway cargo turnover forecast is carried out. The results obtained show that the neural network waterway optimized by genetic algorithm has a higher accuracy than the traditional BP neural network for predicting waterway cargo turnover, and the optimization model can long-term analysis of the characteristics of waterway cargo turnover changes shows that the prediction effect is far better than traditional neural networks.

scholarly journals On the Estrada Indices of Unicyclic Graphs with Fixed Diameters

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2395
Author(s):  
Wenjie Ning ◽  
Kun Wang
Keyword(s):  
Adjacency Matrix ◽  
Connected Graph ◽  
Unicyclic Graph ◽  
Unicyclic Graphs ◽  
Estrada Index

The Estrada index of a graph G is defined as EE(G)=∑i=1neλi, where λ1,λ2,…,λn are the eigenvalues of the adjacency matrix of G. A unicyclic graph is a connected graph with a unique cycle. Let U(n,d) be the set of all unicyclic graphs with n vertices and diameter d. In this paper, we give some transformations which can be used to compare the Estrada indices of two graphs. Using these transformations, we determine the graphs with the maximum Estrada indices among U(n,d). We characterize two candidate graphs with the maximum Estrada index if d is odd and three candidate graphs with the maximum Estrada index if d is even.

scholarly journals Hamiltonian Cycles in Squares of Vertex-Unicyclic Graphs

1976 ◽  
Vol 19 (2) ◽  
pp. 169-172 ◽  
Author(s):  
Herbert Fleischner ◽  
Arthur M. Hobbs
Keyword(s):  
Sufficient Conditions ◽  
Unicyclic Graph ◽  
Necessary And Sufficient Conditions ◽  
Hamiltonian Cycles ◽  
Unicyclic Graphs ◽  
Necessary And Sufficient

In this paper we determine necessary and sufficient conditions for the square of a vertex-unicyclic graph to be Hamiltonian. The conditions are simple and easily checked. Further, we show that the square of a vertex-unicyclic graph is Hamiltonian if and only if it is vertex-pancyclic.

scholarly journals Unicyclic graphs with given number of cut vertices and the maximal Merrifield-Simmons index

Filomat ◽  
2014 ◽  
Vol 28 (3) ◽  
pp. 451-461 ◽  
Author(s):  
Hongbo Hua ◽  
Xinli Xu ◽  
Hongzhuan Wang
Keyword(s):  
Connected Graph ◽  
Independent Sets ◽  
Unicyclic Graph ◽  
Unicyclic Graphs

The Merrifield-Simmons index of a graph G, denoted by i(G), is defined to be the total number of independent sets in G, including the empty set. A connected graph is called a unicyclic graph, if it possesses equal number of vertices and edges. In this paper, we characterize the maximal unicyclic graph w.r.t. i(G) within all unicyclic graphs with given order and number of cut vertices. As a consequence, we determine the connected graph with at least one cycle, given number of cut vertices and the maximal Merrifield-Simmons index.

Multiassociative Memory: Recurrent Synapses Increase Storage Capacity

2017 ◽  
Vol 29 (5) ◽  
pp. 1375-1405 ◽  
Author(s):  
Marcelo Matheus Gauy ◽  
Florian Meier ◽  
Angelika Steger
Keyword(s):  
Mathematical Analysis ◽  
Storage Capacity ◽  
Network Size ◽  
Information Capacity ◽  
Large Network ◽  
Cortical Column ◽  
Association Model ◽  
Network Parameters ◽  
Connection Density ◽  
Strong Synapse

The connection density of nearby neurons in the cortex has been observed to be around 0.1, whereas the longer-range connections are present with much sparser density (Kalisman, Silberberg, & Markram, 2005 ). We propose a memory association model that qualitatively explains these empirical observations. The model we consider is a multiassociative, sparse, Willshaw-like model consisting of binary threshold neurons and binary synapses. It uses recurrent synapses for iterative retrieval of stored memories. We quantify the usefulness of recurrent synapses by simulating the model for small network sizes and by doing a precise mathematical analysis for large network sizes. Given the network parameters, we can determine the precise values of recurrent and afferent synapse densities that optimize the storage capacity of the network. If the network size is like that of a cortical column, then the predicted optimal recurrent density lies in a range that is compatible with biological measurements. Furthermore, we show that our model is able to surpass the standard Willshaw model in the multiassociative case if the information capacity is normalized per strong synapse or per bits required to store the model, as considered in Knoblauch, Palm, and Sommer ( 2010 ).

scholarly journals Unicyclic Graphs Whose Completely Regular Endomorphisms form a Monoid

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 240
Author(s):  
Rui Gu ◽  
Hailong Hou
Keyword(s):  
Sufficient Conditions ◽  
Unicyclic Graph ◽  
Necessary And Sufficient Conditions ◽  
Unicyclic Graphs ◽  
Completely Regular ◽  
Odd Cycle ◽  
Necessary And Sufficient

In this paper, completely regular endomorphisms of unicyclic graphs are explored. Let G be a unicyclic graph and let c E n d ( G ) be the set of all completely regular endomorphisms of G. The necessary and sufficient conditions under which c E n d ( G ) forms a monoid are given. It is shown that c E n d ( G ) forms a submonoid of E n d ( G ) if and only if G is an odd cycle or G = G ( n , m ) for some odd n ≥ 3 and integer m ≥ 1 .

Unicyclic graphs with regular endomorphism monoids

2016 ◽  
Vol 08 (02) ◽  
pp. 1650020 ◽  
Author(s):  
Xiaobin Ma ◽  
Dein Wong ◽  
Jinming Zhou
Keyword(s):  
Unicyclic Graph ◽  
Endomorphism Monoid ◽  
Unicyclic Graphs ◽  
Endomorphism Monoids ◽  
Odd Cycle ◽  
Open Question

The motivation of this paper comes from an open question: which graphs have regular endomorphism monoids? In this paper, we give a definitely answer for unicyclic graphs, proving that a unicyclic graph [Formula: see text] is End-regular if and only if, either [Formula: see text] is an even cycle with 4, 6 or 8 vertices, or [Formula: see text] contains an odd cycle [Formula: see text] such that the distance of any vertex to [Formula: see text] is at most 1, i.e., [Formula: see text]. The join of two unicyclic graphs with a regular endomorphism monoid is explicitly described.

scholarly journals Spectral radius and extremal graphs for class of unicyclic graph with pendant vertices

2017 ◽  
Vol 9 (7) ◽  
pp. 168781401770713 ◽  
Author(s):  
Lu Zhi ◽  
Meijin Xu ◽  
Xiujuan Liu ◽  
Xiaodong Chen ◽  
Chen Chen ◽  
...  
Keyword(s):  
Spectral Radius ◽  
Upper Bounds ◽  
Unicyclic Graph ◽  
Extremal Graphs ◽  
Unicyclic Graphs

In this article, we research on the spectral radius of extremal graphs for the unicyclic graphs with girth g mainly by the graft transformation and matching and obtain the upper bounds of the spectral radius of unicyclic graphs.

scholarly journals A SURVEY OF THE EFFECT OF NETWORK PARAMETERS ON COMMUNICATION LINKS IN WIRELESS SENSOR NETWORKS

2013 ◽  
pp. 187-189
Author(s):  
KHYATI SHRIVASTAV ◽  
ASWATH A.R.
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Sensor Network ◽  
Network Size ◽  
Sensor Nodes ◽  
Wireless Sensor ◽  
Network Systems ◽  
Network Parameters ◽  
Size Number ◽  
Communication Links

In the wireless sensor networks, the communication links between sensor nodes is important. This paper presents the analysis on the effect of parameters of network size, number of nodes and communication ranges on the number of communication links in the sensor network systems. The MATLAB tool is used for deployment of sensor nodes in various area fields.

The harmonic index of unicyclic graphs

2017 ◽  
Vol 10 (03) ◽  
pp. 1750039 ◽  
Author(s):  
R. Rasi ◽  
S. M. Sheikholeslami
Keyword(s):  
Maximum Degree ◽  
Unicyclic Graph ◽  
Unicyclic Graphs ◽  
Harmonic Index ◽  
Degree Of A Vertex

The harmonic index of a graph [Formula: see text], denoted by [Formula: see text], is defined as the sum of weights [Formula: see text] over all edges [Formula: see text] of [Formula: see text], where [Formula: see text] denotes the degree of a vertex [Formula: see text]. Hu and Zhou [WSEAS Trans. Math. 12 (2013) 716–726] proved that for any unicyclic graph [Formula: see text] of order [Formula: see text], [Formula: see text] with equality if and only if [Formula: see text]. Recently, Zhong and Cui [Filomat 29 (2015) 673–686] generalized the above bound and proved that for any unicyclic graph [Formula: see text] of order [Formula: see text] other than [Formula: see text], [Formula: see text]. In this paper, we generalize the aforemention results and show that for any connected unicyclic graph [Formula: see text] of order [Formula: see text] with maximum degree [Formula: see text], [Formula: see text] and classify the extremal unicyclic graphs.

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