Identifying networks with common organizational principles

Wegner, Anatol E.; Ospina-Forero, Luis; Gaunt, Robert E.; Deane, Charlotte M.; Reinert, Gesine

doi:10.48550/arxiv.1704.00387

Cited by 1 publication

(5 citation statements)

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“…Besides GCD, there are also other graphlet/orbitbased measures that can similarly be generalized to multilayer networks. These include the graphlet degree distribution agreement (GDDA) [16], the relative graphlet frequency distance (RGFD) [29], Netdis [18] (requires the definition of multilayer ego-networks), and NetEmd [14]. In the next section, GCD is taken as the multilayer distance measure of choice, and in Supplementary Materials section J, multilayer NetEmd (section J.1) and multilayer GDDA (section J.2) are investigated in more detail.…”

Section: Graphlet-based Methods and Measuresmentioning

confidence: 99%

“…A common use case is to compute topological similarity and dissimilarity of pairs of networks using graphlets. This type of alignmentfree methods [13] are less computationally intensive than methods where the full network would need to be aligned [14,15]. Further, they can be used to group together networks that share common features, for example, because they are created via similar mechanisms [16,17,18,14].…”

Section: Introductionmentioning

confidence: 99%

“…This type of alignmentfree methods [13] are less computationally intensive than methods where the full network would need to be aligned [14,15]. Further, they can be used to group together networks that share common features, for example, because they are created via similar mechanisms [16,17,18,14]. Graphlet-based methods are built on graphlet degree distributions, which are generalizations of the degree distribution of a network [16].…”

Section: Introductionmentioning

confidence: 99%

“…Graphlet-based methods are built on graphlet degree distributions, which are generalizations of the degree distribution of a network [16]. For example, they are used to assess the distance between two different networks [17,14,13]. Graphlet degrees for nodes can be defined based on the full network [16,17,14] or on the ego-networks of nodes [18].…”

Section: Introductionmentioning

confidence: 99%

“…For example, they are used to assess the distance between two different networks [17,14,13]. Graphlet degrees for nodes can be defined based on the full network [16,17,14] or on the ego-networks of nodes [18]. Mathematically, the graphlet degree of a node is defined by how many times it is found on a specific automorphism orbit, a node equivalence class based on network automorphisms within the graphlets of the network (orbit for short).…”

Section: Introductionmentioning

confidence: 99%

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Graphlets in multilayer networks

Sallmen

Tarmo

Kivelä

2021

Journal of Complex Networks

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Representing various networked data as multiplex networks, networks of networks and other multilayer networks can reveal completely new types of structures in these systems. We introduce a general and principled graphlet framework for multilayer networks which allows one to break any multilayer network into small multilayered building blocks. These multilayer graphlets can be either analysed themselves or used to do tasks such as comparing different systems. The method is flexible in terms of multilayer isomorphism, automorphism orbit definition and the type of multilayer network. We illustrate our method for multiplex networks and show how it can be used to distinguish networks produced with multiple models from each other in an unsupervised way. In addition, we include an automatic way of generating the hundreds of dependency equations between the orbit counts needed to remove redundant orbit counts. The framework introduced here allows one to analyse multilayer networks with versatile semantics, and these methods can thus be used to analyse the structural building blocks of myriad multilayer networks.

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