Related papers: New Model of Internet Topology Using k-shell Decom…
Complex networks are critical in many scientific, technological, and societal contexts due to their ability to represent and analyze intricate systems with interdependent components. Often, after labeling the nodes of a network with a…
Network dismantling is to identify a minimal set of nodes whose removal breaks the network into small components of subextensive size. Because finding the optimal set of nodes is an NP-hard problem, several heuristic algorithms have been…
Although two-dimensional periodic structures have functioned as the primary platform for exploring topological phenomena, recent advances have substantially expanded this research boundary to include more intricate, aperiodic structures:…
The connectivity of a graph is an important parameter to evaluate its reliability. $k$-restricted connectivity (resp. $R^h$-restricted connectivity) of a graph $G$ is the minimum cardinality of a set $S$ of vertices in $G$, if exists, whose…
The structural analysis of shape boundaries leads to the characterization of objects as well as to the understanding of shape properties. The literature on graphs and networks have contributed to the structural characterization of shapes…
Real world complex networks are scale free and possess meso-scale properties like core-periphery and community structure. We study evolution of the core over time in real world networks. This paper proposes evolving models for both…
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…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
Network reconstruction lies at the heart of phylogenetic research. Two well studied classes of phylogenetic networks include tree-child networks and level-$k$ networks. In a tree-child network, every non-leaf node has a child that is a tree…
We present a method to decompose biochemical networks into subnetworks based on the global geometry of the network. This method enables us to analyse the full hierarchical organisation of biochemical networks and is applied to 43 organisms…
We survey an abstract theory of connectivity, based on symmetric submodular set functions. We start by developing Robertson and Seymour's fundamental duality between branch decompositions (related to the better-known tree decompositions)…
Due to the advent of the expressions of data other than tabular formats, the topological compositions which make samples interrelated came into prominence. Analogically, those networks can be interpreted as social connections, dataflow…
Complex networks are a powerful paradigm to model complex systems. Specific network models, e.g., multilayer networks, temporal networks, and signed networks, enrich the standard network representation with additional information to better…
Finding the dense regions in a graph is an important problem in network analysis. Core decomposition and truss decomposition address this problem from two different perspectives. The former is a vertex-driven approach that assigns density…
We study the large-scale topological and dynamical properties of real Internet maps at the autonomous system level, collected in a three years time interval. We find that the connectivity structure of the Internet presents average…
Information on any given topic is often scattered across the web. Previously this scatter has been characterized through the distribution of a set of facts (i.e. pieces of information) across web pages, showing that typically a few pages…
Considering systems of separations in a graph that separate every pair of a given set of vertex sets that are themselves not separated by these separations, we determine conditions under which such a separation system contains a nested…
Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems…
Comparative analyses of graph structured datasets underly diverse problems. Examples of these problems include identification of conserved functional components (biochemical interactions) across species, structural similarity of large…
We organize a table of regular graphs with minimal diameters and minimal mean path lengths, large bisection widths and high degrees of symmetries, obtained by enumerations on supercomputers. These optimal graphs, many of which are newly…