Densification Power Law Research Articles

Bi-DNE: bilayer evolutionary pattern preserved embedding for dynamic networks

AbstractNetwork embedding is a technique used to generate low-dimensional vectors representing each node in a network while maintaining the original topology and properties of the network. This technology enables a wide range of learning tasks, including node classification and link prediction. However, the current landscape of network embedding approaches predominantly revolves around static networks, neglecting the dynamic nature that characterizes real social networks. Dynamics at both the micro- and macrolevels are fundamental drivers of network evolution. Microlevel dynamics provide a detailed account of the network topology formation process, while macrolevel dynamics reveal the evolutionary trends of the network. Despite recent dynamic network embedding efforts, a few approaches accurately capture the evolution patterns of nodes at the microlevel or effectively preserve the crucial dynamics of both layers. Our study introduces a novel method for embedding networks, i.e., bilayer evolutionary pattern-preserving embedding for dynamic networks (Bi-DNE), that preserves the evolutionary patterns at both the micro- and macrolevels. The model utilizes strengthened triadic closure to represent the network structure formation process at the microlevel, while a dynamic equation constrains the network structure to adhere to the densification power-law evolution pattern at the macrolevel. The proposed Bi-DNE model exhibits significant performance improvements across a range of tasks, including link prediction, reconstruction, and temporal link analysis. These improvements are demonstrated through comprehensive experiments carried out on both simulated and real-world dynamic network datasets. The consistently superior results to those of the state-of-the-art methods provide empirical evidence for the effectiveness of Bi-DNE in capturing complex evolutionary patterns and learning high-quality node representations. These findings validate the methodological innovations presented in this work and mark valuable progress in the emerging field of dynamic network representation learning. Further exploration demonstrates that Bi-DNE is sensitive to the analysis task parameters, leading to a more accurate representation of the natural evolution process during dynamic network embedding.

Revealing the dynamic landscape of drug-drug interactions through network analysis.

Introduction: The landscape of drug-drug interactions (DDIs) has evolved significantly over the past 60years, necessitating a retrospective analysis to identify research trends and under-explored areas. While methodologies like bibliometric analysis provide valuable quantitative perspectives on DDI research, they have not successfully delineated the complex interrelations between drugs. Understanding these intricate relationships is essential for deciphering the evolving architecture and progressive transformation of DDI research structures over time. We utilize network analysis to unearth the multifaceted relationships between drugs, offering a richer, more nuanced comprehension of shifts in research focus within the DDI landscape. Methods: This groundbreaking investigation employs natural language processing, techniques, specifically Named Entity Recognition (NER) via ScispaCy, and the information extraction model, SciFive, to extract pharmacokinetic (PK) and pharmacodynamic (PD) DDI evidence from PubMed articles spanning January 1962 to July 2023. It reveals key trends and patterns through an innovative network analysis approach. Static network analysis is deployed to discern structural patterns in DDI research, while evolving network analysis is employed to monitor changes in the DDI research trend structures over time. Results: Our compelling results shed light on the scale-free characteristics of pharmacokinetic, pharmacodynamic, and their combined networks, exhibiting power law exponent values of 2.5, 2.82, and 2.46, respectively. In these networks, a select few drugs serve as central hubs, engaging in extensive interactions with a multitude of other drugs. Interestingly, the networks conform to a densification power law, illustrating that the number of DDIs grows exponentially as new drugs are added to the DDI network. Notably, we discovered that drugs connected in PK and PD networks predominantly belong to the same categories defined by the Anatomical Therapeutic Chemical (ATC) classification system, with fewer interactions observed between drugs from different categories. Discussion: The finding suggests that PK and PD DDIs between drugs from different ATC categories have not been studied as extensively as those between drugs within the same categories. By unearthing these hidden patterns, our study paves the way for a deeper understanding of the DDI landscape, providing valuable information for future DDI research, clinical practice, and drug development focus areas.

Utilizing the average node degree to assess the temporal growth rate of Twitter

Several models have been proposed that describe the evolution of the graph properties of many online social networks (OSNs) and explain the behavior of their users. These models are essential for understanding the growth dynamics of the underlying social graph. One of the most prominent OSNs is Twitter, since it covers a significant part of the online worldwide population. Nevertheless, investigating the validity of these models on Twitter entails many difficulties. The size of Twitter and the limitations of its access API make extremely difficult the estimation of many graph properties and therefore the evaluation of the proposed models. In this study, we present a simple and efficient method to fit an already existing model, which describes the densification power law property of modern OSNs. This model states that the average degree of an OSN increases over time. In a case study, we assess this model in two large samples of Twitter, and we demonstrate how it can portray the altering growth periods of Twitter. Finally, we make some remarks on several events during the early period of Twitter that may have affected its growth rates.

A Parametric Model Approach for Structural Reconstruction of Scale-Free Networks

We propose a parametric network generation model which we call network reconstruction model (NRM) for structural reconstruction of scale-free real networks with power-law exponent greater than 2 in the tail of its degree distribution. The reconstruction method for a real network is concerned with finding the optimal values of the model parameters by utilizing the power-law exponents of model network and the real network. The method is validated for certain real world networks. The usefulness of NRM in order to solve structural reconstruction problem is demonstrated by comparing its performance with some existing popular network generative models. We show that NRM can generate networks which follow edge-densification and densification power-law when the model parameters satisfy an inequality. Computable expressions of the expected number of triangles and expected diameter are obtained for model networks generated by NRM. Finally, we numerically establish that NRM can generate networks with shrinking diameter and modular structure when specific model parameters are chosen.

A community-based sampling method using DPL for online social networks

In this paper, we propose a new graph sampling method for online social networks that achieves the following. First, a sample graph should reflect the ratio between the number of nodes and the number of edges of the original graph. Second, a sample graph should reflect the topology of the original graph. Third, sample graphs should be consistent with each other when they are sampled from the same original graph. The proposed method employs two techniques: hierarchical community extraction and densification power law. The proposed method partitions the original graph into a set of communities to preserve the topology of the original graph. It also uses the densification power law which captures the ratio between the number of nodes and the number of edges in online social networks. In experiments, we use several real-world online social networks, create sample graphs using the existing methods and ours, and analyze the differences between the sample graph by each sampling method and the original graph.

Calling Network

Modern software systems' structures and behaviors are becoming very complicated. Existing models either lack systematic considerations on the whole system's behavior patterns or are inefficient in runtime monitoring. In this paper, the Calling Network (CN) model is proposed to provide new perspectives to analyze the dynamic execution process of a software system. CN is consisted of one or a series of Calling Graph (CG), which is a dynamic version of Call Graph and encodes method call frequencies. Some new perspectives such as Growing Network and Network (Graph) Sequence are also embodied in CN model. Based on a data set of 10 real-world Java programs, we show that CN presents several interesting features, such as Power-law degree distribution, Densification Power Law, and the stability of an entropy value -- Local Entropy. Experiments have been conducted to show the applications of CN in software significant module identification and runtime failure diagnosis.

Geometric Protean Graphs

We study the link structure of online social networks (OSNs) and introduce a new model for such networks that may help in inferring their hidden underlying reality. In the geo-protean (GEO-P) model for OSNs, nodes are identified with points in Euclidean space, and edges are stochastically generated by a mixture of the relative distance of nodes and a ranking function. With high probability, the GEO-P model generates graphs satisfying many observed properties of OSNs, such as power-law degree distributions, the small-world property, densification power law, and bad spectral expansion. We introduce the dimension of an OSN based on our model and examine this new parameter using actual OSN data. We discuss how the geo-protean model may eventually be used as a tool to group users with similar attributes using only the link structure of the network.

A social network evolution model based on seniority

A social network is a representation that describes the relationships between individuals. In recent years, several interesting phenomena, such as the densification power law, have been observed in social networks and a number of models have been proposed to explain them. In this paper, we investigate an interesting phenomenon called the seniority difference distribution of new connections, which we observed in our data. The distribution reveals that there exists a seniority preference when a new network node tries to establish connections with existing nodes. To explain the phenomenon, we propose several models based on different local selection policies, namely, equal-probability selection, freshness-based selection, oldness-based selection, and combined freshness/oldness selection. The results of simulations show that, by combining the concepts of freshness and oldness, it is possible to reproduce a social network that matches the observation.

Stochastic kronecker graphs

AbstractA random graph model based on Kronecker products of probability matrices has been recently proposed as a generative model for large‐scale real‐world networks such as the web. This model simultaneously captures several well‐known properties of real‐world networks; in particular, it gives rise to a heavy‐tailed degree distribution, has a low diameter, and obeys the densification power law. Most properties of Kronecker products of graphs (such as connectivity and diameter) are only rigorously analyzed in the deterministic case. In this article, we study the basic properties of stochastic Kronecker products based on an initiator matrix of size two (which is the case that is shown to provide the best fit to many real‐world networks). We will show a phase transition for the emergence of the giant component and another phase transition for connectivity, and prove that such graphs have constant diameters beyond the connectivity threshold, but are not searchable using a decentralized algorithm. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 38, 453–466, 2011

Models of Online Social Networks

We present a deterministic model for online social networks (OSNs) based on transitivity and local knowledge in social interactions. In the iterated local transitivity (ILT) model, at each time step and for every existing node _x_, a new node appears that joins to the closed neighbor set of _x_. The ILT model provably satisfies a number of both local and global properties that have been observed in OSNs and other real-world complex networks, such as a densification power law, decreasing average distance, and higher clustering than in random graphs with the same average degree. Experimental studies of social networks demonstrate poor expansion properties as a consequence of the existence of communities with low numbers of intercommunity edges. Bounds on the spectral gap for both the adjacency and normalized Laplacian matrices are proved for graphs arising from the ILT model indicating such bad expansion properties. The cop and domination numbers are shown to remain the same as those of the graph from the initial time step _G_₀, and the automorphism group of _G_₀ is a subgroup of the automorphism group of graphs generated at all later time steps. A randomized version of the ILT model is presented that exhibits a tunable densification power-law exponent and maintains several properties of the deterministic model.

Evolving debates in online communication: a graph analytical approach

PurposeThe aim of this paper is to analyse the structure of evolving debates in online discussion forums to see how science‐related debates evolve over time.Design/methodology/approachA graph‐based approach is applied to analyse the structure of graphs of connected terms in online debates. A number of different graph properties, such as the Densification Power Law (DPL), diameter (γ) and effective diameter (δ), are used to observe the properties of the graphs over time.FindingsThe graphs of connected terms obey the DPL and the effective diameters (δ) of the graphs tend to shrink as the debates progress. Slight fluctuations can occur, however, when new terms are integrated into the graphs. These two properties suggest that a graph of connected terms can be modelled through a number of blocks of terms, each of which becomes densely connected over time as indicated byδand DPL plots.Originality/valueThis paper proposes observing the dynamic changes of evolving debates by using graphs of connected terms. The structures and properties of these graphs may be useful for understanding the evolution of public debates about controversial science‐related topics, such as embryonic stem cell research, and to track debates that can potentially explode into major issues.