Features Of Real-world Networks Research Articles

HEM: An Improved Parametric Link Prediction Algorithm Based on Hybrid Network Evolution Mechanism.

Link prediction plays an important role in the research of complex networks. Its task is to predict missing links or possible new links in the future via existing information in the network. In recent years, many powerful link prediction algorithms have emerged, which have good results in prediction accuracy and interpretability. However, the existing research still cannot clearly point out the relationship between the characteristics of the network and the mechanism of link generation, and the predictability of complex networks with different features remains to be further analyzed. In view of this, this article proposes the corresponding link prediction indexes Reg, DFPA and LW on a regular network, scale-free network and small-world network, respectively, and studies their prediction properties on these three network models. At the same time, we propose a parametric hybrid index HEM and compare the prediction accuracies of HEM and many similarity-based indexes on real-world networks. The experimental results show that HEM performs better than other Birnbaum-Saunders. In addition, we study the factors that play a major role in the prediction of HEM and analyze their relationship with the characteristics of real-world networks. The results show that the predictive properties of factors are closely related to the features of networks.

Generalised popularity-similarity optimisation model for growing hyperbolic networks beyond two dimensions

Hyperbolic network models have gained considerable attention in recent years, mainly due to their capability of explaining many peculiar features of real-world networks. One of the most widely known models of this type is the popularity-similarity optimisation (PSO) model, working in the native disk representation of the two-dimensional hyperbolic space and generating networks with small-world property, scale-free degree distribution, high clustering and strong community structure at the same time. With the motivation of better understanding hyperbolic random graphs, we hereby introduce the dPSO model, a generalisation of the PSO model to any arbitrary integer dimension d>2. The analysis of the obtained networks shows that their major structural properties can be affected by the dimension of the underlying hyperbolic space in a non-trivial way. Our extended framework is not only interesting from a theoretical point of view but can also serve as a starting point for the generalisation of already existing two-dimensional hyperbolic embedding techniques.

Formalising and Detecting Community Structures in Real World Complex Networks

Community structure is an integral characteristic of real world networks whichever processes or areas they emerge from. This paper addresses the problem of community structure detection theoretically as well as computationally. The authors introduce a number of concepts such as the neighbourhood and strength of a subgraph, p-community, local maximal p-community, hubs, and outliers that play elemental role in formalising the concept of community structure in complex networks. A few preliminary results have been derived that lead to the development of an algorithm for community structure detection in undirected unweighted networks. The algorithm is based on a local seed expansion strategy that uses the concept of interaction coefficient. The authors have analysed the algorithm on a number of parameters such as accuracy, stability, and quality on synthetic and real world networks from different areas.

Epidemic spreading of evolving community structure

Abstract Many complex systems have common community structure characteristics. Studying the community structure can reveal the mechanism of complex systems, so as to better understand and control complex systems. In the present work, we regard a community as an approximate homogeneous network. We use a mean-field approach to obtain an epidemic spreading dynamic model of community structure evolution. The epidemic threshold is given. Randomness is one of the striking characteristics of real-world networks as they evolve. Based on the specific stochastic block model (SBM) to generate synthetic networks with community structure, we use nonnegative matrix theory to analyze the changes in the spread of epidemics during the growth, contraction, division or merger of communities. A reduction in the number of communities, a reduction in the size of communities or a division of communities is conductive to increasing epidemic threshold, and thus mitigating the spread of epidemics. Our conclusion can explain some phenomena. The numerical simulations of real-world and random networks support and enrich our conclusions.

On neighbourhood degree sequences of complex networks

Network topology is a fundamental aspect of network science that allows us to gather insights into the complicated relational architectures of the world we inhabit. We provide a first specific study of neighbourhood degree sequences in complex networks. We consider how to explicitly characterise important physical concepts such as similarity, heterogeneity and organization in these sequences, as well as updating the notion of hierarchical complexity to reflect previously unnoticed organizational principles. We also point out that neighbourhood degree sequences are related to a powerful subtree kernel for unlabeled graph classification. We study these newly defined sequence properties in a comprehensive array of graph models and over 200 real-world networks. We find that these indices are neither highly correlated with each other nor with classical network indices. Importantly, the sequences of a wide variety of real world networks are found to have greater similarity and organisation than is expected for networks of their given degree distributions. Notably, while biological, social and technological networks all showed consistently large neighbourhood similarity and organisation, hierarchical complexity was not a consistent feature of real world networks. Neighbourhood degree sequences are an interesting tool for describing unique and important characteristics of complex networks.

Scalable and exact sampling method for probabilistic generative graph models

Interest in modeling complex networks has fueled the development of multiple probabilistic generative graph models (PGGMs). PGGMs are statistical methods that model the network distribution and match common characteristics of real world networks. Recently, scalable sampling algorithms for well known PGGMs, made the analysis of large-scale, sparse networks feasible for the first time. However, it has been demonstrated that these scalable sampling algorithms do not sample from the original underlying distribution, and sometimes produce very unlikely graphs. To address this, we extend the algorithm proposed in Moreno et al. (in: IEEE 14th international conference on data mining, pp 440–449, 2014) for a single model and develop a general solution for a broad class of PGGMs. Our approach exploits the fact that PGGMs are typically parameterized by a small set of unique probability values—this enables fast generation via independent sampling of groups of edges with the same probability value. By sampling within groups, we remove bias due to conditional sampling and probability reallocation. We show that our grouped sampling methods are both provably correct and efficient. Our new algorithm reduces time complexity by avoiding the expensive rejection sampling step previously necessary, and we demonstrate its generality, by outlining implementations for six different PGGMs. We conduct theoretical analysis and empirical evaluation to demonstrate the strengths of our algorithms. We conclude by sampling a network with over a billion edges in 95 s on a single processor.

Upper and lower bounds for the q-entropy of network models with application to network model selection

Graphs are important tools for modeling data in different biological, social and technological domains. The measurement of their complexity has theoretical and practical applications in many areas such as pattern recognition, graph clustering, network inference and network analysis. A widely used measure is the q-entropy. While this measure has extensively been studied for Erdos–Renyi (ER) random graphs, only few results have been reported for real-world networks that are typically scale-free or small-world graphs. In this paper, we study the q-entropy of scale-free graphs (generated by the Barabasi–Albert model) and small-world graphs (generated by the Watts–Strogatz model). We derive upper and lower bounds for the q-entropy and confirm our analytical studies by numerical simulations. We study the effect of the network parameters on the q-entropy for both scale-free and small-world graphs which yields to reveal some novel and interesting insights. For example, we show that the q-entropy of a Barabasi–Albert graph is usually larger than the q-entropy of a small-world graph with the same size and density, independent of the randomness degree of the small-world graph. We use the derived bounds as characteristics of real-world networks as well as network models. Therefore, based on the derived bounds, we propose a network model selection algorithm, that given a real-world network and a set of models, determines which of the models most likely generates the real-world network.

Improving Community Detection in Time-Evolving Networks Through Clustering Fusion

Abstract Traditional community detection algorithms are easily interfered by noises and outliers. Therefore, we propose to leverage a clustering fusion method to improve the results of community detection. Usually, there are two issues in clustering ensembles: how to generate efficient diversified cluster members, and how to ensembles the results of all members. Specifically: (1) considering the time evolving characteristic of real world networks, we propose to generate clustering members based on the snapshot of networks, where the split based clustering algorithms are performed; (2) considering the difference in the distribution of the cluster centers in each clustering member and the actual distribution, we ensemble the results based on a maximum likelihood method. Moreover, we conduct experiments to show that our method can discover high quality communities.

Reaction–diffusion processes and metapopulation models in heterogeneous networks

Dynamical reaction-diffusion processes and meta-population models are standard modeling approaches for a wide variety of phenomena in which local quantities - such as density, potential and particles - diffuse and interact according to the physical laws. Here, we study the behavior of two basic reaction-diffusion processes ($B \to A$ and $A+B \to 2B$) defined on networks with heterogeneous topology and no limit on the nodes' occupation number. We investigate the effect of network topology on the basic properties of the system's phase diagram and find that the network heterogeneity sustains the reaction activity even in the limit of a vanishing density of particles, eventually suppressing the critical point in density driven phase transitions, whereas phase transition and critical points, independent of the particle density, are not altered by topological fluctuations. This work lays out a theoretical and computational microscopic framework for the study of a wide range of realistic meta-populations models and agent-based models that include the complex features of real world networks.