directed-graph | : busstop : An implementation of a directed graph | Animation library

What you want is a data structure for a problem called 'incremental reachability'. There are multiple ways to construct such a data structure, all have some different update/query time tradeoffs. A very simple way to achieve the goal is to use an adjacency list and use BFS every time a user queries if node "x" is reachable from 1. This gets you update time: O(1) and query time: O(m).

A more complicated idea is 'even-shiloach' trees [1], here a BFS tree is maintained efficiently. Total update time: O(nm) Query time: O(1).

An experimental analysis of similar algorithms can be found in [2].

[1] Shimon Even, Yossi Shiloach: An On-Line Edge-Deletion Problem. J. ACM 28(1): 1-4 (1981) https://dl.acm.org/doi/10.1145/322234.322235

[2] Fully Dynamic Single-Source Reachability in Practice: An Experimental Study, Kathrin Hanauer, Monika Henzinger and Christian Schulz https://arxiv.org/abs/1905.01216

Now I checked again and I noticed that I put the function to wrong place. I will answer it below.

In your function random(), you don't change the underlying data, you only change how it is represented. Each circle holds a reference to an element in the nodes array, but you set cx and cy within random(), you don't update the underlying data d.x and d.y. And even then, the values the circle has for cx and cy are not reactive. That is, they are not re-evaluated when d.x or d.y changes.

So I would split your code. Have a function random() that is called every 800ms and shuffles the nodes around a bit by changing d.x and d.y. And then the simulation is in charge of actually drawing the circles and the links - the way it already seems to be doing.

A cycle is detected if a visiting node (gray) encounters an edge with another visiting node. The issue I had with initial code was there was no way to set a node VISITED (black) in a backtracking way. The new code now has ENTER = 0 and EXIT = 1. Enter = 0 means its the first time I visited that node and I set it to gray (visiting) the second time I visit the node exit will be 1 so i can then set it to black (fully visited).

Here's a complete example.

Iterators are generalizations of pointers. Pointers are iterators, but more complicated things like whatever std::vector::begin and std::vector::return return and whatever std::back_inserter constructs are also iterators. The key thing about them that you appear to be missing is that if it is an iterator, then the value associated with it is accessed as *it, not it. Because you cannot dereference an int, that is not a valid iterator.

You need to do exactly what the documentation says: provide iterators that define a range that contains 5. Because pointers are iterators, you could do

You can draw edge labels with draw_networkx_edge_labels().

Change $ sign into @ like in docs.

• self edges : you just have to scan each node of your graph and check if there is a self edge. If there is : add X -> X to the list of cycles

• multi graph : the first algorithm will produce paths as a sequence of vertices X1 -> X2 -> X3 -> .... When you have this list, iterate over all the possible edges going from X1 to X2, then all the possible edges going from X2 to X3, etc ...

• "clever" hack : from your multigraph G, create a new graph G2, where the edges of G also appear as vertices :