Showing papers on "Degree distribution published in 2023"

Determinants of collective failure in excitable networks.

Abstract: We study collective failures in biologically realistic networks that consist of coupled excitable units. The networks have broad-scale degree distribution, high modularity, and small-world properties, while the excitable dynamics is determined by the paradigmatic FitzHugh-Nagumo model. We consider different coupling strengths, bifurcation distances, and various aging scenarios as potential culprits of collective failure. We find that for intermediate coupling strengths, the network remains globally active the longest if the high-degree nodes are first targets for inactivation. This agrees well with previously published results, which showed that oscillatory networks can be highly fragile to the targeted inactivation of low-degree nodes, especially under weak coupling. However, we also show that the most efficient strategy to enact collective failure does not only non-monotonically depend on the coupling strength, but it also depends on the distance from the bifurcation point to the oscillatory behavior of individual excitable units. Altogether, we provide a comprehensive account of determinants of collective failure in excitable networks, and we hope this will prove useful for better understanding breakdowns in systems that are subject to such dynamics.

Robustness and stability of spin-glass ground states to perturbed interactions

Abstract: Across many problems in science and engineering, it is important to consider how much the output of a given system changes due to perturbations of the input. Here, we investigate the glassy phase of ±J spin glasses at zero temperature by calculating the robustness of the ground states to flips in the sign of single interactions. For random graphs and the Sherrington-Kirkpatrick model, we find relatively large sets of bond configurations that generate the same ground state. These sets can themselves be analyzed as subgraphs of the interaction domain, and we compute many of their topological properties. In particular, we find that the robustness, equivalent to the average degree, of these subgraphs is much higher than one would expect from a random model. Most notably, it scales in the same logarithmic way with the size of the subgraph as has been found in genotype-phenotype maps for RNA secondary structure folding, protein quaternary structure, gene regulatory networks, as well as for models for genetic programming. The similarity between these disparate systems suggests that this scaling may have a more universal origin.

Empirical Analysis of the Cruise Shipping Network in Asia

Abstract: The cruise shipping market has been growing dynamically in the past two decades. This study presented an empirical analysis of the Asian cruise shipping network (ACSN) in which the nodes are cruise ports and links are cruise routes connecting the ports, using complex network analysis. An analysis of 245 voyages operated by 16 cruise lines between 215 ports in 26 countries found that ports in the ACSN are connected by 704 links. The ACSN is a small-world network with a small average path length and a high clustering coefficient, and its degree distribution follows an exponential function. A small number of ports have high connectivity, and most ports have low connections. Most high-degree ports connect to low-degree ports. The important roles and properties of ports vary depending on centrality measures.

Asymptotic enumeration of graphs by degree sequence, and the degree sequence of a random graph

Abstract: In this paper we relate a fundamental parameter of a random graph, its degree sequence, to a simple model of nearly independent binomial random variables. As a result, many interesting functions of the joint distribution of graph degrees, such as the distribution of the median degree, become amenable to estimation. Our result is established by proving an asymptotic formula conjectured in 1990 for the number of graphs with given degree sequence. In particular, this gives an asymptotic formula for the number of $d$-regular graphs for all $d$, as $n\to\infty$. The key to our results is a new approach to estimating ratios between point probabilities in the space of degree sequences of the random graph, including analysis of fixed points of the associated operators.

Evolving Network Modeling Driven by the Degree Increase and Decrease Mechanism

Abstract: Ever since the Barabási–Albert (BA) scale-free network has been proposed, network modeling has been studied intensively in light of the network growth and the preferential attachment (PA). However, numerous real systems are featured with a dynamic evolution including network reduction in addition to network growth. In this article, we propose a novel mechanism for evolving networks from the perspective of vertex degree. We construct a queueing system to describe the increase and decrease of vertex degree, which drives the network evolution. In our mechanism, the degree increase rate is regarded as a function positively correlated to the degree of a vertex, ensuring the PA in a new way. Degree distributions are investigated under two expressions of the degree increase rate, one of which manifests a “long tail”, and another one varies with different values of parameters. In simulations, we compare our theoretical distributions with simulation results and also apply them to real networks, which presents the validity and applicability of our model.

The probability of edge existence due to node degree: a baseline for network-based predictions

Abstract: Important tasks in biomedical discovery such as predicting gene functions, gene-disease associations, and drug repurposing opportunities are often framed as network edge prediction. The number of edges connecting to a node, termed degree, can vary greatly across nodes in real biomedical networks, and the distribution of degrees varies between networks. If degree strongly influences edge prediction, then imbalance or bias in the distribution of degrees could lead to nonspecific or misleading predictions. We introduce a network permutation framework to quantify the effects of node degree on edge prediction. Our framework decomposes performance into the proportions attributable to degree and the network's specific connections. We discover that performance attributable to factors other than degree is often only a small portion of overall performance. Degree's predictive performance diminishes when the networks used for training and testing-despite measuring the same biological relationships-were generated using distinct techniques and hence have large differences in degree distribution. We introduce the permutation-derived edge prior as the probability that an edge exists based only on degree. The edge prior shows excellent discrimination and calibration for 20 biomedical networks (16 bipartite, 3 undirected, 1 directed), with AUROCs frequently exceeding 0.85. Researchers seeking to predict new or missing edges in biological networks should use the edge prior as a baseline to identify the fraction of performance that is nonspecific because of degree. We released our methods as an open-source Python package ( https://github.com/hetio/xswap/ ).

Epidemic Dynamics in Temporal Clustered Networks with Local-World Structure

Abstract: Population demography can change the network structure, which further plays an important role in the spreading of infectious disease. In this paper, we study the epidemic dynamics in temporal clustered networks where the local-world structure and clustering are incorporated into the attachment mechanism of new nodes. It is found that increasing the local-world size of new nodes has little influence on the clustering coefficient but increases the degree heterogeneity of networks. Besides, when the network evolves faster, increasing the local-world size of new nodes leads to a faster initial growth rate and a larger steady density of infectious nodes, while it has small impacts on the steady density of infectious disease when the network evolves slowly. Furthermore, if the average degree is fixed, increasing the probability of triad formation p enlarges the clustering coefficient of a network, which reduces the initial growth rate and steady density of infectious nodes in the network. This work could provide a theoretical foundation for the control of infectious disease.

Disentangling Degree-related Biases and Interest for Out-of-Distribution Generalized Directed Network Embedding

Abstract: The goal of directed network embedding is to represent the nodes in a given directed network as embeddings that preserve the asymmetric relationships between nodes. While a number of directed network embedding methods have been proposed, we empirically show that the existing methods lack out-of-distribution generalization abilities against degree-related distributional shifts. To mitigate this problem, we propose ODIN (Out-of-Distribution Generalized Directed Network Embedding), a new directed NE method where we model multiple factors in the formation of directed edges. Then, for each node, ODIN learns multiple embeddings, each of which preserves its corresponding factor, by disentangling interest factors and biases related to in- and out-degrees of nodes. Our experiments on four real-world directed networks demonstrate that disentangling multiple factors enables ODIN to yield out-of-distribution generalized embeddings that are consistently effective under various degrees of shifts in degree distributions. Specifically, ODIN universally outperforms 9 state-of-the-art competitors in 2 LP tasks on 4 real-world datasets under both identical distribution (ID) and non-ID settings. The code is available at https://github.com/hsyoo32/odin.

Clustering and percolation on superpositions of Bernoulli random graphs

Abstract: A simple but powerful network model with n $$ n $$ nodes and m $$ m $$ partly overlapping layers is generated as an overlay of independent random graphs G 1 , … , G m $$ {G}_1,\dots, {G}_m $$ with variable sizes and densities. The model is parameterized by a joint distribution P n $$ {P}_n $$ of layer sizes and densities. When m $$ m $$ grows linearly and P n → P $$ {P}_n\to P $$ as n → ∞ $$ n\to \infty $$ , the model generates sparse random graphs with a rich statistical structure, admitting a nonvanishing clustering coefficient together with a limiting degree distribution and clustering spectrum with tunable power-law exponents. Remarkably, the model admits parameter regimes in which bond percolation exhibits two phase transitions: the first related to the emergence of a giant connected component, and the second to the appearance of gigantic single-layer components.

Threshold Cascade Dynamics in Coevolving Networks

Abstract: We study the coevolutionary dynamics of network topology and social complex contagion using a threshold cascade model. Our coevolving threshold model incorporates two mechanisms: the threshold mechanism for the spreading of a minority state such as a new opinion, idea, or innovation and the network plasticity, implemented as the rewiring of links to cut the connections between nodes in different states. Using numerical simulations and a mean-field theoretical analysis, we demonstrate that the coevolutionary dynamics can significantly affect the cascade dynamics. The domain of parameters, i.e., the threshold and mean degree, for which global cascades occur shrinks with an increasing network plasticity, indicating that the rewiring process suppresses the onset of global cascades. We also found that during evolution, non-adopting nodes form denser connections, resulting in a wider degree distribution and a non-monotonous dependence of cascades sizes on plasticity.

Optimal Network Robustness Against Attacks in Varying Degree Distributions

Abstract: In varying degree distributions, we investigate the optimally robust networks against targeted attacks to nodes with higher degrees. In considering that a network tends to have more robustness with a smaller variance of degree distributions, we clarify the optimal robustness at random regular graphs in their comprehensive discrete or random perturbations. By comparing robustness measurements on them, we find that random regular graphs have the optimal robustness against attacks in varying degree distributions.

Emergence of power-law distributions in protein-protein interaction networks through study bias

Abstract: Protein-protein interaction (PPI) networks have been found to be power-law-distributed, i. e., in observed PPI networks, the fraction of nodes with degree k often follows a power-law (PL) distribution k-α. The emergence of this property is typically explained by evolutionary or functional considerations. However, the experimental procedures used to detect PPIs are known to be heavily affected by technical and study bias. For instance, proteins known to be involved in cancer are often heavily overstudied and proteins used as baits in large-scale experiments tend to have many false-positive interaction partners. This raises the question whether PL distributions in observed PPI networks could be explained by these biases alone. Here, we address this question using statistical analyses of the degree distributions of 1000s of observed PPI networks of controlled provenance as well as simulation studies. Our results indicate that study bias and technical bias can indeed largely explain the fact that observed PPI networks tend to be PL-distributed. This implies that it is problematic to derive hypotheses about the degree distribution and emergence of the true biological interactome from the PL distributions in observed PPI networks.

Droplet Finite-Size Scaling of the Majority Vote Model on Quenched Scale-Free Networks

Abstract: We consider the Majority Vote model coupled with scale-free networks. Recent works point to a non-universal behavior of the Majority Vote model, where the critical exponents depend on the connectivity while the network's effective dimension $D_\mathrm{eff}$ is unity for a degree distribution exponent $5/2<\gamma<7/2$. We present a finite-size theory of the Majority Vote Model for uncorrelated networks and present generalized scaling relations with good agreement with Monte-Carlo simulation results. The presented finite-size theory has two main sources of size dependence. The first source is an external field describing a mass media influence on the consensus formation and the second source is the scale-free network cutoff. The model indeed presents non-universal critical behavior where the critical exponents depend on the degree distribution exponent $5/2<\gamma<7/2$. For $\gamma \geq 7/2$, the model is on the same universality class of the Majority Vote model on Erd\"os-Renyi random graphs, while for $\gamma=7/2$, the critical behavior presents additional logarithmic corrections.

Using a Bayesian approach to reconstruct graph statistics after edge sampling

Abstract: Abstract Often, due to prohibitively large size or to limits to data collecting APIs, it is not possible to work with a complete network dataset and sampling is required. A type of sampling which is consistent with Twitter API restrictions is uniform edge sampling. In this paper, we propose a methodology for the recovery of two fundamental network properties from an edge-sampled network: the degree distribution and the triangle count (we estimate the totals for the network and the counts associated with each edge). We use a Bayesian approach and show a range of methods for constructing a prior which does not require assumptions about the original network. Our approach is tested on two synthetic and three real datasets with diverse sizes, degree distributions, degree-degree correlations and triangle count distributions.

Load balancing with sparse dynamic random graphs

Abstract: Consider a system of $n$ single-server queues where tasks arrive at each server in a distributed fashion. A graph is used to locally balance the load by dispatching every incoming task to one of the shortest queues in the neighborhood where the task appears. In order to globally balance the load, the neighborship relations are constantly renewed by resampling the graph at rate $\mu_n$ from some fixed random graph law. We derive the fluid limit of the occupancy process as $n \to \infty$ and $\mu_n \to \infty$ when the resampling procedure is symmetric with respect to the servers. The maximum degree of the graph may remain bounded as $n$ grows and the total number of arrivals between consecutive resampling times may approach infinity. The fluid limit only depends on the random graph laws through their limiting degree distribution and can be interpreted as a generalized power-of-$(d + 1)$ scheme where $d$ is random and has the limiting degree distribution. We use the fluid limit to obtain valuable insights into the performance impact and optimal design of sparse dynamic graphs with a bounded average degree. In particular, we establish a phase transition in performance when the probability that a server is isolated switches from zero to positive, and we show that performance improves as the degree distribution becomes more concentrated.

Percolation in simple directed random graphs with a given degree distribution

Abstract: We study site and bond percolation in simple directed random graphs with a given degree distribution. We derive the percolation threshold for the giant strongly connected component and the fraction of vertices in this component as a function of the percolation probability. The results are obtained for degree sequences in which the maximum degree may depend on the total number of nodes n, being asymptotically bounded by $n^{\frac{1}{9}}$ .

Fractal Features of Fracture Networks and Key Attributes of Their Models

Abstract: This work is devoted to the modeling of fracture networks. The main attention is focused on the fractal features of the fracture systems in geological formations and reservoirs. Two new kinds of fracture network models are introduced. The first is based on the Bernoulli percolation of straight slots in regular lattices. The second explores the site percolation in scale-free networks embedded in the two- and three-dimensional lattices. The key attributes of the model fracture networks are sketched. Surprisingly, we found that the number of effective spatial degrees of freedom of the scale-free fracture network models is determined by the network embedding dimension and does not depend on the degree distribution. The effects of degree distribution on the other fractal features of the model fracture networks are scrutinized.

Robustness analysis of highway network based on complex network

Abstract: Taking Chongqing, Hunan, Shandong, Shaanxi and Sichuan as examples, this paper conducts a comparative study on the robustness of their highway networks, which is helpful for the subsequent construction of China's highway networks. The topology structure of highway networks is studied by complex network theory. The degree distribution, average degree, average clustering coefficient, average path length, network diameter and other parameters of the network were calculated, and the robustness of the highway network in five provinces and cities was compared from four aspects: connectivity, network efficiency, turn rate and robustness r. The results show that Chongqing and Shaanxi have a good performance of highway network robustness, Shandong and Sichuan have a more balanced performance, and Hunan has a weak performance. Enhance network robustness by placing route planning directions in place with fewer route options to provide drivers with more route options.

The Myth of the Robust-Yet-Fragile Nature of Scale-Free Networks: An Empirical Analysis

Abstract: In addition to their defining skewed degree distribution, the class of scale-free networks are generally described as robust-yet-fragile. This description suggests that, compared to random graphs of the same size, scale-free networks are more robust against random failures but more vulnerable to targeted attacks. Here, we report on experiments on a comprehensive collection of networks across different domains that assess the empirical prevalence of scale-free networks fitting this description. We find that robust-yet-fragile networks are a distinct minority, even among those networks that come closest to being classified as scale-free.

Reconstructing Degree Distribution and Triangle Counts from Edge-Sampled Graphs

Abstract: Often, due to prohibitively large size or to limits to data collecting APIs, it is not possible to work with a complete network dataset and sampling is required. A type of sampling which is consistent with Twitter API restrictions is uniform edge sampling. In this paper, we propose a methodology for the recovery of two fundamental network properties from an edge-sampled network: the degree distribution and the triangle count (we estimate the totals for the network and the counts associated with each edge). We use a Bayesian approach and show a range of methods for constructing a prior which does not require assumptions about the original network. Our approach is tested on two synthetic and two real datasets with diverse degree and triangle count distributions.

The Generation Mechanism of Degree Distribution with Power Exponent >2 and the Growth of Edges in Temporal Social Networks

Abstract: The structures of social networks with power laws have been widely investigated. People have a great interest in the scale-invariant generating mechanism. We address this problem by introducing a simple model, i.e., a heuristic probabilistic explanation for the occurrence of a power law. In particular, the proposed model can be used to explain the generative mechanism that leads to the scale-invariant of the degree distribution with a power exponent of τ>2. Furthermore, a stochastic model (the pure birth points process) is used to describe the cumulative growth trend of edges of a temporal social network. We applied our model to online temporal social networks and found that both the degree distribution scaling behaviors and the growth law of edges can be quantitatively reproduced. We gained further insight into the evolution nature of scale-invariant temporal social networks from the empirical observation that the power exponent τ gradually decreases and approaches 2 or less than 2 over evolutionary time.

On the Internet-graph clustering coefficient

Abstract: We consider a configuration graph with N vertices whose degrees are independent and identically distributed according to the power law depending on a slowly varying function. Configuration graphs are widely used for modeling complex communication networks such as the Internet. The parameter of the power-law distribution is usually selected so that the vertex degree distribution has a finite expectation and infinite variance. An important characteristic of the topology of a configuration graph is the global clustering coefficient. Clustering measures the extent to which neighbours of vertices are also each other’s neighbours. We prove the limit theorem for the clustering coefficient as N tends to infinity.

Analysis of the Characteristics and Speed of Spread of the “FUNA” on Twitter

Abstract: The funa is a prevalent concept in Chile that aims to expose a person’s bad behavior, punish the aggressor publicly, and warn the community about it. Despite its massive use on the social networks of Chilean society, the real dissemination of funas among communities is unknown. In this paper, we extract, generate, analyze, and compare the Twitter social network’s spread of three tweets related to “funas” against three other trending topics, through the analysis of global network characteristics over time (degree distribution, clustering coefficient, hop plot, and betweenness centrality). As observed, funas have a specific behavior, and they disseminate as quickly as a common tweet or more quickly; however, they spread thanks to several network users, generating a cohesive group.

A random growth model with any real or theoretical degree distribution

Abstract: The degree distributions of complex networks are usually considered to follow a power law distribution. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree distribution. The degree distribution can either be theoretical or extracted from a real-world network. The main idea is to invert the recurrence equation commonly used to compute the degree distribution in order to find a convenient attachment function for node connections - commonly chosen as linear. We compute this attachment function for some classical distributions, as the power-law, the broken power-law, and the geometric distributions. We also use the model on an undirected version of the Twitter network, for which the degree distribution has an unusual shape. We finally show that the divergence of chosen attachment functions is directly linked to the heavy-tailed property of the obtained degree distributions.

Measuring the variability of local characteristics in complex networks: Empirical and analytical analysis.

Abstract: We examine the dynamics for the average degree of a node's neighbors in complex networks. It is a Markov stochastic process, and at each moment of time, this quantity takes on its values in accordance with some probability distribution. We are interested in some characteristics of this distribution: its expectation and its variance, as well as its coefficient of variation. First, we look at several real communities to understand how these values change over time in social networks. The empirical analysis of the behavior of these quantities for real networks shows that the coefficient of variation remains at high level as the network grows. This means that the standard deviation and the mean degree of the neighbors are comparable. Then, we examine the evolution of these three quantities over time for networks obtained as simulations of one of the well-known varieties of the Barabási-Albert model, the growth model with nonlinear preferential attachment (NPA) and a fixed number of attached links at each iteration. We analytically show that the coefficient of variation for the average degree of a node's neighbors tends to zero in such networks (albeit very slowly). Thus, we establish that the behavior of the average degree of neighbors in Barabási-Albert networks differs from its behavior in real networks. In this regard, we propose a model based on the NPA mechanism with the rule of random number of edges added at each iteration in which the dynamics of the average degree of neighbors is comparable to its dynamics in real networks.