135,996 research outputs found
Degree based Topological indices of Hanoi Graph
International audienceThere are various topological indices for example distance based topological indices and degree based topological indices etc. In QSAR/QSPR study, physiochemical properties and topological indices for example atom bond connectivity index, fourth atom bond connectivity index, Randic connectivity index, sum connectivity index, and so forth are used to characterize the chemical compound. In this paper we computed the edge version of atom bond connectivity index, fourth atom bond connectivity index, Randic connectivity index, sum connectivity index, geometric-arithmetic index and fifth geometric-arithmetic index of Double-wheel graph and Hanoi graph. The results are analyzed and the general formulas are derived for the above mentioned families of graphs
Emergence of scale-free behavior in networks from limited-horizon linking and cost trade-offs
We study network growth from a fixed set of initially isolated nodes placed
at random on the surface of a sphere. The growth mechanism we use adds edges to
the network depending on strictly local gain and cost criteria. Only nodes that
are not too far apart on the sphere may be considered for being joined by an
edge. Given two such nodes, the joining occurs only if the gain of doing it
surpasses the cost. Our model is based on a multiplicative parameter lambda
that regulates, in a function of node degrees, the maximum geodesic distance
that is allowed between nodes for them to be considered for joining. For n
nodes distributed uniformly on the sphere, and for lambda*sqrt(n) within limits
that depend on cost-related parameters, we have found that our growth mechanism
gives rise to power-law distributions of node degree that are invariant for
constant lambda*sqrt(n). We also study connectivity- and distance-related
properties of the networks
Computing edge version of eccentric connectivity index of nanostar dendrimers
Let G be a molecular graph, the edge version of eccentric connectivity index of G are defined as ( ) ( ) å ∈ ( ) = ⋅ GEf c e ξ (G) deg f ecc f , where deg( f ) denotes the degree of an edge f and ecc( f ) is the largest distance between f and any other edge g of G , namely, eccentricity of f . In this paper exact formulas for the edge version of eccentric connectivity index of two classes of nanostar dendrimers were computed
A Network Model characterized by a Latent Attribute Structure with Competition
The quest for a model that is able to explain, describe, analyze and simulate
real-world complex networks is of uttermost practical as well as theoretical
interest. In this paper we introduce and study a network model that is based on
a latent attribute structure: each node is characterized by a number of
features and the probability of the existence of an edge between two nodes
depends on the features they share. Features are chosen according to a process
of Indian-Buffet type but with an additional random "fitness" parameter
attached to each node, that determines its ability to transmit its own features
to other nodes. As a consequence, a node's connectivity does not depend on its
age alone, so also "young" nodes are able to compete and succeed in acquiring
links. One of the advantages of our model for the latent bipartite
"node-attribute" network is that it depends on few parameters with a
straightforward interpretation. We provide some theoretical, as well
experimental, results regarding the power-law behaviour of the model and the
estimation of the parameters. By experimental data, we also show how the
proposed model for the attribute structure naturally captures most local and
global properties (e.g., degree distributions, connectivity and distance
distributions) real networks exhibit. keyword: Complex network, social network,
attribute matrix, Indian Buffet processComment: 34 pages, second version (date of the first version: July, 2014).
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Communicability Angles Reveal Critical Edges for Network Consensus Dynamics
We consider the question of determining how the topological structure
influences a consensus dynamical process taking place on a network. By
considering a large dataset of real-world networks we first determine that the
removal of edges according to their communicability angle -an angle between
position vectors of the nodes in an Euclidean communicability space- increases
the average time of consensus by a factor of 5.68 in real-world networks. The
edge betweenness centrality also identifies -in a smaller proportion- those
critical edges for the consensus dynamics, i.e., its removal increases the time
of consensus by a factor of 3.70. We justify theoretically these findings on
the basis of the role played by the algebraic connectivity and the
isoperimetric number of networks on the dynamical process studied, and their
connections with the properties mentioned before. Finally, we study the role
played by global topological parameters of networks on the consensus dynamics.
We determine that the network density and the average distance-sum -an
analogous of the node degree for shortest-path distances, account for more than
80% of the variance of the average time of consensus in the real-world networks
studied.Comment: 15 pages, 2 figure
Precise Partitions Of Large Graphs
First by using an easy application of the Regularity Lemma, we extend some known results about cycles of many lengths to include a specified edge on the cycles. The results in this chapter will help us in rest of this thesis. In 2000, Enomoto and Ota posed a conjecture on the existence of path decomposition of graphs with fixed start vertices and fixed lengths. We prove this conjecture when |G| is large. Our proof uses the Regularity Lemma along with several extremal lemmas, concluding with an absorbing argument to retrieve misbehaving vertices. Furthermore, sharp minimum degree and degree sum conditions are proven for the existance of a Hamiltonian cycle passing through specified vertices with prescribed distances between them in large graphs. Finally, we prove a sharp connectivity and degree sum condition for the existence of a subdivision of a multigraph in which some of the vertices are specified and the distance between each pair of vertices in the subdivision is prescribed (within one)
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