Defense

class graph_tiger.defenses.Defense(graph, runs=10, steps=50, attack='id_node', defense=None, k_d=0, **kwargs)

Bases: graph_tiger.simulations.Simulation

This class simulates a variety of defense techniques on an undirected NetworkX graph

Parameters

• graph – an undirected NetworkX graph

• runs – an integer number of times to run the simulation

• steps – an integer number of steps to run a single simulation

• attack – a string representing the attack strategy to run

• defense – a string representing the defense strategy to run

• k_d – an integer number of nodes to defend

• **kwargs –

  see parent class Simulation for additional options

reset_simulation()

Resets the simulation between each run

run_single_sim()

Run the defense simulation

track_simulation(step)

Keeps track of important simulation information at each step of the simulation

Parameters

step – current simulation iteration

graph_tiger.defenses.add_edge_degree(graph, k=3)

Add k edges to defend based on top edge degree centrality entries [16].

Parameters

• graph – an undirected NetworkX graph

• k – number of edges to add

Returns

a list of edges to add

graph_tiger.defenses.add_edge_eig(graph, k=3)

Get k edges to defend based on top edge eigenvector centrality entries [16].

Parameters

• graph – an undirected NetworkX graph

• k – number of edges to add

Returns

a dictionary of the edges to be ‘added’

graph_tiger.defenses.add_edge_pr(graph, k=3)

Get k edges to defend based on top edge PageRank entries [16].

Parameters

• graph – an undirected NetworkX graph

• k – number of edges to add

Returns

a dictionary of the edges to be ‘added’

graph_tiger.defenses.add_edge_pref(graph, k=3)

Adds an edge connecting two nodes with the lowest degrees [2].

Parameters

• graph – an undirected NetworkX graph

• k – number of edges to add

Returns

a dictionary of the edges to be ‘added’

graph_tiger.defenses.add_edge_rnd(graph, k=3)

Add k random edges to the graph

Parameters

• graph – an undirected NetworkX graph

• k – number of edges to add

Returns

a dictionary of the edges to be ‘added’

graph_tiger.defenses.get_central_edges(graph, k, method='eig')

Internal function to compute edge PageRank, eigenvector centrality and degree centrality

Parameters

• graph – undirected NetworkX graph

• k – int number of nodes to defend

• method – string representing defense method

Returns

list of edges to add

graph_tiger.defenses.get_defense_category(method)

Gets the defense category e.g., ‘node’, ‘edge’ defense.

Parameters

method – a string representing the defense method

Returns

a string representing the defense type (‘node’ or ‘edge’)

graph_tiger.defenses.get_defense_methods()

Gets a list of available defense methods as a list of functions.

Returns

a list of all defense functions

graph_tiger.defenses.get_node_eig(graph, k=3)

Get k nodes to defend based on top eigenvector centrality entries

Parameters

• graph – an undirected NetworkX graph

• k – number of nodes to defend

Returns

a list of nodes to defend

graph_tiger.defenses.get_node_ib(graph, k=3, approx=inf)

Get k nodes to defend based on Initial Betweenness (IB) Removal [13].

Parameters

• graph – an undirected NetworkX graph

• k – number of nodes to defend

• approx – number of nodes to approximate the betweenness centrality, k=0.1n is a good approximation, where n

is the number of nodes in the graph

Returns

a list of nodes to defend

graph_tiger.defenses.get_node_id(graph, k=3)

Get k nodes to defend based on Initial Degree (ID) Removal [13].

Parameters

• graph – an undirected NetworkX graph

• k – number of nodes to defend

Returns

a list of nodes to defend

graph_tiger.defenses.get_node_ns(graph, k=3)

Get k nodes to defend based on the Netshield algorithm [17].

Parameters

• graph – an undirected NetworkX graph

• k – number of nodes to defend

Returns

a list of nodes to defend

graph_tiger.defenses.get_node_pr(graph, k=3)

Get k nodes to defend based on top PageRank entries [15].

Parameters

• graph – an undirected NetworkX graph

• k – number of nodes to defend

Returns

a list of nodes to defend

graph_tiger.defenses.get_node_rb(graph, k=3, approx=inf)

Get k nodes to defend based on Recalculated Betweenness (RB) Removal [13]

Parameters

• graph – an undirected NetworkX graph

• k – number of nodes to defend

• approx – number of nodes to approximate the betweenness centrality, k=0.1n is a good approximation, where n

is the number of nodes in the graph

Returns

a list of nodes to defend

graph_tiger.defenses.get_node_rd(graph, k=3)

Get k nodes to defend based on Recalculated Degree (RD) Removal [13].

Parameters

• graph – an undirected NetworkX graph

• k – number of nodes to defend

Returns

a list of nodes to defend

graph_tiger.defenses.get_node_rnd(graph, k=3)

Randomly select k distinct nodes to defend

Parameters

• graph – an undirected NetworkX graph

• k – number of nodes to defend

Returns

a list of nodes to defend

graph_tiger.defenses.main()

graph_tiger.defenses.rewire_edge_pref(graph, k=3)

Selects node with highest degree, randomly removes a neighbor; adds edge to random node in graph [2].

Parameters

• graph – an undirected NetworkX graph

• k – number of edges to rewire

Returns

a dictionary of the edges to be ‘removed’ and edges to be ‘added’

graph_tiger.defenses.rewire_edge_pref_rnd(graph, k=3)

Selects an edge, disconnects the higher degree node, and reconnects to a random one [2].

Parameters

• graph – an undirected NetworkX graph

• k – number of edges to rewire

Returns

a dictionary of the edges to be ‘removed’ and edges to be ‘added’

graph_tiger.defenses.rewire_edge_rnd(graph, k=3)

Removes a random edge and adds one randomly [2].

Parameters

• graph – an undirected NetworkX graph

• k – number of edges to rewire

Returns

a dictionary of the edges to be ‘removed’ and edges to be ‘added’

graph_tiger.defenses.rewire_edge_rnd_neighbor(graph, k=3)

Randomly selects a neighbor of a node and removes the edge; then adds a random edge [2].

Parameters

• graph – an undirected NetworkX graph

• k – number of edges to rewire

Returns

a dictionary of the edges to be ‘removed’ and edges to be ‘added’

graph_tiger.defenses.run_defense_method(graph, method, k=3, seed=None)

Runs a specified defense on an undirected graph, returning a list of nodes to defend.

Parameters

• graph – an undirected NetworkX graph

• method – a string representing one of the attack methods

• k – number of nodes or edges to attack

• seed – sets the seed in order to obtain reproducible defense runs

Returns

a list of nodes or edge tuples to defend