Related papers: Community Correlations and Testing Independence Be…
In this paper, we introduce the concept of principal communities and propose a principal graph encoder embedding method that concurrently detects these communities and achieves vertex embedding. Given a graph adjacency matrix with vertex…
Most of the existing graph embedding methods focus on nodes, which aim to output a vector representation for each node in the graph such that two nodes being "close" on the graph are close too in the low-dimensional space. Despite the…
Most real-world networks are weighted graphs with the weight of the edges reflecting the relative importance of the connections. In this work, we study non degree dependent correlations between edge weights, generalizing thus the…
We estimate fair graphs from graph-stationary nodal observations such that connections are not biased with respect to sensitive attributes. Edges in real-world graphs often exhibit preferences for connecting certain pairs of groups. Biased…
Identifying how dependence relationships vary across different conditions plays a significant role in many scientific investigations. For example, it is important for the comparison of biological systems to see if relationships between…
Group testing, a problem with diverse applications across multiple disciplines, traditionally assumes independence across nodes' states. Recent research, however, focuses on real-world scenarios that often involve correlations among nodes,…
Community detection finds homogeneous groups of nodes in a graph. Existing approaches either partition the graph into disjoint, non-overlapping, communities, or determine only overlapping communities. To date, no method supports both…
We consider graphs that represent pairwise marginal independencies amongst a set of variables (for instance, the zero entries of a covariance matrix for normal data). We characterize the directed acyclic graphs (DAGs) that faithfully…
Graph matching consists of aligning the vertices of two unlabeled graphs in order to maximize the shared structure across networks; when the graphs are unipartite, this is commonly formulated as minimizing their edge disagreements. In this…
Let $v$ be a vertex of a graph $G$. By the local complementation of $G$ at $v$ we mean to complement the subgraph induced by the neighbors of $v$. This operator can be generalized as follows. Assume that, each edge of $G$ has a label in the…
Empirical observations suggest that in practice, community membership does not completely explain the dependency between the edges of an observation graph. The residual dependence of the graph edges are modeled in this paper, to first…
We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy…
In this paper we propose methodology for inference of binary-valued adjacency matrices from various measures of the strength of association between pairs of network nodes, or more generally pairs of variables. This strength of association…
The `random intersection graph with communities' models networks with communities, assuming an underlying bipartite structure of groups and individuals. Each group has its own internal structure described by a (small) graph, while groups…
For any positive edge density $p$, a random graph in the Erd\H{o}s-Renyi $G_{n,p}$ model is connected with non-zero probability, since all edges are mutually independent. We consider random graph models in which edges that do not share…
Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…
Mixed data refers to a type of data in which variables can be of multiple types, such as continuous, discrete, or categorical. This data is routinely collected in various fields, including healthcare and social sciences. A common goal in…
In this paper, we proposed a novel two-stage optimization method for network community partition, which is based on inherent network structure information. The introduced optimization approach utilizes the new network centrality measure of…
Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. A set $I_0(G) \subseteq V(G)$ is a vertex independent set if no two vertices in $I_0(G)$ are adjacent in $G$. We study $\alpha_1(G)$, which is the maximum cardinality of a set…
Community detection in networks refers to the process of seeking strongly internally connected groups of nodes which are weakly externally connected. In this work, we introduce and study a community definition based on internal edge…