Related papers: Which Sampling Densities are Suitable for Spectral…
Bootstrap percolation in (random) graphs is a contagion dynamics among a set of vertices with certain threshold levels. The process is started by a set of initially infected vertices, and an initially uninfected vertex with threshold $k$…
We study the sampling of spatial fields using sensors that are location-unaware but deployed according to a known statistical distribution. It has been shown that uniformly distributed location-unaware sensors cannot infer bandlimited…
The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and…
Graph clustering (or community detection) has long drawn enormous attention from the research on web mining and information networks. Recent literature on this topic has reached a consensus that node contents and link structures should be…
We derive a message passing method for computing the spectra of locally tree-like networks and an approximation to it that allows us to compute closed-form expressions or fast numerical approximates for the spectral density of random graphs…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
We analyze the spectral properties of the high-dimensional random geometric graph $G(n, d, p)$, formed by sampling $n$ i.i.d vectors $\{v_i\}_{i=1}^{n}$ uniformly on a $d$-dimensional unit sphere and connecting each pair $\{i,j\}$ whenever…
Higher-order connectivity patterns such as small induced sub-graphs called graphlets (network motifs) are vital to understand the important components (modules/functional units) governing the configuration and behavior of complex networks.…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
We conjecture that the distribution of the edge-disjoint union of two random regular graphs on the same vertex set is asymptotically equivalent to a random regular graph of the combined degree, provided it grows as the number of vertices…
We present an exclusion process based approach for sampling densest $k$-sub-graphs from regular graphs $L$ with connected complement. By interpreting an exclusion process as a Markov chain on a corresponding Token Graph $\mathfrak{L}_k$, we…
Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…
Spectral clustering is a widely used algorithm to find clusters in networks. Several researchers have studied the stability of spectral clustering under local differential privacy with the additional assumption that the underlying networks…
Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer networks or social…
In the present paper, we studied a Dynamic Stochastic Block Model (DSBM) under the assumptions that the connection probabilities, as functions of time, are smooth and that at most $s$ nodes can switch their class memberships between two…
Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…
Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…
Spectral analysis connects graph structure to the eigenvalues and eigenvectors of associated matrices. Much of spectral graph theory descends directly from spectral geometry, the study of differentiable manifolds through the spectra of…
Uncertainty principles present an important theoretical tool in signal processing, as they provide limits on the time-frequency concentration of a signal. In many real-world applications the signal domain has a complicated irregular…