Consider the following model to grow simple networks. At time t = 1 we start with a complete network with no = 6 nodes. At each time step t> 1 a new node is added to the network. The node arrives together with m = 2 new links, which are connected to m = 2 different nodes already present in the network. The probability II, that a new link is connected to node i is: N(t-1) II₁ = ki - 1 Z == with Z = (k; -1) j=1 where k; is the degree of node i, and N(t - 1) is the number of nodes in the network at timet - 1. (e) Write down the master equation of the model, i.e. the equation that describes the evolution of the average number N(t) of nodes that at time t have degree k.

Consider the following model to grow simple networks. At time t = 1 we start with a complete network with no = 6 nodes. At each time step t> 1 a new node is added to the network. The node arrives together with m = 2 new links, which are connected to m = 2 different nodes already present in the network. The probability II, that a new link is connected to node i is: N(t-1) II₁ = ki - 1 Z == with Z = (k; -1) j=1 where k; is the degree of node i, and N(t - 1) is the number of nodes in the network at timet - 1. (e) Write down the master equation of the model, i.e. the equation that describes the evolution of the average number N(t) of nodes that at time t have degree k.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...

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