Self-similar non-clustered planar graphs as models for complex networks

Comellas, Francesc; Zhang, Zhongzhi; Chen, Lichao

doi:10.1088/1751-8113/42/4/045103

Cited by 7 publications

(6 citation statements)

References 23 publications

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“…(17) We now return to compute equation (12). For convenience, we use Γ η,i t to denote the set of non-hub vertices belonging to class P i in M (η) t .…”

Section: Generation Of the Graphs M D (T)mentioning

confidence: 99%

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Planar unclustered scale-free graphs as models for technological and biological networks

Miralles

Comellas

Chen

et al. 2010

Physica A: Statistical Mechanics and its Applications

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Many real life networks present an average path length logarithmic with the number of\ud nodes and a degree distribution which follows a power law. Often these networks have\ud also a modular and self-similar structure and, in some cases usually associated with\ud topological restrictions their clustering is low and they are almost planar. In this paper\ud we introduce a family of graphs which share all these properties and are defined by two\ud parameters. As their construction is deterministic, we obtain exact analytic expressions\ud for relevant properties of the graphs including the degree distribution, degree correlation,\ud diameter, and average distance, as a function of the two defining parameters. Thus, the\ud graphs are useful to model some complex networks, in particular several families of\ud technological and biological networks, and in the design of new practical communication\ud algorithms in relation to their dynamical processes. They can also help understanding the\ud underlying mechanisms that have produced their particular structure.Postprint (published version

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“…(17) We now return to compute equation (12). For convenience, we use Γ η,i t to denote the set of non-hub vertices belonging to class P i in M (η) t .…”

Section: Generation Of the Graphs M D (T)mentioning

confidence: 99%

“…A generalization of these former methods introduces at each iteration a more complex substructure than a single node which is added to the network in a deterministic way. Substructures considered are triangles [11], circles [12] and paths [13].…”

Section: Introductionmentioning

confidence: 99%

Planar unclustered scale-free graphs as models for technological and biological networks

Miralles

Comellas

Chen

et al. 2010

Physica A: Statistical Mechanics and its Applications

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“…Small-world effect (any two vertices in the system can be connected by relatively short paths and local clustering characterizes the tendency of groups of vertices to be all connected to each other) and Scale-free property (vertices degree distribution follow a power-law) are common in most real-life networks(Ref. [6], [7], [9], [18], [21], [22], [23], [29], [30], [31]), transportation systems or social and economic networks and so on. Complex networks with these two characteristics are called small-world scale-free networks.The time sees three steps on studying complex systems and networks.…”

Section: Introductionmentioning

confidence: 99%

Scale-free Network Models With Parameters

Ma¹,

Su²,

Yao³

et al. 2016

Proceedings of the 2016 Joint International Information Technology, Mechanical and Electronic Engineering

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Based on typical scale-free network models, we set up the partial differential equation satisfied more general dynamic systems, and then we not only find another important topological property of scale-free networks, but also discuss the real background meaning of every function in the dynamical systems. Meanwhile we generalize the BA-network-model growth way ("star-graph-growth-way"). Starting from a more general situation, we establish a network model containing "star-graph-growth-way" and "triangle-growth-way". By analysis, this model is not only scale-free but also small-wall. Finally, distinguish the connect between the scope of the power law parameters.

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“…Small-world effect and Scale-free property are common in most real-life networks (Ref. [6,7,9,17,20,21,22], [26][27][28][29][30]), such as the Internet, protein-protein interactions Ref. [10,16]), transportation systems or social and economic networks and so on.…”

Section: Introductionmentioning

confidence: 99%