Identification of Chordless Cycles in Ecological Networks

Sokhn, Nayla; Baltensperger, Richard; Bersier, Louis–Félix; Hennebert, Jean; Ultes-Nitsche, Ulrich

doi:10.1007/978-3-319-03473-7_28

Cited by 7 publications

(13 citation statements)

References 10 publications

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“…In ecology, it is often of interest to identify competition structures among species that rely on the same resources 1 . The formation of cycles in graphs representing interactions among species can reveal such competitive behaviours (Sokhn et al (2012); Koutrouli et al (2020)). Hence, a research question arising here is the following: To what extent are cycles formed from the aggressive interactions between fish in the network data?…”

Section: Ecological Application and Proposed Metricmentioning

confidence: 99%

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Bayesian modelling and computation utilising cycles in multiple network data

Mantziou¹,

Mitra²,

Lunagómez³

2021

Preprint

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Modelling multiple network data is crucial for addressing a wide range of applied research questions. However, there are many challenges, both theoretical and computational, to address. Network cycles are often of particular interest in many applications, e.g. ecological studies, and an unexplored area has been how to incorporate networks' cycles within the inferential framework in an explicit way. The recently developed Spherical Network Family of models (SNF) offers a flexible formulation for modelling multiple network data that permits any type of metric. This has opened up the possibility to formulate network models that focus on network properties hitherto not possible or practical to consider. In this article we propose a novel network distance metric that measures similarities between networks with respect to their cycles, and incorporate this within the SNF model to allow inferences that explicitly capture information on cycles. These network motifs are of particular interest in ecological studies. We further propose a novel computational framework to allow posterior inferences from the intractable SNF model for moderate sized networks. Lastly, we apply the resulting methodology to a set of ecological network data studying aggressive interactions between species of fish. We show our model is able to make cogent inferences concerning the cycle behaviour amongst the species, and beyond those possible from a model that does not consider this network motif.

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Section: Ecological Application and Proposed Metricmentioning

confidence: 99%

“…certain species vying over a particular food source or type of habitat. In a network these behaviours would be characterised through cycles (Sokhn et al (2012); Koutrouli et al (2020)).…”

Section: Introductionmentioning

confidence: 99%

Bayesian modelling and computation utilising cycles in multiple network data

Mantziou¹,

Mitra²,

Lunagómez³

2021

Preprint

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“…Another problem that can be addressed using this method is to identify chordless loops of various sizes in a network. A chordless loop is a sequence of vertices with more than three vertices if for all i = 1, • • • , k there is exactly one link from vertex v i to v i+1 and there is no other link between any two of the vertices in this sequence [16]. Recent studies on ecological networks have discovered the existence of many chordless cycles in these networks [17], therefore enumeration of all chordless cycles can make a significant impact on understanding the structure of these networks.…”

Section: Applying Reliability Concepts To Other Network Analysis Prob...mentioning

confidence: 99%

Analyzing network reliability using structural motifs

Khorramzadeh

Youssef

Eubank³

et al. 2015

Phys. Rev. E

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This paper uses the reliability polynomial, introduced by Moore and Shannon in 1956, to analyze the effect of network structure on diffusive dynamics such as the spread of infectious disease. We exhibit a representation for the reliability polynomial in terms of what we call structural motifs that is well suited for reasoning about the effect of a network’s structural properties on diffusion across the network. We illustrate by deriving several general results relating graph structure to dynamical phenomena.

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“…There are very few algorithms in the literature for listing chordless cycles and/or paths, where some of them have no guaranteed performance [12,16]. The most notable and elegant listing algorithm is by Uno [15], with a cost of O(m 2 + m • C) time for chordless cycles and O(m 2 + m • P ) time for chordless st-paths, hence amortized O(m) time delay.…”

Section: Introductionmentioning

confidence: 99%

Amortized $\tilde{O}(|V|)$ -Delay Algorithm for Listing Chordless Cycles in Undirected Graphs

Ferreira

Grossi

Rizzi

et al. 2014

Algorithms - ESA 2014

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Chordless cycles are very natural structures in undirected graphs, with an important history and distinguished role in graph theory. Motivated also by previous work on the classical problem of listing cycles, we study how to list chordless cycles. The best known solution to list all the C chordless cycles contained in an undirected graph G = (V, E) takes O(|E| 2 +|E|•C) time. In this paper we provide an algorithm taking O(|E| + |V | • C) time. We also show how to obtain the same complexity for listing all the P chordless st-paths in G (where C is replaced by P ).

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Identification of Chordless Cycles in Ecological Networks

Cited by 7 publications

References 10 publications

Bayesian modelling and computation utilising cycles in multiple network data

Bayesian modelling and computation utilising cycles in multiple network data

Analyzing network reliability using structural motifs

Amortized $\tilde{O}(|V|)$ -Delay Algorithm for Listing Chordless Cycles in Undirected Graphs

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