scholarly journals The Fractional Preferential Attachment Scale-Free Network Model

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 509
Author(s):  
Rafał Rak ◽  
Ewa Rak
Keyword(s):  
Network Model ◽  
Real World ◽  
Degree Distribution ◽  
Preferential Attachment ◽  
Clustering Coefficient ◽  
Node Degree ◽  
Scale Free Network ◽  
Scale Free ◽  
Degree Correlation ◽  
Free Network

Many networks generated by nature have two generic properties: they are formed in the process of preferential attachment and they are scale-free. Considering these features, by interfering with mechanism of the preferential attachment, we propose a generalisation of the Barabási–Albert model—the ’Fractional Preferential Attachment’ (FPA) scale-free network model—that generates networks with time-independent degree distributions p ( k ) ∼ k − γ with degree exponent 2 < γ ≤ 3 (where γ = 3 corresponds to the typical value of the BA model). In the FPA model, the element controlling the network properties is the f parameter, where f ∈ ( 0 , 1 ⟩ . Depending on the different values of f parameter, we study the statistical properties of the numerically generated networks. We investigate the topological properties of FPA networks such as degree distribution, degree correlation (network assortativity), clustering coefficient, average node degree, network diameter, average shortest path length and features of fractality. We compare the obtained values with the results for various synthetic and real-world networks. It is found that, depending on f, the FPA model generates networks with parameters similar to the real-world networks. Furthermore, it is shown that f parameter has a significant impact on, among others, degree distribution and degree correlation of generated networks. Therefore, the FPA scale-free network model can be an interesting alternative to existing network models. In addition, it turns out that, regardless of the value of f, FPA networks are not fractal.

scholarly journals A Novel BA Complex Network Model on Color Template Matching

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Risheng Han ◽  
Shigen Shen ◽  
Guangxue Yue ◽  
Hui Ding
Keyword(s):  
Complex Network ◽  
Network Model ◽  
Template Matching ◽  
Preferential Attachment ◽  
Color Space ◽  
Scale Free Network ◽  
Color Distribution ◽  
Scale Free ◽  
Matching Process ◽  
Free Network

A novel BA complex network model of color space is proposed based on two fundamental rules of BA scale-free network model: growth and preferential attachment. The scale-free characteristic of color space is discovered by analyzing evolving process of template’s color distribution. And then the template’s BA complex network model can be used to select important color pixels which have much larger effects than other color pixels in matching process. The proposed BA complex network model of color space can be easily integrated into many traditional template matching algorithms, such as SSD based matching and SAD based matching. Experiments show the performance of color template matching results can be improved based on the proposed algorithm. To the best of our knowledge, this is the first study about how to model the color space of images using a proper complex network model and apply the complex network model to template matching.

scholarly journals Complex interaction networks of cytokines after transarterial chemotherapy in patients with hepatocellular carcinoma

2019 ◽  
Author(s):  
Dong Wook Jekarl ◽  
Seungok Lee ◽  
Jung Hyun Kwon ◽  
Soon Woo Nam ◽  
Jeong Won Jang ◽  
...  
Keyword(s):  
Adverse Outcome ◽  
Temporal Changes ◽  
Clustering Coefficient ◽  
Scale Free Network ◽  
Serum Samples ◽  
Cytokine Network ◽  
Scale Free ◽  
Degree Correlation ◽  
Free Network ◽  
Assortative Network

AbstractInflammation in the tumor microenvironment influences all stages of HCC development and progression as well as the anti-cancer response by immune system. In this study, we studied cytokine networks before and after transarterial chemotherapy (TACE). Serum samples obtained from 203 HCC patients treated with TACE were analyzed for inflammatory cytokines including interleukin (IL)-1β, IL-2, IL-4, IL-5, IL-6, IL-9, IL-10, IL-12, IL-13, IL-17, IL-22, TNF-α, IFN-γ, and C-reactive protein (CRP) levels. Cytokine concentrations were measured at day 0 (D0, baseline), day3 (D3), day7 (D7), and day 60 (D60) after TACE. Network analysis revealed that modules within cytokine network at D0 were lost by D60 and modularity value (Mc) was decreased from 0.177 at D0 to −0.091 at D60. D60 had the lowest network heterogeneity and lower diameter, clustering coefficient, network density and recruited nodes. Degree correlation revealed that assortative network turned to disassortative network by D60 indicating that the network gained scale free feature. CRP, IL-2 were components of modules related with adverse outcome and IL-13, favorable outcome. Median survival month of patient group with high and low values with P-values were as follows: D0 CRP, 9.5 month (M), 54.2M (P<0.0001); D0 IL-2, 39.9M, 56.1M (P=0.0084); D3 CRP, 31.3M, 55.1 M (P=0.0056); D7 CRP, 28.7M, 50.7M (P=0.0065); IL-13, 51.9M, 33.6M (P=0.06). Network modularity decreased with temporal changes. Components of modules that included CRP, IL-2 and IL-6 were associated with adverse outcome and short overall survival. These modules were dissolved by D60 after TACE. Degree correlation decreased by D60, indicating that the cytokine network gained the scale free network property as in other biological network. TACE treatment converted cytokine network from that with inflammatory module to that with scale free network feature and without modules. Further studies are required to verify temporal changes of cytokine network in HCC patients after TACE.

The Barabási and Albert scale-free network model

2018 ◽  
Vol 35 (1) ◽  
pp. 123-132 ◽  
Author(s):  
Lei Zhu ◽  
Lei Wang ◽  
Xiang Zheng ◽  
Yuzhang Xu
Keyword(s):  
Network Model ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network

scholarly journals HIERARCHICAL AND MIXING PROPERTIES OF STATIC COMPLEX NETWORKS EMERGING FROM FLUCTUATING CLASSICAL RANDOM GRAPHS

2006 ◽  
Vol 17 (09) ◽  
pp. 1303-1311 ◽  
Author(s):  
SUMIYOSHI ABE ◽  
STEFAN THURNER
Keyword(s):  
Complex Network ◽  
Preferential Attachment ◽  
Hierarchical Organization ◽  
Scale Free Network ◽  
Mixing Properties ◽  
Scale Free ◽  
Free Network ◽  
Growing Network ◽  
Arbitrary Connectivity

The Erdös–Rényi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to lead to a static complex network with an arbitrary connectivity distribution. In particular, a scale-free network with the hierarchical organization is constructed without assuming any knowledge about the global linking structure, in contrast to the preferential attachment rule for a growing network. The hierarchical and mixing properties of the static scale-free network thus constructed are studied. The present approach establishes a bridge between a scalar characterization of individual vertices and topology of an emerging complex network. The result may offer a clue for understanding the origin of a few abundance of connectivity distributions in a wide variety of static real-world networks.

Clique Size and Centrality Metrics for Analysis of Real-World Network Graphs

2019 ◽  
pp. 1183-1198
Author(s):  
Natarajan Meghanathan
Keyword(s):  
Real World ◽  
Random Network ◽  
Maximal Clique ◽  
Closeness Centrality ◽  
Node Degree ◽  
Degree Centrality ◽  
Eigenvector Centrality ◽  
Scale Free ◽  
Centrality Metrics ◽  
Free Network

The authors present correlation analysis between the centrality values observed for nodes (a computationally lightweight metric) and the maximal clique size (a computationally hard metric) that each node is part of in complex real-world network graphs. They consider the four common centrality metrics: degree centrality (DegC), eigenvector centrality (EVC), closeness centrality (ClC), and betweenness centrality (BWC). They define the maximal clique size for a node as the size of the largest clique (in terms of the number of constituent nodes) the node is part of. The real-world network graphs studied range from regular random network graphs to scale-free network graphs. The authors observe that the correlation between the centrality value and the maximal clique size for a node increases with increase in the spectral radius ratio for node degree, which is a measure of the variation of the node degree in the network. They observe the degree-based centrality metrics (DegC and EVC) to be relatively better correlated with the maximal clique size compared to the shortest path-based centrality metrics (ClC and BWC).

Clique Size and Centrality Metrics for Analysis of Real-World Network Graphs

2018 ◽  
pp. 6507-6521
Author(s):  
Natarajan Meghanathan
Keyword(s):  
Real World ◽  
Random Network ◽  
Maximal Clique ◽  
Closeness Centrality ◽  
Node Degree ◽  
Degree Centrality ◽  
Eigenvector Centrality ◽  
Scale Free ◽  
Centrality Metrics ◽  
Free Network

We present correlation analysis between the centrality values observed for nodes (a computationally lightweight metric) and the maximal clique size (a computationally hard metric) that each node is part of in complex real-world network graphs. We consider the four common centrality metrics: degree centrality (DegC), eigenvector centrality (EVC), closeness centrality (ClC) and betweenness centrality (BWC). We define the maximal clique size for a node as the size of the largest clique (in terms of the number of constituent nodes) the node is part of. The real-world network graphs studied range from regular random network graphs to scale-free network graphs. We observe that the correlation between the centrality value and the maximal clique size for a node increases with increase in the spectral radius ratio for node degree, which is a measure of the variation of the node degree in the network. We observe the degree-based centrality metrics (DegC and EVC) to be relatively better correlated with the maximal clique size compared to the shortest path-based centrality metrics (ClC and BWC).

scholarly journals The Formation of Social Network Assortativity: A Cultural Trait-Matching Mechanism

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Wei Wang ◽  
Xiaoming Sun ◽  
Yalan Wang ◽  
Wentian Cui
Keyword(s):  
Preferential Attachment ◽  
Scale Free Network ◽  
Selection Probability ◽  
Network Nodes ◽  
Scale Free ◽  
Cultural Trait ◽  
Free Network ◽  
Matching Mechanism ◽  
Simulation Results ◽  
Attachment Mechanism

The preferential attachment mechanism that forms scale-free network cannot display assortativity, i.e., the degree of one node is positively correlated with that of their neighbors in the network. Given the attributes of network nodes, a cultural trait-matching mechanism is further introduced in this paper. Both theoretical analysis and simulation results indicate that the higher selection probability of such mechanism, the more obvious the assortativity is shown in networks. Further, the degree of nodes presents a positive logarithm correlation with that of adjacent ones. Finally, this study discusses the theoretical and practical significances of the introduction of such a cultural trait-matching mechanism.

Sign in / Sign up

Export Citation Format

Share Document