Related papers: General Clique Percolation in Network Evolution
Many important real-world networks manifest "small-world" properties such as scale-free degree distributions, small diameters, and clustering. The most common model of growth for these networks is "preferential attachment", where nodes…
Complex networks display various types of percolation transitions. We show that the degree distribution and the degree-degree correlation alone are not sufficient to describe diverse percolation critical phenomena. This suggests that a…
Community detection is a popular approach to understand the organization of interactions in static networks. For that purpose, the Clique Percolation Method (CPM), which involves the percolation of k-cliques, is a well-studied technique…
In complex network research clique percolation, introduced by Palla et al., is a deterministic community detection method, which allows for overlapping communities and is purely based on local topological properties of a network. Here we…
The social networks that infectious diseases spread along are typically clustered. Because of the close relation between percolation and epidemic spread, the behavior of percolation in such networks gives insight into infectious disease…
Missing link prediction in indirected and un-weighted network is an open and challenge problem which has been studied intensively in recent years. In this paper, we studied the relationships between community structure and link formation…
Listing dense subgraphs in large graphs plays a key task in varieties of network analysis applications like community detection. Clique, as the densest model, has been widely investigated. However, in practice, communities rarely form as…
Community structure is one of the most prominent features of complex networks. Community structure detection is of great importance to provide insights into the network structure and functionalities. Most proposals focus on static networks.…
Percolation problems appear in a large variety of different contexts ranging from the design of composite materials to vaccination strategies on community networks. The key observable for many applications is the percolation threshold.…
In this study we introduce and analyze the statistical structural properties of a model of growing networks which may be relevant to social networks. At each step a new node is added which selects 'k' possible partners from the existing…
A $k$-defective clique is a relaxation of the traditional clique definition, allowing up to $k$ missing edges. This relaxation is crucial in various real-world applications such as link prediction, community detection, and social network…
We study percolation on the hierarchical lattice of order $N$ where the probability of connection between two points separated by distance $k$ is of the form $c_k/N^{k(1+\delta)},\; \delta >-1$. Since the distance is an ultrametric, there…
We study the generalized Tur\'an problem regarding cliques with restricted intersections, which highlights the motivation from extremal set theory. Let $L=\{\ell_1,\dots,\ell_s\}\subset [0,r-1]$ be a fixed integer set with $|L|\notin…
Many dynamic processes on complex networks, from disease outbreaks to cascading failures, can rapidly accelerate once a critical threshold is exceeded, potentially leading to severe social and economic costs. Therefore, in order to develop…
We propose a new distribution-free model of social networks. Our definitions are motivated by one of the most universal signatures of social networks, triadic closure---the property that pairs of vertices with common neighbors tend to be…
To investigate the network-growth rule dependence of certain geometric aspects of percolation clusters, we propose a generalized network-growth rule introducing a generalized parameter $q$ and we study the time evolution of the network. The…
We propose a numerical method to evaluate the upper critical dimension $d_c$ of random percolation clusters in Erd\H{o}s-R\'{e}nyi networks and in scale-free networks with degree distribution ${\cal P}(k) \sim k^{-\lambda}$, where $k$ is…
The distribution of masses of clusters smaller than the infinite cluster is evaluated at the percolation threshold. The clusters are ranked according to their masses and the distribution $P(M/L^D,r)$ of the scaled masses M for any rank r…
We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation…
We study the cluster-size distribution of supercritical long-range percolation on $\mathbb{Z}^d$, where two vertices $x,y\in\mathbb{Z}^d$ are connected by an edge with probability $\mathrm{p}(\|x-y\|):=p\min(1,\beta\|x-y\|)^{-d\alpha}$ for…