Specialization Models of Network Growth

Bunimovich, Leonid; Smith, Dallas; Webb, Benjamin

doi:10.1093/comnet/cny024

Cited by 9 publications

(13 citation statements)

References 34 publications

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“…Finally, stationary phenomena may likewise be the product of temporal mechanisms. Age differentiation and dedifferentation show that the positive manifold is a dynamic phenomenon, and hierarchically organized systems can emerge during network growth (Bunimovich et al, 2018).…”

Section: Wired Intelligencementioning

confidence: 99%

Evolving Networks of Human Intelligence

Savi¹,

Marsman²,

Maas³

2021

Preprint

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Twentieth century theory formation in human intelligence was dominated by factor theories; network theories will dominate the twenty first. Network theories answer a broad call for formal theories in psychological science, provide a strong approach to an idiographic science, and create an opportunity to study the developmental mechanisms of human's cognitive dynamics. Although the current century already delivered two formal stationary network theories of human intelligence—mutualism and wired intelligence—integrating dynamic mechanisms remains a serious challenge. This challenge translates into clear priorities: the identification of robust developmental phenomena, the study of the mechanisms that drive these phenomena, the integration of these mechanisms into network theories of growth, the integration of network theories from different explanatory levels, and the empirical characterization of the structure of network theories.

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Section: Wired Intelligencementioning

confidence: 99%

Evolving Networks of Human Intelligence

Savi¹,

Marsman²,

Maas³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The class of graphs we consider, without any loss in generality, in this paper are weighted directed graphs. To motivate the specialization model introduced in [6] of a graph G, representing some network, we consider the following example of disambiguation in a Wikipedia network, a subset of the World Wide Web.…”

Section: The Specialization Processmentioning

confidence: 99%

“…Previously, in [6] the authors introduced the specialization model of network growth built on this notion of specialization. This model is based on the idea that as a network specializes the function of one or more of its components, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Figure 1 and 2). Repeated application of this specialization process results in networks with a highly modular [26,29], hierarchical [13,22], as well as sparse topology [28,21] each of which is a defining feature of real networks, which are not captured by previous models (see [6] for more details).…”

Section: Introductionmentioning

confidence: 99%

“…We show that if such dynamical systems, which we refer to as dynamical networks, are intrinsically stable then any specialized version of the network is also intrinsically stable. Section 5 discusses a number of variants of the specialization method introduced in [6] and described in Section 2 as well as their spectral and dynamic consequences to a network. Proofs of the paper's main results together with the necessary parts of the theory of isospectral network transformations are placed in Section 6.…”

Section: Introductionmentioning

confidence: 99%

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Spectral and Dynamic Consequences of Network Specialization

Bunimovich

Passey

Smith

et al. 2020

Int. J. Bifurcation Chaos

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One of the hallmarks of real networks is the ability to perform increasingly complex tasks as their topology evolves. To explain this, it has been observed that as a network grows certain subsets of the network begin to specialize the function(s) they perform. A recent model of network growth based on this notion of specialization has been able to reproduce some of the most well-known topological features found in real-world networks including right-skewed degree distributions, the small world property, modular as well as hierarchical topology, etc. Here we describe how specialization under this model also effects the spectral properties of a network. This allows us to give the conditions under which a network is able to maintain its dynamics as its topology evolves. Specifically, we show that if a network is intrinsically stable, which is a stronger version of the standard notion of global stability, then the network maintains this type of dynamics as the network evolves. This is one of the first steps toward unifying the rigorous study of the two types of dynamics exhibited by networks. These are the dynamics of a network, which is the topological evolution of the network’s structure, modeled here by the process of network specialization, and the dynamics on a network, which is the changing state of the network elements, where the type of dynamics we consider is global stability. The main examples we apply our results to are recurrent neural networks, which are the basis of certain types of machine learning algorithms.

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On Attractors of Isospectral Compressions of Networks

Bunimovich

Shu

2018

Springer Proceedings in Mathematics &Amp; Statistics

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In the recently developed theory of isospectral transformations of networks isospectral compressions are performed with respect to some chosen characteristic (attribute) of nodes (or edges) of networks. Each isospectral compression (when a certain characteristic is fixed) defines a dynamical system on the space of all networks. It is shown that any orbit of such dynamical system which starts at any finite network (as the initial point of this orbit) converges to an attractor. Such attractor is a smaller network where a chosen characteristic has the same value for all nodes (or edges). We demonstrate that isospectral contractions of one and the same network defined by different characteristics of nodes (or edges) may converge to the same as well as to different attractors. It is also shown that spectrally equivalent with respect to some characteristic networks could be non-spectrally equivalent for another characteristic of nodes (edges). These results suggest a new constructive approach to analysis of networks structures and to comparison of topologies of different networks. Mathematics Subject Classification: 05C50, 15A18

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Specialization Models of Network Growth

Cited by 9 publications

References 34 publications

Evolving Networks of Human Intelligence

Evolving Networks of Human Intelligence

Spectral and Dynamic Consequences of Network Specialization

On Attractors of Isospectral Compressions of Networks

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