Topological transition features and synchronizability of a weighted hybrid preferential network

Qiao

et al. 2007

Advs. Complex Syst.

The current interest in complex networks is a part of a broader movement towards research on complex systems. Motivation of this work raises the two challenging questions: (i) Are real networks fundamentally random preferential attached without any deterministic attachment for both un-weighted and weighted networks? (ii) Is there a coherent physical idea and model for unifying the study of the formation mechanism of complex networks? To answer these questions, we propose a harmonious unifying hybrid preferential model (HUHPM) to a certain class of complex networks, which is controlled by a hybrid ratio, d/r, and study their behavior both numerically and analytically. As typical examples, we apply the concepts and method of the HUHPM to un-weighted scale-free networks proposed by Barabasi and Albert (BA), weighted evolving networks proposed by Barras, Bartholomew and Vespignani (BBV), and the traffic driven evolution (TDE) networks proposed by Wang et al., to get the so-called HUHPM-BA, HUHPM-BBV and HUHPM-TDE networks. All the findings of topological properties in the above three typical HUHPM networks give certain universal meaningful results which reveal some essential hybrid mechanisms for the formation of nontrivial scale-free and small-world networks.Keywords: Network science; harmonious unifying hybrid preferential model; hybrid ratio d/r; un-weighted and weighted networks; universal properties; small-world; effects; scalefree property; sensitivity of exponent to hybrid ratio. Advs. Complex Syst. 2007.10:117-141. Downloaded from www.worldscientific.com by CARLETON UNIVERSITY on 03/16/15. For personal use only.

Section: Assortativity Coefficient and Synchronizabilitysupporting

confidence: 64%

Toward a Harmonious Unifying Hybrid Model for Any Evolving Complex Networks

Qiao

et al. 2007

Advs. Complex Syst.

“…To describe the determinist and randomness of the harmony and unity of the real world, as well as the complexity and diversity of complex network growth, we have put forward a UHNM, and gradually formed a unified hybrid network theory frame including three models. The simulation and theoretical analysis have revealed some evolution features and universal characteristics depending on four hybrid ratios, and can be applied to most current un-weighted and weighted complex network evolution models Lu et al, 2006;Fang, 2006;Fang et al, 2007cFang et al, , 2007dFang et al, , 2007e, 2009Fang and Li, 2008;Li et al, 2007). The key idea of the unified hybrid network theory frame can be described as follows.…”

Section: Unified Hybrid Network Theory Frame: From the Level-3 To Thementioning

confidence: 99%

“…In the RWNs, randomness and regular are two categories related to multiple hybrid fashions. To describe diverse complex networks and improve the HUHPM, further more, we extend the HUHPM towards a Large Unifying Hybrid Network Model (LUHNM) 2007b, 2007c, 2007dLu et al, 2006;Fang, 2006;Fang and Li, 2008;Li et al, 2007) as the level-2 of the CNP. Its characteristics are the introduction of two hybrid ratios (see equations (2) and (3) In the level-2, we have observed much more complex relation of topological properties depending on three hybrid ratios (dr, fd, gr), in which degree-degree correlation r c or the assortative coefficient r c is one of the interesting quantities.…”

Section: The Level-2 Of the Cnp: The Luhnmmentioning

confidence: 99%

“…The level-4 of the CNP is the Weighted Evolving Network Models (WENM) (Fang and Liang, 2005;Dorogovtsev and Mendes, 2000b;Yook et al, 2001;Bianconi and Barabási, 2001;Zheng et al, 2003;Antal and Krapivsky, 2005;Barrat et al, 2004aBarrat et al, , 2004bWang et al, 2005), which is developed from the unweighted networks above, and further revealed three power-law distributions. The level-3 of the CNP is the Harmonious Unification Hybrid Preferential Model (HUHPM), which has found both the SW (smallest Average Path Length (APL) and largest Average Clustering Coefficient (ACC)) and the SF properties depending on total hybrid ratio dr sensitively Lu et al, 2006;Fang, 2006). The level-2 of the CNP is the Large Unified Hybrid Network Model (LUHNM) depending on three hybrid ratios (dr, fd, gr), and revealed more complex phenomena Fang and Li, 2008;Li et al, 2007).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Network Complexity Pyramid with five levels

2009

IJSCC

Self Cite

“…In additional, we have also investigated the effects of hybrid ratio d/r on the degree-degree correlation and dynamical synchronizability for the HUHPM networks [19,20] . The main result is that the synchronizability of the weighted HUHP-BBV network is enhanced if the total hybrid ratio increases and the HUHPM network satisfies the so-called type-I synchronization condition; while the synchronizability of the HUHP-BBV network is weakened if it satisfies the so-called type-II synchronization condition.…”

Section: The Relation Of the Acc And The Network Size Nmentioning

confidence: 99%

A harmonious unifying hybrid preferential model and its universal properties for complex dynamical networks

Qiao

et al. 2007

SCI CHINA SER G

To describe the real world which is a harmonious unification world with both determinism and randomness, we propose a harmonious unifying hybrid preferential model (HUHPM) of a certain class of complex dynamical networks. HUHPM is governed only by the total hybrid ratio d/r according to the practical need. As some typical examples, the concepts and methods of the HUHPM are applied to the un-weighted BA model proposed by Barabási et al., the weighted BBV model proposed by Barat et al. and the weighted TDE model proposed by Wang et al. to get the so-called HUHPM-BA network, HUHPM-BBV network and HUHPM-TDE network.These HUHPM networks are investigated both analytically and numerically. It is found that the HUHPM reveals several universal properties, which more approach to the real-world networks for both un-weighted and weighted networks and have potential for applications.harmonious unifying hybrid preferential model, total hybrid ratio, small world effect, scale-free property, un-weighted and weighted networks Interdisciplinary studies and conferences on complex networks have become a hot activity all over the world since the small world (SW) effect and the scale-free (SF) property were discovered by Watts and Strogats (so called WS model) in 1998 [1] and by Barabási and Albert (so-called BA model) in 1999 [2] , respectively. These two discoveries symbolized that the complex network research has broken through the imprisonment of random graph analysis that started from the 1960s, and has since made unprecedented progress in the following forty years [3][4][5][6][7][8][9][10][11][12][13][14][15][16] . Domestic and international research is springing up like mushrooms after a spring rain, and basically has synchronization progress. Even so, currently how to really portray the actual network characteristic www.