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The study of complex networks has significantly advanced our understanding of community structures which serves as a crucial feature of real-world graphs. Detecting communities in graphs is a challenging problem with applications in…
We introduce a novel definition of curvature for hypergraphs, a natural generalization of graphs, by introducing a multi-marginal optimal transport problem for a naturally defined random walk on the hypergraph. This curvature, termed…
Community detection is considered as a fundamental task in analyzing social networks. Even though many techniques have been proposed for community detection, most of them are based exclusively on the connectivity structures. However, there…
In the present work, we study the properties of biological networks by applying analogous notions of fundamental concepts in Riemannian geometry and optimal mass transport to discrete networks described by weighted graphs. Specifically, we…
Topology and weights are closely related in weighted complex networks and this is reflected in their modular structure. We present a simple network model where the weights are generated dynamically and they shape the developing topology. By…
In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
Community detection algorithms are fundamental tools to understand organizational principles in social networks. With the increasing power of social media platforms, when detecting communities there are two possi- ble sources of information…
Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…
Algorithms to find communities in networks rely just on structural information and search for cohesive subsets of nodes. On the other hand, most scholars implicitly or explicitly assume that structural communities represent groups of nodes…
Community detection is one of the most active fields in complex networks analysis, due to its potential value in practical applications. Many works inspired by different paradigms are devoted to the development of algorithmic solutions…
In real-world scenarios, large graphs represent relationships among entities in complex systems. Mining these large graphs often containing millions of nodes and edges helps uncover structural patterns and meaningful insights. Dividing a…
We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of…
A goal in network science is the geometrical characterization of complex networks. In this direction, we have recently introduced Forman's discretization of Ricci curvature to the realm of undirected networks. Investigation of this…
We introduce Forman-Ricci curvature and its corresponding flow as characteristics for complex networks attempting to extend the common approach of node-based network analysis by edge-based characteristics. Following a theoretical…
In the last few years many real-world networks have been found to show a so-called community structure organization. Much effort has been devoted in the literature to develop methods and algorithms that can efficiently highlight this hidden…
There are hierarchical characteristics in the network and how to effectively reveal the hierarchical characteristics in the network is a problem in the research of network structure. If a node is assigned to the community to which it…
A wide range of complex systems can be modeled as networks with corresponding constraints on the edges and nodes, which have been extensively studied in recent years. Nowadays, with the progress of information technology, systems that…
Graphs are widely used in various fields of computer science. They have also found application in unrelated areas, leading to a diverse range of problems. These problems can be modeled as relationships between entities in various contexts,…