Related papers: K-Scaffold subgraphs of Complex networks
Multiplex networks are convenient mathematical representations for many real-world -- biological, social, and technological -- systems of interacting elements, where pairwise interactions among elements have different flavors. Previous…
Complex networks in natural, social, and technological systems generically exhibit an abundance of rich information. Extracting meaningful structural features from data is one of the most challenging tasks in network theory. Many methods…
In this paper we consider the fundamental problem of finding subgraphs in highly dynamic distributed networks - networks which allow an arbitrary number of links to be inserted / deleted per round. We show that the problems of $k$-clique…
Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function.…
The concept of 'complexity' plays a central role in complex network science. Traditionally, this term has been taken to express heterogeneity of the node degrees of a therefore complex network. However, given that the degree distribution is…
Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…
The k-truss is a type of cohesive subgraphs proposed recently for the study of networks. While the problem of computing most cohesive subgraphs is NP-hard, there exists a polynomial time algorithm for computing k-truss. Compared with k-core…
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of…
Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater…
Two previous papers, arXiv:1803.00284 and arXiv:1803.00281, introduced and studied strong subgraph $k$-connectivity of digraphs obtaining characterizations, lower and upper bounds and computational complexity results for the new digraph…
A standard approach to reduce the complexity of very large networks is to group together sets of nodes into clusters according to some criterion which reflects certain structural properties of the network. Beyond the well-known modularity…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
Due to the limited resources and the scale of the graphs in modern datasets, we often get to observe a sampled subgraph of a larger original graph of interest, whether it is the worldwide web that has been crawled or social connections that…
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…
Graph Neural Networks (GNNs) draw their strength from explicitly modeling the topological information of structured data. However, existing GNNs suffer from limited capability in capturing the hierarchical graph representation which plays…
In recent years numerous attempts to understand the human brain were undertaken from a network point of view. A network framework takes into account the relationships between the different parts of the system and enables to examine how…
Graphs have been utilized as a powerful tool to model pairwise relationships between people or objects. Such structure is a special type of a broader concept referred to as hypergraph, in which each hyperedge may consist of an arbitrary…
Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…
Finding dense substructures in a graph is a fundamental graph mining operation, with applications in bioinformatics, social networks, and visualization to name a few. Yet most standard formulations of this problem (like clique, quasiclique,…
Identifying central entities and interactions is a fundamental problem in network science. While well-studied for graphs (pairwise relations), many biological and social systems exhibit higher-order interactions best modeled by hypergraphs.…