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22
THE SUN GRAPH IS DETERMINED BY ITS SIGNLESS LAPLACIAN SPECTRUM
, 2010
"... For a simple undirected graph G, the corresponding signless Laplacian matrix is ..."
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For a simple undirected graph G, the corresponding signless Laplacian matrix is
EDGE BIPARTITENESS AND SIGNLESS LAPLACIAN SPREAD OF GRAPHS
 APPL. ANAL. DISCRETE MATH. 6 (2012), 31–45.
, 2012
"... Let G be a connected graph, and let ǫb(G) and SQ(G) be the edge bipartiteness and the signless Laplacian spread of G, respectively. We establish some important relationships between ǫb(G) and SQ(G), and prove ..."
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Let G be a connected graph, and let ǫb(G) and SQ(G) be the edge bipartiteness and the signless Laplacian spread of G, respectively. We establish some important relationships between ǫb(G) and SQ(G), and prove
ON THE LEAST SIGNLESS LAPLACIAN EIGENVALUE OF SOME GRAPHS
, 2013
"... For a graph, the least signless Laplacian eigenvalue is the least eigenvalue of its signless Laplacian matrix. This paper investigates how the least signless Laplacian eigenvalue of a graph changes under some perturbations, and minimizes the least signless Laplacian eigenvalue among all the nonbipa ..."
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For a graph, the least signless Laplacian eigenvalue is the least eigenvalue of its signless Laplacian matrix. This paper investigates how the least signless Laplacian eigenvalue of a graph changes under some perturbations, and minimizes the least signless Laplacian eigenvalue among all the nonbipartite graphs with given matching number and edge cover number, respectively.
Spectral characterizations of dumbbell graphs
"... A dumbbell graph, denoted by Da,b,c, is a bicyclic graph consisting of two vertexdisjoint cycles Ca, Cb and a path Pc+3 (c � −1) joining them having only its endvertices in common with the two cycles. In this paper, we study the spectral characterization w.r.t. the adjacency spectrum of Da,b,0 (wit ..."
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A dumbbell graph, denoted by Da,b,c, is a bicyclic graph consisting of two vertexdisjoint cycles Ca, Cb and a path Pc+3 (c � −1) joining them having only its endvertices in common with the two cycles. In this paper, we study the spectral characterization w.r.t. the adjacency spectrum of Da,b,0 (without cycles C4) with gcd(a,b) � 3, and we complete the research started in [J.F. Wang et al., A note on the spectral characterization of dumbbell graphs, Linear Algebra Appl. 431 (2009) 1707–1714]. In particular we show that Da,b,0 with 3 � gcd(a,b) < a or gcd(a,b) = a and b ̸ = 3a is determined by the spectrum. For b = 3a, we determine the unique graph cospectral with Da,3a,0. Furthermore we give the spectral characterization w.r.t. the signless Laplacian spectrum of all dumbbell graphs. 1
Games of Dynamic Network Formation
"... We combine a network game introduced in Ballester et al. (2006), where the Nash equilibrium action of each agent is proportional to her Bonacich centrality (Bonacich, 1987), with an endogenous network formation process. Links are formed on the basis of centrality while the network is exposed to a v ..."
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We combine a network game introduced in Ballester et al. (2006), where the Nash equilibrium action of each agent is proportional to her Bonacich centrality (Bonacich, 1987), with an endogenous network formation process. Links are formed on the basis of centrality while the network is exposed to a volatile environment introducing interruptions in the connections between agents. Taking into account bounded rational decision making, new links are formed to the neighbors’ neighbors with the highest centrality. The volatile environment causes existing links to decay to the neighbor with the lowest centrality. We show analytically that there exist stationary networks and that their topological properties completely match with features exhibited by social and economic networks. Moreover, we find that there exists a sharp transition in efficiency and network density from highly centralized to decentralized networks.
THE SMALLEST SIGNLESS LAPLACIAN EIGENVALUE OF GRAPHS UNDER PERTURBATION
, 2012
"... In this paper, we investigate how the smallest signless Laplacian eigenvalue of a graph behaves when the graph is perturbed by deleting a vertex, subdividing edges or moving edges. ..."
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In this paper, we investigate how the smallest signless Laplacian eigenvalue of a graph behaves when the graph is perturbed by deleting a vertex, subdividing edges or moving edges.
ON THE MAIN SIGNLESS LAPLACIAN EIGENVALUES Of A Graph
, 2013
"... A signless Laplacian eigenvalue of a graph G is called a main signless Laplacian eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this paper, some necessary and sufficient conditions for a graph with one main signless Laplacian eigenvalue or two main signless La ..."
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A signless Laplacian eigenvalue of a graph G is called a main signless Laplacian eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this paper, some necessary and sufficient conditions for a graph with one main signless Laplacian eigenvalue or two main signless Laplacian eigenvalues are given. And the trees and unicyclic graphs with exactly two main signless Laplacian eigenvalues are characterized, respectively.
Characterizing the Structure of Affiliation Networks
"... Our society contains all types of organizations, such as companies, research groups and hobby clubs. Affiliation networks, as a large and important portion of social networks, consist of individuals and their affiliation relations: Two individuals are connected by a link if they belong to the same o ..."
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Our society contains all types of organizations, such as companies, research groups and hobby clubs. Affiliation networks, as a large and important portion of social networks, consist of individuals and their affiliation relations: Two individuals are connected by a link if they belong to the same organization(s). Affiliation networks naturally contain many fully connected cliques, since the nodes of the same organization are all connected with each other by definition. In this paper, we present methods which facilitate the computation for characterizing the realworld affiliation networks of ArXiv coauthorship, IMDB actors collaboration and SourceForge collaboration. We propose a growing hypergraph model with preferential attachment for affiliation networks which reproduces the clique structure of affiliation networks. By comparing computational results of our model with measurements of the realworld affiliation networks of ArXiv coauthorship, IMDB actors collaboration and SourceForge collaboration, we show that our model captures the fundamental properties including the powerlaw distributions of group size, group degree, overlapping depth, individual degree and interestsharing number of realworld affiliation networks, and reproduces the properties of high clustering, assortative mixing and short average path length of realworld affiliation networks.
Some results on the bounds of signless Laplacian eigenvalues *
"... Abstract: Let G be a simple graph with n vertices and G c be its complement. The matrix Q(G) ..."
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Abstract: Let G be a simple graph with n vertices and G c be its complement. The matrix Q(G)
SPECTRAL PROPERTIES OF ORIENTED HYPERGRAPHS
 ELA
, 2014
"... An oriented hypergraph is a hypergraph where each vertexedge incidence is given a label of +1 or −1. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and Laplacian matrices of an oriented hypergraph which depend on structural p ..."
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An oriented hypergraph is a hypergraph where each vertexedge incidence is given a label of +1 or −1. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and Laplacian matrices of an oriented hypergraph which depend on structural parameters of the oriented hypergraph are found. An oriented hypergraph and its incidence dual are shown to have the same nonzero Laplacian eigenvalues. A family of oriented hypergraphs with uniformally labeled incidences is also studied. This family provides a hypergraphic generalization of the signless Laplacian of a graph and also suggests a natural way to define the adjacency and Laplacian matrices of a hypergraph. Some results presented generalize both graph and signed graph results to a hypergraphic setting.