arXiv subjects

Gareth J. Baxter

Publications and source records attributed to Gareth J. Baxter.

5 recordsLinked to original sources

arXiv2026

Strongly clustered random graphs via triadic closure: Degree correlations and clustering spectrum

Real-world networks often exhibit strong transitivity with nontrivial local clustering spectra and degree correlations. Such features are not easily modeled in tractable network models, creating an obstacle to the theoretical understanding of such complex network structures. Here, we address this problem using a model for strongly clustered random graphs in which each triad of a random network backbone is closed with a certain probability. Despite the intricate loopy local structure of the graphs obtained, we provide exact expressions for the local clustering spectrum and the degree correlations, filling the gap in the theoretical description of this model for random graphs. In particular, we find positive degree assortativity accompanying high transitivity, and nontrivial structure in the clustering spectrum. Exact asymptotic analytical results, obtained for uncorrelated locally tree-like backbones, are complemented with extensive numerical characterization of finite-size effects.

physics.soc-ph↗

arXiv2024

Inference of Causal Networks using a Topological Threshold

We propose a constraint-based algorithm, which automatically determines causal relevance thresholds, to infer causal networks from data. We call these topological thresholds. We present two methods for determining the threshold: the first seeks a set of edges that leaves no disconnected nodes in the network; the second seeks a causal large connected component in the data. We tested these methods both for discrete synthetic and real data, and compared the results with those obtained for the PC algorithm, which we took as the benchmark. We show that this novel algorithm is generally faster and more accurate than the PC algorithm. The algorithm for determining the thresholds requires choosing a measure of causality. We tested our methods for Fisher Correlations, commonly used in PC algorithm (for instance in \cite{kalisch2005}), and further proposed a discrete and asymmetric measure of causality, that we called Net Influence, which provided very good results when inferring causal networks from discrete data. This metric allows for inferring directionality of the edges in the process of applying the thresholds, speeding up the inference of causal DAGs.

stat.ML↗

arXiv2016

Cycles and Clustering in Multiplex Networks

In multiplex networks, cycles cannot be characterized only by their length, as edges may occur in different layers in different combinations. We define a classification of cycles by the number of edges in each layer and the number of switches between layers. We calculate the expected number of cycles of each type in the configuration model of a large sparse multiplex network. Our method accounts for the full degree distribution including correlations between degrees in different layers. In particular, we obtain the numbers of cycles of length 3 of all possible types. Using these, we give a complete set of clustering coefficients and their expected values. We show that correlations between the degrees of a vertex in different layers strongly affect the number of cycles of a given type, and the number of switches between layers. Both increase with assortative correlations and are strongly decreased by disassortative correlations. The effect of correlations on clustering coefficients is equally pronounced.

physics.soc-ph↗

arXiv2016

Correlated Edge Overlaps in Multiplex Networks

We develop the theory of sparse multiplex networks with partially overlapping links based on their local tree-likeness. This theory enables us to find the giant mutually connected component in a two-layer multiplex network with arbitrary correlations between connections of different types. We find that correlations between the overlapping and non-overlapping links markedly change the phase diagram of the system, leading to multiple hybrid phase transitions. For assortative correlations we observe recurrent hybrid phase transitions.

physics.soc-ph↗

arXiv2014

Weak percolation on multiplex networks

Bootstrap percolation is a simple but non-trivial model. It has applications in many areas of science and has been explored on random networks for several decades. In single layer (simplex) networks, it has been recently observed that bootstrap percolation, which is defined as an incremental process, can be seen as the opposite of pruning percolation, where nodes are removed according to a connectivity rule. Here we propose models of both bootstrap and pruning percolation for multiplex networks. We collectively refer to these two models with the concept of "weak" percolation, to distinguish them from the somewhat classical concept of ordinary ("strong") percolation. While the two models coincide in simplex networks, we show that they decouple when considering multiplexes, giving rise to a wealth of critical phenomena. Our bootstrap model constitutes the simplest example of a contagion process on a multiplex network and has potential applications in critical infrastructure recovery and information security. Moreover, we show that our pruning percolation model may provide a way to diagnose missing layers in a multiplex network. Finally, our analytical approach allows us to calculate critical behavior and characterize critical clusters.

cond-mat.dis-nn↗