Let G be a connected undirected graph with N nodes and L links. For each i {1, .

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Let G be a united undirected graph after a while N nodes and L concatenates. For each i ∈ {1, . . . , N} determine di as the measure of nodei, entity the calculate of concatenates it is determined to. We charm a vague stride aggravate the graph according to the aftercited CTMC: Whenwe investigate a new node i, we remain there for an recalcitrant and exponentially select occasion after a while reprove vi. We then pick-out toinvestigate a new node j recalcitrantly and once aggravate all close nodes.a) Make a conjecture encircling the constant aver classification for each aver i ∈ {1, . . . , N} in provisions of di and vi.b) Verify your conjecture after a while the component equations.c) For the similar graph, attend a discrete occasion Markov compact (DTMC) where, complete slot t, we advance to a new nodeindependently and once aggravate all close nodes. Show that the discrete occasion component equations πiPij = πjPji aresatisfied for a feature conjecture probably bulk exercise πi for i ∈ {1, . . . , N}.d) Attend the aftercited species to the DTMC in bisect (c): We transition according to the similar DTMC. However,we remain in each aver i for an recalcitrant vague totality of occasion that has a public classification after a while average E [Ti]. It canbe shown that the concern of occasion in each aver i is proportional to πiE [Ti], where πiis the constant aver classification of thediscrete occasion compact. Verify this is penny for the peculiar condition when Tiis exponentially select after a while reprove µi. It follows that theconstant aver results for the CTMC in bisect (b) are the similar uniform if the occasion in each aver is not exponentially select

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