Related papers: On the Relation between Graph Ricci Curvature and …
Ricci curvature and Ricci flow have proven to be powerful tools for analyzing the geometry of discrete structures, particularly on undirected graphs, where they have been applied to tasks ranging from community detection to graph…
Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among…
A precise definition of what constitutes a community in networks has remained elusive. Consequently, network scientists have compared community detection algorithms on benchmark networks with a particular form of community structure and…
Hypergraph data appear and are hidden in many places in the modern age. They are data structure that can be used to model many real data examples since their structures contain information about higher order relations among data points. One…
Most real-world networks are embedded in latent geometries. If a node in a network is found in the vicinity of another node in the latent geometry, the two nodes have a disproportionately high probability of being connected by a link. The…
We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this…
Measuring the topological overlap of two graphs becomes important when assessing the changes between temporally adjacent graphs in a time-evolving network. Current methods depend on the fraction of nodes that have persisting edges. This…
Modularity maximization is one of the state-of-the-art methods for community detection that has gained popularity in the last decade. Yet it suffers from the resolution limit problem by preferring under certain conditions large communities…
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…
Community structure is one of the key properties of real-world complex networks. It plays a crucial role in their behaviors and topology. While an important work has been done on the issue of community detection, very little attention has…
The association between tie strength and social structure is a fundamental topic in the social sciences. We study this association by analyzing tie strength in higher-order networks, an increasingly relevant model which can encode group…
Community detection and link prediction are both of great significance in network analysis, which provide very valuable insights into topological structures of the network from different perspectives. In this paper, we propose a novel…
The topology of social networks can be understood as being inherently dynamic, with edges having a distinct position in time. Most characterizations of dynamic networks discretize time by converting temporal information into a sequence of…
Community detection in a complex network is an important problem of much interest in recent years. In general, a community detection algorithm chooses an objective function and captures the communities of the network by optimizing the…
Turing patterns, arising from the interplay between competing species of diffusive particles, has long been an important concept for describing non-equilibrium self-organization in nature, and has been extensively investigated in many…
Networks built to model real world phenomena are characeterised by some properties that have attracted the attention of the scientific community: (i) they are organised according to community structure and (ii) their structure evolves with…
Community detection is a fundamental problem in the analysis of complex networks. It is the analogue of clustering in network data mining. Within community detection methods, hierarchical algorithms are popular. However, their iterative…
This study relates the local property of node dominance to local and global properties of a network. Iterative removal of dominated nodes yields a distributed algorithm for computing a core-periphery decomposition of a social network, where…
The communities of a social network are sets of vertices with more connections inside the set than outside. We theoretically demonstrate that two commonly observed properties of social networks, heavy-tailed degree distributions and large…
Characterizing shapes of high-dimensional objects via Ricci curvatures plays a critical role in many research areas in mathematics and physics. However, even though several discretizations of Ricci curvatures for discrete combinatorial…