Abstract Community detection is a common task in social network analysis with applications variety of fields including medicine, criminology and business. Despite the popularity community detection, there no clear consensus on most effective methodology for signed networks. In this article, we summarize development networks evaluate current state-of-the-art techniques several real-world dataset...

We introduce a family of multi-way Cheeger-type constants {h k , k = 1, 2, . . . , N} on a signed graph Γ = (G, σ) such that h k = 0 if and only if Γ has k balanced connected components. These constants are switching invariant and bring together in a unified viewpoint a number of important graph-theoretical concepts, including the classical Cheeger constant, the non-bipartiteness parameter of D...

This paper studies the consensus of first-order discrete-time multi-agent systems with fixed and switching topology, there exists cooperative antagonistic interactions among agents. A signed graph is used to model agents, some sufficient conditions for are obtained by analyzing eigenvalues a Laplacian matrix in case topology. The results indicate that having spanning tree only necessary conditi...

RNA secondary structure consists of elements such as stems, bulges, loops. The most obvious and important scalar number that can be attached to an RNA structure is its free energy, with a landscape that governs the folding pathway. However, because of the unique geometry of RNA secondary structure, another interesting single-signed scalar number based on geometrical scales exists that can assis...

Eigenvalues of a graph are the eigenvalues of its adjacency matrix. The multiset of eigenvalues is called its spectrum. There are many properties which can be explained using the spectrum like energy, connectedness, vertex connectivity, chromatic number, perfect matching etc. Laplacian spectrum is the multiset of eigenvalues of Laplacian matrix. The Laplacian energy of a graph is the sum of the...

We investigate the limiting behavior of solutions to inhomogeneous $p$-Laplacian equation $-\Delta_p u = \mu_p$ subject Neumann boundary conditions. For right hand sides which are arbitrary signed measures we show that converge a Kantorovich potential associated with geodesic Wasserstein-$1$ distance. In regular case continuous characterize limit as viscosity solution an infinity Laplacian / ei...

for a simple digraph $g$ of order $n$ with vertex set${v_1,v_2,ldots, v_n}$, let $d_i^+$ and $d_i^-$ denote theout-degree and in-degree of a vertex $v_i$ in $g$, respectively. let$d^+(g)=diag(d_1^+,d_2^+,ldots,d_n^+)$ and$d^-(g)=diag(d_1^-,d_2^-,ldots,d_n^-)$. in this paper we introduce$widetilde{sl}(g)=widetilde{d}(g)-s(g)$ to be a new kind of skewlaplacian matrix of $g$, where $widetilde{d}(g...

The Laplacian eigenvalues of a network play an important role in the analysis of many structural and dynamical network problems. In this paper, we study the relationship between the eigenvalue spectrum of the normalized Laplacian matrix and the structure of ‘local’ subgraphs of the network. We call a subgraph local when it is induced by the set of nodes obtained from a breath-first search (BFS)...

This paper studies the problem of fault detection and isolation (FDI) for multi-agent systems (MAS) via complex Laplacian subject to actuator faults. A planar formation of point agents in the plane using simple and linear interaction rules related to complex Laplacian is achieved. The communication network is a directed, and yet connected graph with a fixed topology. The loss of symmetry in the...

Abstract In this paper, we give the spectrum of a matrix by using the quotient matrix, then we apply this result to various matrices associated to a graph and a digraph, including adjacency matrix, (signless) Laplacian matrix, distance matrix, distance (signless) Laplacian matrix, to obtain some known and new results. Moreover, we propose some problems for further research. AMS Classification: ...