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- P L Krapivsky, S Redner
- Physical review. E, Statistical, nonlinear, and…
- 2001

The organizational development of growing random networks is investigated. These growing networks are built by adding nodes successively, and linking each to an earlier node of degree k with an attachment probability A(k). When A(k) grows more slowly than linearly with k, the number of nodes with k links, N(k)(t), decays faster than a power law in k, while… (More)

- P L Krapivsky, S Redner, F Leyvraz
- Physical review letters
- 2000

A solution for the time- and age-dependent connectivity distribution of a growing random network is presented. The network is built by adding sites that link to earlier sites with a probability A(k) which depends on the number of preexisting links k to that site. For homogeneous connection kernels, A(k) approximately k(gamma), different behaviors arise for… (More)

- P L Krapivsky, S Redner
- Physical review letters
- 2003

We introduce a two-state opinion dynamics model where agents evolve by majority rule. In each update, a group of agents is specified whose members then all adopt the local majority state. In the mean-field limit, where a group consists of randomly selected agents, consensus is reached in a time that scales ln(N, where N is the number of agents. On… (More)

- P L Krapivsky, G J Rodgers, S Redner
- Physical review letters
- 2001

The in-degree and out-degree distributions of a growing network model are determined. The in-degree is the number of incoming links to a given node (and vice versa for out-degree). The network is built by (i) creation of new nodes which each immediately attach to a preexisting node, and (ii) creation of new links between preexisting nodes. This process… (More)

We study an opinion dynamics model in which agents reach compromise via pairwise interactions. When the opinions of two agents are sufficiently close, they both acquire the average of their initial opinions; otherwise, they do not interact. Generically, the system reaches a steady state with a finite number of isolated, noninteracting opinion clusters… (More)

- T Antal, P L Krapivsky, S Redner
- Physical review. E, Statistical, nonlinear, and…
- 2005

We study the evolution of social networks that contain both friendly and unfriendly pairwise links between individual nodes. The network is endowed with dynamics in which the sense of a link in an imbalanced triad--a triangular loop with one or three unfriendly links--is reversed to make the triad balanced. With this dynamics, an infinite network undergoes… (More)

- Paul L. Krapivsky, Sidney Redner
- Computer Networks
- 2002

Approaches from statistical physics are applied to investigate the structure of network models whose growth rules mimic aspects of the evolution of the World Wide Web. We first determine the degree distribution of a growing network in which nodes are introduced one at a time and attach to an earlier node of degree k with rate Ak k. Very different behaviors… (More)

- Tibor Antal, P L Krapivsky
- Physical review. E, Statistical, nonlinear, and…
- 2007

Synthetic biomolecular spiders with "legs" made of single-stranded segments of DNA can move on a surface which is also covered by single-stranded segments of DNA complementary to the leg DNA. In experimental realizations, when a leg detaches from a segment of the surface for the first time it alters that segment, and legs subsequently bind to these altered… (More)

- P L Krapivsky, S Redner
- Physical review. E, Statistical, nonlinear, and…
- 2005

We introduce a growing network model in which a new node attaches to a randomly selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultrasmall network where the average node degree grows logarithmically with network size while the network diameter equals 2. We determine basic geometrical network properties, such… (More)

- J Kim, P L Krapivsky, B Kahng, S Redner
- Physical review. E, Statistical, nonlinear, and…
- 2002

We investigate a model protein interaction network whose links represent interactions between individual proteins. This network evolves by the functional duplication of proteins, supplemented by random link addition to account for mutations. When link addition is dominant, an infinite-order percolation transition arises as a function of the addition rate.… (More)