Toward a Harmonious Unifying Hybrid Model for Any Evolving Complex Networks

Abstract

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.

Advances in theoretical models of network science

“…For the three typical networks, (a) HUHPM-BA, (b) HUHPM-BBV, and (c) HUHPM-TDE, under their different parameters, the simulation results are consistent with the theoretical results. Finally, similar results for the power-laws of the node strength and the edged weight governed by the total hybrid ratio d/r are also obtained in the HUHPM-BBV and HUHPM-TDE [30].…”

“…For the HUHPM-BA and the HUHPM-BBV networks similar relationships are also obtained [30]. Furthermore, by comparing the APL with the network size N for the three kinds of models, which are the HUHPM, the original BA model and random graph model, Fig.…”

Transition Features from Simplicity-Universality to Complexity-Diversification Under UHNTF

“…If dr ≤ 1, then 1 ≤ γ ≤ 3 which consistent with the RPA playing leading role in generalized random networks. Theoretically, we have deduced the complicated analytical relation expression of the power exponent γ with the dr for the HUHPM-BA: [8][9]11] γ…”

“…where γ 0 = 3. Similarly, we have obtained the γ and dr relation for the weighted HUHPM-BBV by considering change of δ or w. The power exponent γ of the HUHPM-BBV model is given by [8][9]11] γ…”

Composite centrality: A natural scale for complex evolving networks

“…Any of such networks is generated by and/or hosts an underlying flow between its nodes, such as information, contacts, goods or diseases. Considering the description and analysis of evolving network structures, most efforts have been made regarding network modelling [14,15,16,17,18], while the de- * andreas.ch.joseph@gmail.com velopment of sophisticated analysis tools and methodologies has seen less progress. This yet will be the topic of this work.…”