Related papers: Balance Maximization in Signed Networks via Edge D…
Pinning control of a complex network aims at forcing the states of all nodes to track an external signal by controlling a small number of nodes in the network. In this paper, an algebraic graph-theoretic condition is introduced to optimize…
We consider a cost sharing problem on a weighted undirected graph, where all the nodes want to connect to a special node called source, and they need to share the total cost (weights) of the used edges. Each node except for the source has a…
The reassembling of a simple connected graph G = (V,E) is an abstraction of a problem arising in earlier studies of network analysis. The reassembling process has a simple formulation (there are several equivalent formulations) relative to…
Network centrality plays an important role in many applications. Central nodes in social networks can be influential, driving opinions and spreading news or rumors.In hyperlinked environments, such as the Web, where users navigate via…
This paper aims at addressing distributed averaging problems for signed networks in the presence of general directed topologies that are represented by signed digraphs. A new class of improved Laplacian potential functions is proposed by…
A good edge-labelling of a simple, finite graph is a labelling of its edges with real numbers such that, for every ordered pair of vertices (u,v), there is at most one nondecreasing path from u to v. In this paper we prove that any graph on…
Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with…
Random walks play an important role in probing the structure of complex networks. On traditional networks, they can be used to extract community structure, understand node centrality, perform link prediction, or capture the similarity…
The connectivity structure of a network can be very sensitive to removal of certain nodes in the network. In this paper, we study the sensitivity of the largest component size to node removals. We prove that minimizing the largest component…
Many algorithms have been proposed for detecting disjoint communities (relatively densely connected subgraphs) in networks. One popular technique is to optimize modularity, a measure of the quality of a partition in terms of the number of…
We investigate the vulnerabilities of consensus-based distributed optimization protocols to nodes that deviate from the prescribed update rule (e.g., due to failures or adversarial attacks). We first characterize certain fundamental…
Detailed network models of social, biological and other complex systems are often dense, which increases their computational complexity in simulations and analysis. To address this challenge, graph sparsification is used to remove edges…
We study homomorphism problems of signed graphs. A signed graph is an undirected graph where each edge is given a sign, positive or negative. An important concept for signed graphs is the operation of switching at a vertex, which is to…
Let $G$ be an undirected graph. An edge of $G$ dominates itself and all edges adjacent to it. A subset $E'$ of edges of $G$ is an edge dominating set of $G$, if every edge of the graph is dominated by some edge of $E'$. We say that $E'$ is…
Despite significant advancements in causal research on graphs and its application to cracking label imbalance, the role of edge features in detecting the causal effects within graphs has been largely overlooked, leaving existing methods…
Graphs are fundamental mathematical structures used in various fields to model statistical and physical relationships between data, signals, and processes. In some applications, such as data processing in graphs that represent physical…
Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…
We consider the problem of adding a fixed number of new edges to an undirected graph in order to minimize the diameter of the augmented graph, and under the constraint that the number of edges added for each vertex is bounded by an integer.…
In recent years, the notion of r-robustness for the communication graph of the network has been introduced to address the challenge of achieving consensus in the presence of misbehaving agents. Higher r-robustness typically implies higher…
A signed graph is a graph whose edges are labeled either positive or negative. Corresponding to the two signed distance matrices defined for signed graphs, we define two signed distance laplacian matrices. We characterize balance in signed…