Related papers: An Efficient Entropy Flow on Weighted Graphs: Theo…
We introduce a new approach to the maximum flow problem in undirected, capacitated graphs using $\alpha$-\emph{congestion-approximators}: easy-to-compute functions that approximate the congestion required to route single-commodity demands…
The aim of this paper is to check feasibility of using the maximal-entropy random walk in algorithms finding communities in complex networks. A number of such algorithms exploit an ordinary or a biased random walk for this purpose. Their…
In this work, we propose to utilize discrete graph Ricci flow to alter network entropy through feedback control. Given such feedback input can reverse entropic changes, we adapt the moniker of Maxwells Demon to motivate our approach. In…
We present a monotonic expression for the Ricci flow, valid in all dimensions and without curvature assumptions. It is interpreted as an entropy for a certain canonical ensemble. Several geometric applications are given. In particular, (1)…
Connectivity (or equivalently, unweighted maximum flow) is an important measure in graph theory and combinatorial optimization. Given a graph $G$ with vertices $s$ and $t$, the connectivity $\lambda(s,t)$ from $s$ to $t$ is defined to be…
Motivated by the methods and results of manifold sampling based on Ricci curvature, we propose a similar approach for networks. To this end we make appeal to three types of discrete curvature, namely the graph Forman-, full Forman- and…
Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…
Graph mining to extract interesting components has been studied in various guises, e.g., communities, dense subgraphs, cliques. However, most existing works are based on notions of frequency and connectivity and do not capture subjective…
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…
Decomposing a network flow into weighted paths has numerous applications. Some applications require any decomposition that is optimal w.r.t. some property such as number of paths, robustness, or length. Many bioinformatic applications…
Educational data mining has become an important research field in studying the social behavior of college students using massive data. However, traditional campus friendship network and their community detection algorithms, which lack time…
With the emergence of social networks, online platforms dedicated to different use cases, and sensor networks, the emergence of large-scale graph community detection has become a steady field of research with real-world applications.…
Eigenvalues of a graph are of high interest in graph analytics for Big Data due to their relevance to many important properties of the graph including network resilience, community detection and the speed of viral propagation. Accurate…
This paper studies the problem of detecting the presence of a small dense community planted in a large Erd\H{o}s-R\'enyi random graph $\mathcal{G}(N,q)$, where the edge probability within the community exceeds $q$ by a constant factor.…
The concept of entropy rate for a dynamical process on a graph is introduced. We study diffusion processes where the node degrees are used as a local information by the random walkers. We describe analitically and numerically how the degree…
Integrating structural information and metadata, such as gender, social status, or interests, enriches networks and enables a better understanding of the large-scale structure of complex systems. However, existing approaches to metadata…
In this paper, we introduce a novel community detection algorithm in graphs, called SCoDA (Streaming Community Detection Algorithm), based on an edge streaming setting. This algorithm has an extremely low memory footprint and a…
In this paper, we introduce a new notion of curvature on the edges of a graph that is defined in terms of effective resistances. We call this the Ricci--Foster curvature. We study the Ricci flow resulting from this curvature. We prove the…
Local graph clustering methods aim to detect small clusters in very large graphs without the need to process the whole graph. They are fundamental and scalable tools for a wide range of tasks such as local community detection, node ranking…
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…