Verification of temporal-causal network models by mathematical analysis

2017

Comput Soc Netw

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BackgroundNetwork-Oriented Modelling based on adaptive temporal–causal networks provides a unified approach to model and analyse dynamics and adaptivity of various processes, including mental and social interaction processes.MethodsAdaptive temporal–causal network models are based on causal relations by which the states in the network change over time, and these causal relations are adaptive in the sense that they themselves also change over time.ResultsIt is discussed how modelling and analysis of the dynamics of the behaviour of these adaptive network models can be performed. The approach is illustrated for adaptive network models describing social interaction.ConclusionsIn particular, the homophily principle and the ‘more becomes more’ principles for social interactions are addressed. It is shown how the chosen Network-Oriented Modelling method provides a basis to model and analyse these social phenomena.

Section: Discussionmentioning

confidence: 99%

Section: Mathematical Analysis Of Temporal–causal Network Modelsmentioning

confidence: 99%

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Modelling and analysis of the dynamics of adaptive temporal–causal network models for evolving social interactions

2017

Comput Soc Netw

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“…12 and Ref. 4, and it can also be rei¯ed itself and thus provide second-and higher-order rei¯ed networks to cover networks that are second-or higher-order adaptive.…”

Section: Combination Function Weight Role C Role Matrix Mcfwmentioning

confidence: 99%

Relating Emerging Adaptive Network Behavior to Network Structure: A Declarative Network Analysis Perspective

2020

Vietnam J. Comp. Sci.

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In this paper, the challenge for dynamic network modeling is addressed how emerging behavior of an adaptive network can be related to characteristics of the adaptive network’s structure. By applying network reification, the adaptation structure is modeled in a declarative manner as a subnetwork of a reified network extending the base network. This construction can be used to model and analyze any adaptive network in a neat and declarative manner, where the adaptation principles are described by declarative mathematical relations and functions in reified temporal-causal network format. In different examples, it is shown how certain adaptation principles known from the literature can be formulated easily in such a declarative reified temporal-causal network format. The main focus of this paper on how emerging adaptive network behavior relates to network structure is addressed, among others, by means of a number of theorems of the format “properties of reified network structure characteristics imply emerging adaptive behavior properties”. In such theorems, classes of networks are considered that satisfy certain network structure properties concerning connectivity and aggregation characteristics. Results include, for example, that under some conditions on the network structure characteristics, all states eventually get the same value. Similar analysis methods are applied to reification states, in particular for adaptation principles for Hebbian learning and for bonding by homophily, respectively. Here results include how certain properties of the aggregation characteristics of the network structure of the reified network for Hebbian learning entail behavioral properties relating to the maximal final values of the adaptive connection weights. Similarly, results are discussed on how properties of the aggregation characteristics of the reified network structure for bonding by homophily entail behavioral properties relating to clustering and community formation in a social network.

“…The research presented here has been initiated from the angle of mathematical analysis and verification of network models in comparison to simulations for these models. For more background on this angle, see, for example, Treur (2016b) or (Treur, 2016a, Ch 12). Just as verification in Software Engineering is very useful for the quality of developed software (e.g., Drechsler, 2004;Fisher, 2007), so too verification in network modeling is a useful means to get implementations of network models in accordance with the specifications of the models and eliminate implementation errors.…”

Section: S83mentioning

confidence: 99%

Analysis of a network’s asymptotic behavior via its structure involving its strongly connected components

2019

Net Sci

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In this paper, it is addressed how network structure can be related to asymptotic network behavior. If such a relation is studied, that usually concerns only strongly connected networks and only linear functions describing the dynamics. In this paper, both conditions are generalized. A couple of general theorems is presented that relates asymptotic behavior of a network to the network’s structure characteristics. The network structure characteristics, on the one hand, concern the network’s strongly connected components and their mutual connections; this generalizes the condition of being strongly connected to a very general condition. On the other hand, the network structure characteristics considered generalize from linear functions to functions that are normalized, monotonic, and scalar-free, so that many nonlinear functions are also covered. Thus, the contributed theorems generalize the existing theorems on the relation between network structure and asymptotic network behavior addressing only specific cases such as acyclic networks, fully, and strongly connected networks, and theorems addressing only linear functions. This paper was invited as an extended (by more than 45%) version of a Complex Networks’18 conference paper. In the discussion section, the differences are explained in more detail.