Related papers: Robust subgraph counting with distribution-free ra…
Subgraph counting is a fundamental primitive in graph processing, with applications in social network analysis (e.g., estimating the clustering coefficient of a graph), database processing and other areas. The space complexity of subgraph…
We formalize the problem of detecting a community in a network into testing whether in a given (random) graph there is a subgraph that is unusually dense. We observe an undirected and unweighted graph on N nodes. Under the null hypothesis,…
In complex networks it is common to model a network or generate a surrogate network based on the conservation of the network's degree distribution. We provide an alternative network model based on the conservation of connection density…
This paper discusses the reliability of a graph in which the links are perfectly reliable but the nodes may fail with certain probability p. Calculating graph node reliability is an NP-Hard problem. We introduce an efficient and accurate…
Complex networks have abundant and extensive applications in real life. Recently, researchers have proposed a number of complex networks, in which some are deterministic and others are random. Compared with deterministic networks, random…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
The degree distributions of many real world networks follow power-laws whose exponents tend to fall between two and three. Within the framework of the Barabasi-Albert model (BA model), we explain this empirical observation by a simple fact.…
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…
Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the…
The interactions between the components of complex networks are often directed. Proper modeling of such systems frequently requires the construction of ensembles of digraphs with a given sequence of in- and out-degrees. As the number of…
Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order…
The notions of $r$-robustness and $(r,s)$-robustness of a network have been earlier introduced in the literature to achieve resilient consensus in the presence of misbehaving agents. However, while higher robustness levels enable networks…
Dense subgraph discovery is an important primitive in graph mining, which has a wide variety of applications in diverse domains. In the densest subgraph problem, given an undirected graph $G=(V,E)$ with an edge-weight vector $w=(w_e)_{e\in…
Recently, real world networks having constant/shrinking diameter along with power-law degree distribution are observed and investigated in literature. Taking an inspiration from these findings, we propose a deterministic complex network…
Loops are subgraphs responsible for the multiplicity of paths going from one to another generic node in a given network. In this paper we present an analytic approach for the evaluation of the average number of loops in random scale-free…
Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the…
In their recent work "Scale-free networks are rare", Broido and Clauset address the problem of the analysis of degree distributions in networks to classify them as scale-free at different strengths of "scale-freeness." Over the last two…
In recent years, many large directed networks such as online social networks are collected with the help of powerful data engineering and data storage techniques. Analyses of such networks attract significant attention from both the…
We study the classic subgraph enumeration problem under distributed settings. Existing solutions either suffer from severe memory crisis or rely on large indexes, which makes them impractical for very large graphs. Most of them follow a…
A majority of studied models for scale-free networks have degree distributions with exponents greater than $2$. Real networks, however, can demonstrate essentially more heavy-tailed degree distributions. We explore two models of scale-free…