Multidimensional networks: foundations of structural analysis

Berlingerio, Michele; Coscia, Michele; Giannotti, Fosca; Monreale, Anna; Pedreschi, Dino

doi:10.1007/s11280-012-0190-4

Cited by 130 publications

(112 citation statements)

References 35 publications

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“…(10) e (Holme and Saramäki 2012;Bazzi et al 2014;Berlingerio et al 2013). For example, suppose in a phone calling temporal network, two nodes are linked by an edge in two successive layers.…”

Section: Temporal Networkmentioning

confidence: 99%

Modularity in complex multilayer networks with multiple aspects: a static perspective

et al. 2017

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Complex systems are usually illustrated by networks which captures the topology of the interactions between the entities. To better understand the roles played by the entities in the system one needs to uncover the underlying community structure of the system. In recent years, systems with interactions that have various types or can change over time between the entities have attracted an increasing research attention. However, algorithms aiming to solve the key problem -community detection -in multilayer networks are still limited. In this work, we first introduce the multilayer network model representation with multiple aspects, which is flexible to a variety of networks. Then based on this model, we naturally derive the multilayer modularity -a widely adopted objective function of community detection in networks -from a static perspective as an evaluation metric to evaluate the quality of the communities detected in multilayer networks. It enables us to better understand the essence of the modularity by pointing out the specific kind of communities that will lead to a high modularity score. We also propose a spectral method called mSpec for the optimization of the proposed modularity function based on the supra-adjacency representation of the multilayer networks. Experiments on the electroencephalograph network and the comparison results on several empirical multilayer networks demonstrate the feasibility and reliable performance of the proposed method.

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Section: Temporal Networkmentioning

confidence: 99%

Modularity in complex multilayer networks with multiple aspects: a static perspective

et al. 2017

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“…Similarly, Bonchi et al (2012) find clusters of edges such that edges of a cluster have the same labels. Berlingerio et al (2013) propose multidimensional network analysis, where connections between vertices belong to different dimensions (e.g. cities can have both train and plane connections) and extend a number of network measures to multi-dimensional graphs.…”

Section: Related Workmentioning

confidence: 99%

Exceptional contextual subgraph mining

et al. 2017

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Many relational data result from the aggregation of several individual behaviors described by some characteristics. For instance, a bike-sharing system may be modeled as a graph where vertices stand for bike-share stations and connections represent bike trips made by users from one station to another. Stations and trips are described by additional information such as the description of the geographical environment of the stations (business vs. residential area, closeness to POI, elevation, urbanization density, etc.), or properties of the bike trips (timestamp, user profile, weather, events and other special conditions about the trip). Identifying highly connected components (such as communities or quasi-cliques) in this graph provides interesting insights into global usages but does not capture mobility profiles that characterize a subpopulation. To tackle this problem we propose an approach rooted in exceptional model mining to find exceptional contextual subgraphs, i.e., subgraphs generated from a context or a description of the individual behaviors that is exceptional (behaves in a different way) compared to the whole augmented graph. The dependency between a context and an edge is assessed by a χ 2 test and the weighted relative accuracy measure is used to only retain contexts that strongly characterize connected subgraphs. We present an original algorithm that uses sophisticated pruning techniques to restrict the search space of vertices, context refinements, and edges to be considered. An experimental evaluation on synthetic data and two real-life datasets demonstrates the effectiveness of the proposed pruning mechanisms, as well as the relevance of the discovered patterns.

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“…Different terminologies exist in the literature for multidimensional networks [6], such as multi-layered networks [8,9] and multiplex networks [31,4], as summarized in [23].…”

Section: Low Highmentioning

confidence: 99%

“…, Dimensional degree [6] Degree (v, d) D/N Node dimension activity [31] NDA(d) D Node dimension connectivity [6] NDC (d) D Node exclusive dimension conn. [6] NEDC [6] EDC (d) D Node activity [31] NA(v) N Multiplex participation coeff. [4] MPC (v) N Dimensional clustering coeff.…”

Section: One-dimensional Metricsmentioning

confidence: 99%

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Towards the characterization of realistic models

Szárnyas

Kővári

Salánki

et al. 2016

Proceedings of the ACM/IEEE 19th International Conference on Model Driven Engineering Languages and Systems

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Custom generators of graph-based models are used in MDE for many purposes such as functional testing and performance benchmarking of modeling environments to ensure the correctness and scalability of tools. However, while existing generators may generate large models in increasing size, these models are claimed to be simple and synthetic, which hinders their credibility for industrial and research benchmarking purposes. But how to characterize a realistic model used in software and systems engineering? This question is investigated in the paper by collecting over 17 different widely used graph metrics taken from other disciplines (e.g. network theory) and evaluating them on 83 instance models originating from six modeling domains. Our preliminary results show that certain metrics are similar within a domain, but differ greatly between domains, which makes them suitable input for future instance model generators to derive more realistic models.

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Multidimensional networks: foundations of structural analysis

Cited by 130 publications

References 35 publications

Modularity in complex multilayer networks with multiple aspects: a static perspective

Modularity in complex multilayer networks with multiple aspects: a static perspective

Exceptional contextual subgraph mining

Towards the characterization of realistic models

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