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Many methods have been proposed for community detection in networks. Some of the most promising are methods based on statistical inference, which rest on solid mathematical foundations and return excellent results in practice. In this paper…
We introduce and simulate the random walk that adapts move strategies according to local node preferences on a directed graph. We consider graphs with double-hierarchical connectivity and variable wiring diagram in the universality class of…
We consider the (exact, minimum) $k$-cut problem: given a graph and an integer $k$, delete a minimum-weight set of edges so that the remaining graph has at least $k$ connected components. This problem is a natural generalization of the…
Consider a network consisting of two subnetworks (communities) connected by some external edges. Given the network topology, the community detection problem can be cast as a graph partitioning problem that aims to identify the external…
Many real-world datasets have an underlying dynamic graph structure, where entities and their interactions evolve over time. Machine learning models should consider these dynamics in order to harness their full potential in downstream…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
The task of \emph{community detection} in a graph formalizes the intuitive task of grouping together subsets of vertices such that vertices within clusters are connected tighter than those in disparate clusters. This paper approaches…
Increased attention has been paid over the last four years to dynamic network embedding. Existing dynamic embedding methods, however, consider the problem as limited to the evolution of a topology over a sequence of global, discrete states.…
The splitting-off operation in undirected graphs is a fundamental reduction operation that detaches all edges incident to a given vertex and adds new edges between the neighbors of that vertex while preserving their degrees. Lov\'asz (1974)…
This paper proposes a dynamic sensor scheduling method for sensor networks. In sensor network applications, we often need multiple equally-informative node subsets that are activated sequentially to make a sensor network robust against…
Graph clustering is an important technique to understand the relationships between the vertices in a big graph. In this paper, we propose a novel random-walk-based graph clustering method. The proposed method restricts the reach of the…
We present the first linear time complexity randomized algorithms for unbiased approximation of the celebrated family of general random walk kernels (RWKs) for sparse graphs. This includes both labelled and unlabelled instances. The…
We develop two different methods to achieve subexponential time parameterized algorithms for problems on sparse directed graphs. We exemplify our approaches with two well studied problems. For the first problem, {\sc $k$-Leaf…
Community detection is a fundamental task in graph analysis, with methods often relying on fitting models like the Stochastic Block Model (SBM) to observed networks. While many algorithms can accurately estimate SBM parameters when the…
We give algorithms with running time $2^{O({\sqrt{k}\log{k}})} \cdot n^{O(1)}$ for the following problems. Given an $n$-vertex unit disk graph $G$ and an integer $k$, decide whether $G$ contains (1) a path on exactly/at least $k$ vertices,…
Random walk-based sampling methods are gaining popularity and importance in characterizing large networks. While powerful, they suffer from the slow mixing problem when the graph is loosely connected, which results in poor estimation…
We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the…
Community is a universal structure in various complex networks, and community detection is a fundamental task for network analysis. With the rapid growth of network scale, networks are massive, changing rapidly and could naturally be…
Community detection is expensive, and the cost generally depends at least linearly on the number of vertices in the graph. We propose working with a reduced graph that has many fewer nodes but nonetheless captures key community structure.…
In this paper, we set forth a new algorithm for generating approximately uniformly random spanning trees in undirected graphs. We show how to sample from a distribution that is within a multiplicative $(1+\delta)$ of uniform in expected…