Related papers: The modularity of random graphs on the hyperbolic …
We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the Configuration Model where nodes of different types are connected via…
The modularity of a graph is a parameter that measures its community structure; the higher its value (between $0$ and $1$), the more clustered the graph is. In this paper we show that the modularity of a random $3$-regular graph is at least…
Several networks occurring in real life have modular structures that are arranged in an hierarchical fashion. In this paper, we have proposed a model for such networks, using a stochastic generation method. Using this model we show that,…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
We propose a method to investigate modular structure in networks based on fitted probabilistic model, where the connection probability between nodes is related to a set of introduced local attributes. The attributes, as parameters of the…
Much effort has gone into understanding the modular nature of complex networks. Communities, also known as clusters or modules, are typically considered to be densely interconnected groups of nodes that are only sparsely connected to other…
Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…
This work will appear as a chapter in a forthcoming volume titled `Topics in Probabilistic Graph Theory'. For a given graph $G$, each partition of the vertices has a modularity score, with higher values indicating that the partition better…
A basic question in network community detection is how modular a given network is. This is usually addressed by evaluating the quality of partitions detected in the network. The Girvan-Newman (GN) modularity function is the standard way to…
Complex network topologies and hyperbolic geometry seem specularly connected, and one of the most fascinating and challenging problems of recent complex network theory is to map a given network to its hyperbolic space. The Popularity…
This paper revisits the classical concept of network modularity and its spectral relaxations used throughout graph data analysis. We formulate and study several modularity statistic variants for which we establish asymptotic distributional…
Through detailed analysis of scores of publicly available data sets corresponding to a wide range of large-scale networks, from communication and road networks to various forms of social networks, we explore a little-studied geometric…
Measure the similarity of the nodes in the complex networks have interested many researchers to explore it. In this paper, a new method which is based on the degree centrality and the Relative-entropy is proposed to measure the similarity…
Current modularity-based community detection algorithms attempt to find cluster memberships that maximize modularity within a fixed graph topology. Diverging from this conventional approach, our work introduces a novel strategy that employs…
Modularity is a parameter indicating the presence of community structure in the graph. Nowadays it lies at the core of widely used clustering algorithms. We study the modularity of the most classical random graph, binomial $G(n,p)$. In 2020…
Despite the fact that many important problems (including clustering) can be described using hypergraphs, theoretical foundations as well as practical algorithms using hypergraphs are not well developed yet. In this paper, we propose a…
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…
The ubiquity of modular structure in real-world complex networks is being the focus of attention in many trials to understand the interplay between network topology and functionality. The best approaches to the identification of modular…
Numerous works have been proposed to generate random graphs preserving the same properties as real-life large scale networks. However, many real networks are better represented by hypergraphs. Few models for generating random hypergraphs…
Homophily, the tendency of individuals to connect with others who share similar attributes, is a defining feature of social networks. Understanding how groups interact, both within and across, is crucial for uncovering the dynamics of…