Detecting Motifs in Multiplex Corporate Networks

Takes, Frank W.; Kosters, Walter A.; Witte, Boyd

doi:10.1007/978-3-319-72150-7_41

Cited by 4 publications

(2 citation statements)

References 22 publications

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“…In biological networks, the regulating function of feed-forward loop motifs has frequently been identified [13]. In economic networks, motifs of corporate interlinkage were able to highlight particular corporate structures such as crossholdings [11], as well as unveil the influence of the financial sector in creating complex corporate structures [14]. And in user communication networks, specific network motifs revealed, for example, blocking behavior in online conversations [15].…”

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Efficiently counting complex multilayer temporal motifs in large-scale networks

2019

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This paper proposes novel algorithms for efficiently counting complex network motifs in dynamic networks that are changing over time. Network motifs are small characteristic configurations of a few nodes and edges, and have repeatedly been shown to provide insightful information for understanding the meso-level structure of a network. Here, we deal with counting more complex temporal motifs in large-scale networks that may consist of millions of nodes and edges. The first contribution is an efficient approach to count temporal motifs in multilayer networks and networks with partial timing, two prevalent aspects of many real-world complex networks. We analyze the complexity of these algorithms and empirically validate their performance on a number of real-world user communication networks extracted from online knowledge exchange platforms. Among other things, we find that the multilayer aspects provide significant insights in how complex user interaction patterns differ substantially between online platforms. The second contribution is an analysis of the viability of motif counting algorithms for motifs that are larger than the triad motifs studied in previous work. We provide a novel categorization of motifs of size four, and determine how and at what computational cost these motifs can still be counted efficiently. In doing so, we delineate the “computational frontier” of temporal motif counting algorithms.

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Efficiently counting complex multilayer temporal motifs in large-scale networks

2019

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“…The subgraph isomorphism problem-given a template A, determine if an isomorphic copy of A exists in a larger network B and find the isomorphic copy (or copies) if it exists-has been the subject of voluminous research in the monoplex (i.e., single layer) setting, with approaches based on efficient tree search [38], color coding [3,2], graph homomorphisms [18], rule-based/filter-based matchings [10,29], among others; for a survey of the literature circa 2012, see [24]. In contrast, the problem of multilayer homomorphic/isomorphic subgraph detection is still in its relative infancy, with comparatively fewer existing methods in the literature; see, for example, [41,37,29].…”

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Multiplex graph matching matched filters

Pantazis

Sussman

Park

et al. 2019

2019 IEEE International Conference on Big Data (Big Data)

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We consider the problem of detecting a noisy induced multiplex template network in a larger multiplex background network. Our approach, which extends the framework of [36] to the multiplex setting, leverages a multiplex analogue of the classical graph matching problem to use the template as a matched filter for efficiently searching the background for candidate template matches. The effectiveness of our approach is demonstrated both theoretically and empirically, with particular attention paid to the potential benefits of considering multiple channels.for a definition of multiplex isomorphism), accounting for the reality that relatively large, complex subgraph templates may only errorfully occur in the larger background network. These errors may be due to missing edges/vertices in the template or background, and arise in a variety of real data settings [34]. The subgraph isomorphism problem-given a template A, determine if an isomorphic copy of A exists in a larger network B and find the isomorphic copy (or copies) if it exists-has been the subject of voluminous research in the monoplex (i.e., single layer) setting, with approaches based on efficient tree search [38], color coding [3, 2], graph homomorphisms [18], rule-based/filter-based matchings [10,29], among others; for a survey of the literature circa 2012, see [24]. In contrast, the problem of multilayer homomorphic/isomorphic subgraph detection is still in its relative infancy, with comparatively fewer existing methods in the literature; see, for example, [41,37,29]. Notation: The following notation will be used throughout. For an integer n > 0, we will define [n] := {1, 2, . . . , n}, J n to be the n × n hollow matrix with all off-diagonal entries identically set to 1, 0 n to be the n × n matrix with all entries identically set to 0,

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Multiplex network motifs as building blocks of corporate networks

et al. 2018

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In corporate networks, firms are connected through links of corporate ownership and shared directors, connecting the control over major economic actors in our economies in meaningful and consequential ways. Most research thus far focused on the connectedness of firms as a result of one particular link type, analyzing node-specific metrics or global network-based methods to gain insights in the modelled corporate system.In this paper, we aim to understand multiplex corporate networks with multiple types of connections, specifically investigating the network’s essential building blocks: multiplex network motifs. Motifs, which are small subgraph patterns occurring at significantly higher frequencies than in similar random networks, have demonstrated their usefulness in understanding the structure of many types of real-world networks. However, detecting motifs in multiplex networks is nontrivial for two reasons. First of all, there are no out-of-the-box subgraph enumeration algorithms for multiplex networks. Second, existing null models to test network motif significance, are unable to incorporate the interlayer dependencies in the multiplex network. We solve these two issues by introducing a layer encoding algorithm that incorporates the multiplex aspect in the subgraph enumeration phase. In addition, we propose a null model that is able to preserve the interlayer connectedness, while taking into account that one of the link types is actually the result of a projection of an underlying bipartite network.The experimental section considers the corporate network of Germany, in which tens of thousands of firms are connected through several hundred thousand links. We demonstrate how incorporating the multiplex aspect in motif detection is able to reveal new insights that could not be obtained by studying only one type of relationship. In a general sense, the motifs reflect known corporate governance practices related to the monitoring of investments and the concentration of ownership. A substantial fraction of the discovered motifs is typical for an industrialized country such as Germany, whereas others seem specific for certain economic sectors. Interestingly, we find that motifs involving financial firms are over-represented amongst the larger and more complex motifs. This demonstrates the prominent role of the financial sector in Germany’s largely industry-oriented corporate network.

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Detecting Motifs in Multiplex Corporate Networks

Cited by 4 publications

References 22 publications

Efficiently counting complex multilayer temporal motifs in large-scale networks

Efficiently counting complex multilayer temporal motifs in large-scale networks

Multiplex graph matching matched filters

Multiplex network motifs as building blocks of corporate networks

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