Write a c++program with the following requirements: 1. Use a 5x5 boolean two-dimensional array to represent the connectivity of the graphs that need to be traversed. 2. Use depth first algorithm to traverse the graph. 3. Use breadth first algorithm to traverse the graph. 4. The starting position of the traversal is chosen reasonably based on the connectivity of the graph.

Sure, here's a C++ program that meets your requirements:

#include <iostream>
#include <queue>

using namespace std;

const int N = 5;

// Define the 5x5 boolean two-dimensional array to represent the connectivity of the graphs
bool graph[N][N] = {
    {false, true, false, true, false},
    {true, false, true, false, true},
    {false, true, false, true, false},
    {true, false, true, false, true},
    {false, true, false, true, false}
};

// Define the depth first traversal function
void depth_first_traversal(bool graph[][N], int start, bool visited[]) {
    visited[start] = true;
    cout << start << " ";
    for(int i = 0; i < N; i++) {
        if(graph[start][i] && !visited[i]) {
            depth_first_traversal(graph, i, visited);
        }
    }
}

// Define the breadth first traversal function
void breadth_first_traversal(bool graph[][N], int start, bool visited[]) {
    queue<int> q;
    visited[start] = true;
    q.push(start);
    while(!q.empty()) {
        int vertex = q.front();
        q.pop();
        cout << vertex << " ";
        for(int i = 0; i < N; i++) {
            if(graph[vertex][i] && !visited[i]) {
                visited[i] = true;
                q.push(i);
            }
        }
    }
}

// Choose a reasonable starting position for the traversal based on the connectivity of the graph
int choose_start(bool graph[][N]) {
    int start = 0;
    for(int i = 0; i < N; i++) {
        int count = 0;
        for(int j = 0; j < N; j++) {
            if(graph[i][j]) {
                count++;
            }
        }
        if(count > 0 && count > (int)(count > graph[start])) {
            start = i;
        }
    }
    return start;
}

int main() {
    bool visited[N] = {false};

    // Choose a reasonable starting position for the traversal
    int start = choose_start(graph);

    // Perform depth first traversal
    cout << "Depth First Traversal: ";
    depth_first_traversal(graph, start, visited);
    cout << endl;

    // Reset visited array
    for(int i = 0; i < N; i++) {
        visited[i] = false;
    }

    // Perform breadth first traversal
    cout << "Breadth First Traversal: ";
    breadth_first_traversal(graph, start, visited);
    cout << endl;

    return 0;
}

In this program, we first define the 5x5 boolean two-dimensional array `graph` to represent the connectivity of the graphs that need to be traversed. Then, we define the `depth_first_traversal` function and the `breadth_first_traversal` function to perform depth first and breadth first traversal of the graph respectively.

Next, we define the `choose_start` function to choose a reasonable starting position for the traversal based on the connectivity of the graph. We iterate over each vertex in the graph and count the number of its neighbors. We choose the vertex with the highest number of neighbors as the starting position.

Finally, we call the `depth_first_traversal` function and the `breadth_first_traversal` function with the `graph`, `start` and `visited` arguments to perform the traversals. The output of the program will be the sequence of vertices visited during the traversals.