Related papers: Analysis and Approximate Inference of Large Random…
Finding dense components in graphs is of great importance in analyzing the structure of networks. Popular and computationally feasible frameworks for discovering dense subgraphs are core and truss decompositions. Recently, Sariyuce et al.…
A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…
In this paper, we consider classic randomized low diameter decomposition procedures for planar graphs that obtain connected clusters which are cohesive in that close-by pairs of nodes are assigned to the same cluster with high probability.…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…
Graph convolutional networks (GCNs) are a widely used method for graph representation learning. To elucidate the capabilities and limitations of GCNs, we investigate their power, as a function of their number of layers, to distinguish…
Random K-out graphs are garnering interest in designing distributed systems including secure sensor networks, anonymous crypto-currency networks, and differentially-private decentralized learning. In these security-critical applications, it…
The Graph Reconstruction Conjecture famously posits that any undirected graph on at least three vertices is determined up to isomorphism by its family of (unlabeled) induced subgraphs. At present, the conjecture admits partial resolutions…
k-connectivity of random graphs is a fundamental property indicating reliability of multi-hop wireless sensor networks (WSN). WSNs comprising of sensor nodes with limited power resources are modeled by random graphs with unreliable nodes,…
Gaussian Conditional Random Fields (GCRF), as a structured regression model, is designed to achieve higher regression accuracy than unstructured predictors at the expense of execution time, taking into account the objects similarities and…
Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very…
We determine the size of $k$-core in a large class of dense graph sequences. Let $G_n$ be a sequence of undirected, $n$-vertex graphs with edge weights $\{a^n_{i,j}\}_{i,j \in [n]}$ that converges to a kernel $W:[0,1]^2\to [0,+\infty)$ in…
Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design…
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…
We address the problem of identifying a graph structure from the observation of signals defined on its nodes. Fundamentally, the unknown graph encodes direct relationships between signal elements, which we aim to recover from observable…
We study an inhomogeneous sparse random graph on [N] = {1, . . . , N } as introduced in a seminal paper by Bollobas, Janson and Riordan (2007): vertices have a type (here in a compact metric space S), and edges between different vertices…
We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a…
Recent years are characterized by an unprecedented quantity of available network data which are produced at an astonishing rate by an heterogeneous variety of interconnected sensors and devices. This high-throughput generation calls for the…
Role discovery in graphs is an emerging area that allows analysis of complex graphs in an intuitive way. In contrast to other graph prob- lems such as community discovery, which finds groups of highly connected nodes, the role discovery…
A set $V$ is said to be separated by subsets $V_1,\ldots,V_k$ if, for every pair of distinct elements of $V$, there is a set $V_i$ that contains exactly one of them. Imposing structural constraints on the separating subsets is often…