scholarly journals Scaling up real networks by geometric branching growth

2021 ◽  
Vol 118 (21) ◽  
pp. e2018994118
Author(s):  
Muhua Zheng ◽  
Guillermo García-Pérez ◽  
Marián Boguñá ◽  
M. Ángeles Serrano
Keyword(s):  
Finite Size ◽  
Citation Network ◽  
Network Size ◽  
Link Failures ◽  
Practical Applications ◽  
Best Response ◽  
Sequential Addition ◽  
Self Similar ◽  
Similar Growth ◽  
Fundamental Units

Real networks often grow through the sequential addition of new nodes that connect to older ones in the graph. However, many real systems evolve through the branching of fundamental units, whether those be scientific fields, countries, or species. Here, we provide empirical evidence for self-similar growth of network structure in the evolution of real systems—the journal-citation network and the world trade web—and present the geometric branching growth model, which predicts this evolution and explains the symmetries observed. The model produces multiscale unfolding of a network in a sequence of scaled-up replicas preserving network features, including clustering and community structure, at all scales. Practical applications in real instances include the tuning of network size for best response to external influence and finite-size scaling to assess critical behavior under random link failures.

Collective influence maximization for multiple competing products with an awareness-to-influence model

2021 ◽  
Vol 14 (7) ◽  
pp. 1124-1136
Author(s):  
Dimitris Tsaras ◽  
George Trimponias ◽  
Lefteris Ntaflos ◽  
Dimitris Papadias
Keyword(s):  
Diffusion Processes ◽  
Influence Maximization ◽  
Second Phase ◽  
Social Graph ◽  
Practical Applications ◽  
Influence Model ◽  
Best Response ◽  
The Social ◽  
Game Theoretic ◽  
Collective Influence

Influence maximization (IM) is a fundamental task in social network analysis. Typically, IM aims at selecting a set of seeds for the network that influences the maximum number of individuals. Motivated by practical applications, in this paper we focus on an IM variant, where the owner of multiple competing products wishes to select seeds for each product so that the collective influence across all products is maximized. To capture the competing diffusion processes, we introduce an Awareness-to-Influence (AtI) model. In the first phase, awareness about each product propagates in the social graph unhindered by other competing products. In the second phase, a user adopts the most preferred product among those encountered in the awareness phase. To compute the seed sets, we propose GCW, a game-theoretic framework that views the various products as agents, which compete for influence in the social graph and selfishly select their individual strategy. We show that AtI exhibits monotonicity and submodularity; importantly, GCW is a monotone utility game. This allows us to develop an efficient best-response algorithm, with quality guarantees on the collective utility. Our experimental results suggest that our methods are effective, efficient, and scale well to large social networks.

Hierarchical and Self-Similar Growth of Self-Assembled Crystals

2003 ◽  
Vol 42 (4) ◽  
pp. 413-417 ◽  
Author(s):  
Zhengrong R. Tian ◽  
Jun Liu ◽  
James A. Voigt ◽  
Bonnie Mckenzie ◽  
Huifang Xu
Keyword(s):  
Self Similar ◽  
Self Assembled ◽  
Similar Growth

scholarly journals Growth and arrest of topological cycles in small physical networks

2020 ◽  
Vol 117 (27) ◽  
pp. 15394-15396
Author(s):  
Timothy W. Sirk
Keyword(s):  
Monte Carlo ◽  
Random Graphs ◽  
Kinetic Monte Carlo ◽  
Polymer Networks ◽  
Finite Size ◽  
Characteristic Size ◽  
Network Size ◽  
Embedded Networks ◽  
Metropolis Monte Carlo ◽  
Chordless Cycle

The chordless cycle sizes of spatially embedded networks are demonstrated to follow an exponential growth law similar to random graphs if the number of nodesNxis below a critical valueN*. For covalent polymer networks, increasing the network size, as measured by the number of cross-link nodes, beyondN*results in a crossover to a new regime in which the characteristic size of the chordless cyclesh*no longer increases. From this result, the onset and intensity of finite-size effects can be predicted from measurement ofh*in large networks. Although such information is largely inaccessible with experiments, the agreement of simulation results from molecular dynamics, Metropolis Monte Carlo, and kinetic Monte Carlo suggests the crossover is a fundamental physical feature which is insensitive to the details of the network generation. These results show random graphs as a promising model to capture structural differences in confined physical networks.

SCALING OF FLOW DISTANCE IN RANDOM SELF-SIMILAR CHANNEL NETWORKS

Fractals ◽  
2005 ◽  
Vol 13 (04) ◽  
pp. 265-282 ◽  
Author(s):  
BRENT M. TROUTMAN
Keyword(s):  
Drainage Basin ◽  
Empirical Studies ◽  
Rooted Tree ◽  
Network Size ◽  
Channel Networks ◽  
Tree Graphs ◽  
Affine Structures ◽  
Self Similar ◽  
Function Number ◽  
Behavior Characteristic

Natural river channel networks have been shown in empirical studies to exhibit power-law scaling behavior characteristic of self-similar and self-affine structures. Of particular interest is to describe how the distribution of distance to the outlet changes as a function of network size. In this paper, networks are modeled as random self-similar rooted tree graphs and scaling of distance to the root is studied using methods in stochastic branching theory. In particular, the asymptotic expectation of the width function (number of nodes as a function of distance to the outlet) is derived under conditions on the replacement generators. It is demonstrated further that the branching number describing rate of growth of node distance to the outlet is identical to the length ratio under a Horton-Strahler ordering scheme as order gets large, again under certain restrictions on the generators. These results are discussed in relation to drainage basin allometry and an application to an actual drainage network is presented.

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