Question: The incidence matrix of a directed graph G = (V, E) is a |V| Ã |E| matrix B = (bij) such that Describe what the

The incidence matrix of a directed graph G = (V, E) is a |V| Ã— |E| matrix B = (bij) such that

Describe what the entries of the matrix product B BT represent, where BT is the transpose of B.

-1 if edge j leaves vertex i. if edge j enters vertex i. h. otherwise.

-1 if edge j leaves vertex i. if edge j enters vertex i. h. otherwise.

Step by Step Solution

★★★★★

3.42 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

BBT i j biebj bieb je e E e E If i j then biebje 1 it i... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

C-S-A (124).docx

120 KBs Word File

Students Have Also Explored These Related Algorithms Questions!

The adjacency list representation of a directed graph G is given by the lists in Table 7.6. Construct G from this representation. st 14558000 1 2 3 4 5 6 7 8 1236334536 7-a le d 1 2 3 4 5 6 7 8 9

A path cover of a directed graph G = (V, E) is a set P of vertex-disjoint paths such that every vertex in V is included in exactly one path in P. Paths may start and end anywhere, and they may be of...

The graph in Prob. 8, incidence Matrix of a Digraph; Matrix B = [bkj] with entries find the incidence matrixof; bjk 1 0 if edge e leaves vertex j if edge e enters vertex j otherwise.

Given a directed graph G = (V, E) represented as by an incidence matrix, derive the incidence matrix of the transitive closure G* of G. In G* there is an edge from vi to v; if and only if in G there...

In this question you will be asked to reflect on a project you have been involved in or observed, in which a design evolved, or could have evolved, through applying a theory of user behaviour. You...

Let i and j be positive integers. (i) Prove that there exist natural numbers a and b such that ai = bj+gcd(i, j). You may use standard results provided that you state them clearly. [4 marks] (ii) Let...

Consider the trigonometric series a0 2 + X r=1 (ar cos rx + br sin rx) where a0, a1, a2, . . . and b1, b2, . . . are constants and suppose that f(x) is a periodic function of x with period 2. (a)...

Question 2. (1 marks) We say that a node u of a directed graph G (V, E) is a supersource, if there is an edge from u to every other node in G and there is no edge from any node into u, i.e., for all...

(iii) Now express your decision rule instead using only the quantities p(Ck), p(Cj ), p(x|Ck), p(x|Cj ), and relate it to the diagram above. [2 marks] (iv) If the classifier decision rule assigns...

Question 2. (1 marks) We say that a node u of a directed graph G- (V, E) is a supersource, if there is an edge from u to every m anV Suppose the directed graph G (V E) is given by its adjacency...

a. If viruses that normally form envelopes were prevented from budding, would they still be infectious? Why or why not? b. If only the RNA of an influenza virus were injected into a cell by itself,...

What tax credits are allowed for AMT purposes?

Dennis decided to stay with original Medicare during his initial enrollment period which ended on July 3 . If Dennis now wished to switch to a Medicare Advantage plan, when is the earliest date that...

If the (square) beam in Figure is of Douglas fir, what must be its thickness to keep the compressive stress on it to of its ultimate strength?

Knocking Over a Post One end of a post weighing 400 N and with height h rests on a rough horizontal surface with p" = 0.30. The upper end is held by a rope fastened to the surface and making an angle...

A well-sealed room contains 60 kg of air at 200 kPa and 25C. Now solar energy enters the room at an average rate of 0.8 kJ/s while a 120-W fan is turned on to circulate the air in the room. If heat...

An ideal regenerator is incorporated into the ideal air-standard Brayton cycle of Problem 11.132. Calculate the cycle thermal efficiency with this modification.

Batch processes are often used in chemical and pharmaceutical operations to achieve a desired chemical composition for the final product. Related heat transfer processes are typically transient,...

What are the potential consequences of inaccurately forecasting the demand for a particular product?

8.33 points Consider the following information: State of Economy Probability of State of Economy Rate of Return If State Occurs Stock A Stock B Recession .15 .06 ?.20 Normal .65 .07 .13 Boom .20 .11...

Your investment portfolio consists of $15,000 invested in only one stocklong dashMicrosoft. Suppose the risk-free rate is 4%, Microsoft stock has an expected return of 14% and a volatility of 37%,...

In a perfect market, what kind of response would you expect when your company announces that it has struck gold and plans to pay a special dividend next month? What reaction do you expect over this...