Related papers: Subgraph centrality and walk-regularity
Deterministic equilibrium flows in transport networks can be investigated by means of Markov's processes defined on the dual graph representations of the network. Sustained movement patterns are generated by a subset of automorphisms of the…
The entropy of a graph is a functional depending both on the graph itself and on a probability distribution on its vertex set. This graph functional originated from the problem of source coding in information theory and was introduced by J.…
A constructive proof is given to the fact that any ergodic Markov chain can be realized as a random walk subject to a synchronizing road coloring. Redundancy (ratio of extra entropy) in such a realization is also studied.
Graph embeddings are low dimensional representations of nodes, edges or whole graphs. Such representations allow for data in a network format to be used along with machine learning models for a variety of tasks (e.g., node classification),…
There are several centrality measures that have been introduced and studied for real world networks. They account for the different vertex characteristics that permit them to be ranked in order of importance in the network. Betweenness…
Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or…
Centrality metrics aim to identify the most relevant nodes in a network. In literature, a broad set of metrics exists, either measuring local or global centrality characteristics. Nevertheless, when networks exhibit a high spectral gap, the…
We interpret the subgraph centrality as the partition function of a network. The entropy, the internal energy and the Helmholtz free energy are defined for networks and molecular graphs on the basis of graph spectral theory. Various…
A new heuristic based on vertex invariants is developed to rapidly distinguish non-isomorphic graphs to a desired level of accuracy. The method is applied to sample subgraphs from an E.coli protein interaction network, and as a probe for…
We study the popular centrality measure known as effective conductance or in some circles as information centrality. This is an important notion of centrality for undirected networks, with many applications, e.g., for random walks,…
We show that the von Neumann entropy (from herein referred to as the von Neumann index) of a graph's trace normalized combinatorial Laplacian provides structural information about the level of centralization across a graph. This is done by…
The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world…
In the graph exploration problem, a team of mobile computational entities, called agents, arbitrarily positioned at some nodes of a graph, must cooperate so that each node is eventually visited by at least one agent. In the literature, the…
Numerous centrality measures have been proposed to evaluate the importance of nodes in networks, yet comparative analyses of these measures remain limited. Based on 80 real-world networks, we conducted an empirical analysis of 16…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
Network architecture design is very important for the optimization of industrial networks. The type of network architecture can be divided into small-scale network and large-scale network according to its scale. Graph theory is an efficient…
This report presents a very simple algorithm for overlaping community-detection in large graphs under constraints such as the minimum and maximum number of members allowed. The algorithm is based on the simulation of random walks and…
Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still…
Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…
Network embedding which encodes all vertices in a network as a set of numerical vectors in accordance with it's local and global structures, has drawn widespread attention. Network embedding not only learns significant features of a…