By Sapagovas M.P.
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Extra resources for A Boundary Value Problem with a Nonlocal Condition for a System of Ordinary Differential Equations
Let us suppose that the result is navigate. Therefore we randomly choose (uniform, since in this case the random walker is not biased) one of the neighbours of x0 = 9. We take, for example, x1 = 5 and we move there. 3. At the beginning of the turn t = 2, we must choose between navigating through the edges or to be teleported. We flip a coin that with a probability of 2/3 tell us navigate and with a probability of 1/3 tell us be teleported. In this case the result is be teleported. Hence we randomly choose (uniform in this case, since we take (1/14, · · · , 1/14) ∈ R as personalization vector) any node of the 14 nodes of the network (not necessarily connected with).
25) g∈Pjk where ωg ( ) is 1 if belongs to the geodesic g and 0 otherwise. Hence if dj,k denotes the distance between j and k in the network then BE = 1 1 ∑ |E| j,k∈X njk = 1 1 ∑ |E| j,k∈X njk = 1 1 ∑ njk |E| j,k∈X ∑ njk ( ) ∈E ∑ ∑ ωg ( ) g∈Pjk ∈E ∑ g∈Pjk dj,k = n(n − 1) L(G) |E| and therefore BE (G) measures essentially the same global properties than the characteristic path length L(G). 10 Degree Distributions The degree distribution of a network G = (X, E) is a function P(k) which give us the probability of finding a node in G with degree k.
In  diverse real-world networks are studied, arising three classes of smallworld networks, namely scale-free, broad scale and single scale networks. , P(k) = ak−γ where a is a constant and γ is a positive exponent (this exponent, empirically varies between two and three for the majority of the real world networks). Having a P(k) that has a decaying tail in the power law means that the vast majority of nodes have low degree and that there exist few nodes, the so-called hubs, that have an extremely high connectivity.
A Boundary Value Problem with a Nonlocal Condition for a System of Ordinary Differential Equations by Sapagovas M.P.
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