From fba4c289aff6706f808142709b70854dc45b7518 Mon Sep 17 00:00:00 2001 From: safreita1 Date: Wed, 17 Feb 2021 22:58:51 -0800 Subject: [PATCH] Updated documentation + added citations --- attacks.py | 30 +++++++++--------- defenses.py | 35 ++++++++++----------- docs/build/doctrees/attacks.doctree | Bin 93016 -> 97679 bytes docs/build/doctrees/defenses.doctree | Bin 95619 -> 100381 bytes docs/build/doctrees/environment.pickle | Bin 126363 -> 130709 bytes docs/build/doctrees/measures.doctree | Bin 88368 -> 78078 bytes docs/build/html/attacks.html | 42 ++++++++++++++----------- docs/build/html/bibliography.html | 36 ++++++++++++++------- docs/build/html/defenses.html | 37 +++++++++++----------- docs/build/html/measures.html | 36 ++++++++++----------- docs/build/html/searchindex.js | 2 +- 11 files changed, 118 insertions(+), 100 deletions(-) diff --git a/attacks.py b/attacks.py index 626099c..b8989bb 100644 --- a/attacks.py +++ b/attacks.py @@ -131,7 +131,7 @@ def get_node_eig(graph, k=3): def get_node_id(graph, k=3): """ - Get k nodes to attack based on Initial Degree Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf + Get k nodes to attack based on Initial Degree (ID) Removal :cite:`beygelzimer2005improving`. :param graph: an undirected NetworkX graph :param k: number of nodes to attack @@ -147,7 +147,7 @@ def get_node_id(graph, k=3): def get_node_rd(graph, k=3): """ - Get k nodes to attack based on Recalculated Degree Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf + Get k nodes to attack based on Recalculated Degree (RD) Removal :cite:`beygelzimer2005improving`. :param graph: an undirected NetworkX graph :param k: number of nodes to attack @@ -168,11 +168,12 @@ def get_node_rd(graph, k=3): def get_node_ib(graph, k=3, approx=np.inf): """ - Get k nodes to attack based on Initial Betweenness Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf + Get k nodes to attack based on Initial Betweenness (IB) Removal :cite:`beygelzimer2005improving`. :param graph: an undirected NetworkX graph :param k: number of nodes to attack - :param approx: number of nodes to approximate the betweenness centrality, k=0.1n is a good approximation + :param 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 :return: a list of nodes to attack """ @@ -185,11 +186,12 @@ def get_node_ib(graph, k=3, approx=np.inf): def get_node_rb(graph, k=3, approx=np.inf): """ - Get k nodes to attack based on Recalculated Betweenness Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf + Get k nodes to attack based on Recalculated Betweenness (RB) Removal :cite:`beygelzimer2005improving`. :param graph: an undirected NetworkX graph :param k: number of nodes to attack - :param approx: number of nodes to approximate the betweenness centrality, k=0.1n is a good approximation + :param 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 :return: a list of nodes to attack """ @@ -219,7 +221,7 @@ def get_node_rnd(graph, k=3): def get_edge_line_ns(graph, k=3): """ - Get k edges to attack using Netshield by transforming the graph into a line graph + Get k edges to attack using Netshield by transforming the graph into a line graph :cite:`tong2010vulnerability,tong2012gelling` :param graph: an undirected NetworkX graph :param k: number of edges to attack @@ -237,7 +239,7 @@ def get_edge_line_ns(graph, k=3): def get_edge_line_pr(graph, k=3): """ - Get k edges to attack using PageRank by transforming the graph into a line graph + Get k edges to attack using PageRank by transforming the graph into a line graph :cite:`tong2012gelling`. :param graph: an undirected NetworkX graph :param k: number of edges to attack @@ -251,7 +253,7 @@ def get_edge_line_pr(graph, k=3): def get_edge_line_eig(graph, k=3): """ - Get k edges to attack using eigenvector centrality by transforming the graph into a line graph + Get k edges to attack using eigenvector centrality by transforming the graph into a line graph :cite:`tong2012gelling`. :param graph: an undirected NetworkX graph :param k: number of edges to attack @@ -265,7 +267,7 @@ def get_edge_line_eig(graph, k=3): def get_edge_line_deg(graph, k=3): """ - Get k edges to attack using degree centrality by transforming the graph into a line graph + Get k edges to attack using degree centrality by transforming the graph into a line graph :cite:`tong2012gelling`. :param graph: an undirected NetworkX graph :param k: number of edges to attack @@ -279,7 +281,7 @@ def get_edge_line_deg(graph, k=3): def get_edge_id(graph, k=3): """ - Get k edges to attack based on Initial Degree Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf + Get k edges to attack based on Initial Degree (ID) Removal :cite:`holme2002attack`. :param graph: an undirected NetworkX graph :param k: number of edges to attack @@ -295,7 +297,7 @@ def get_edge_id(graph, k=3): def get_edge_rd(graph, k=3): """ - Get k edges to attack based on Recalculated Degree Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf + Get k edges to attack based on Recalculated Degree (RD) Removal :cite:`holme2002attack`. :param graph: an undirected NetworkX graph :param k: number of edges to attack @@ -316,7 +318,7 @@ def get_edge_rd(graph, k=3): def get_edge_ib(graph, k=3, approx=np.inf): """ - Get k edges to attack based on Initial Betweenness Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf + Get k edges to attack based on Initial Betweenness (IB) Removal :cite:`holme2002attack`. :param graph: an undirected NetworkX graph :param k: number of edges to attack @@ -333,7 +335,7 @@ def get_edge_ib(graph, k=3, approx=np.inf): def get_edge_rb(graph, k=3, approx=np.inf): """ - Get k edges to attack based on Recalculated Betweenness Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf + Get k edges to attack based on Recalculated Betweenness (RB) Removal :cite:`holme2002attack`. :param graph: an undirected NetworkX graph :param k: number of edges to attack diff --git a/defenses.py b/defenses.py index 9c3f6c0..dafa82d 100644 --- a/defenses.py +++ b/defenses.py @@ -21,7 +21,7 @@ def run_defense_method(graph, method, k=3, seed=None): """ - Runs a specified defense on an undirected graph, returning a list of nodes to defend + Runs a specified defense on an undirected graph, returning a list of nodes to defend. :param graph: an undirected NetworkX graph :param method: a string representing one of the attack methods @@ -42,7 +42,7 @@ def run_defense_method(graph, method, k=3, seed=None): def get_defense_methods(): """ - Gets a list of available defense methods as a list of functions + Gets a list of available defense methods as a list of functions. :return: a list of all defense functions """ @@ -52,7 +52,7 @@ def get_defense_methods(): def get_defense_category(method): """ - Gets the defense category e.g., 'node', 'edge' defense + Gets the defense category e.g., 'node', 'edge' defense. :param method: a string representing the defense method :return: a string representing the defense type ('node' or 'edge') @@ -68,7 +68,7 @@ def get_defense_category(method): def get_node_ns(graph, k=3): """ - Get k nodes to defend based on the Netshield algorithm: http://tonghanghang.org/pdfs/icdm10_netshield.pdf + Get k nodes to defend based on the Netshield algorithm :cite:`tong2010vulnerability,chen2015node`. :param graph: an undirected NetworkX graph :param k: number of nodes to defend @@ -81,7 +81,7 @@ def get_node_ns(graph, k=3): def get_node_pr(graph, k=3): """ - Get k nodes to defend based on top PageRank entries + Get k nodes to defend based on top PageRank entries :cite:`page1999pagerank`. :param graph: an undirected NetworkX graph :param k: number of nodes to defend @@ -106,7 +106,7 @@ def get_node_eig(graph, k=3): def get_node_ib(graph, k=3, approx=np.inf): """ - Get k nodes to defend based on Initial Betweenness Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf + Get k nodes to defend based on Initial Betweenness (IB) Removal :cite:`holme2002attack`. :param graph: an undirected NetworkX graph :param k: number of nodes to defend @@ -121,7 +121,7 @@ def get_node_ib(graph, k=3, approx=np.inf): def get_node_rb(graph, k=3, approx=np.inf): """ - Get k nodes to defend based on Recalculated Betweenness Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf + Get k nodes to defend based on Recalculated Betweenness (RB) Removal :cite:`holme2002attack` :param graph: an undirected NetworkX graph :param k: number of nodes to defend @@ -136,7 +136,7 @@ def get_node_rb(graph, k=3, approx=np.inf): def get_node_id(graph, k=3): """ - Get k nodes to defend based on Initial Degree Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf + Get k nodes to defend based on Initial Degree (ID) Removal :cite:`holme2002attack`. :param graph: an undirected NetworkX graph :param k: number of nodes to defend @@ -149,7 +149,7 @@ def get_node_id(graph, k=3): def get_node_rd(graph, k=3): """ - Get k nodes to defend based on Recalculated Degree Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf + Get k nodes to defend based on Recalculated Degree (RD) Removal :cite:`holme2002attack`. :param graph: an undirected NetworkX graph :param k: number of nodes to defend @@ -175,7 +175,6 @@ def get_node_rnd(graph, k=3): def get_central_edges(graph, k, method='eig'): """ Internal function to compute edge PageRank, eigenvector centrality and degree centrality - Based on: http://www.cs.cmu.edu/~htong/pdfs/cikm12_tong.pdf :param graph: undirected NetworkX graph :param k: int number of nodes to defend @@ -210,7 +209,7 @@ def get_central_edges(graph, k, method='eig'): def add_edge_pr(graph, k=3): """ - Get k edges to defend based on top edge PageRank entries + Get k edges to defend based on top edge PageRank entries :cite:`tong2012gelling`. :param graph: an undirected NetworkX graph :param k: number of edges to add @@ -225,7 +224,7 @@ def add_edge_pr(graph, k=3): def add_edge_eig(graph, k=3): """ - Get k edges to defend based on top edge eigenvector centrality entries + Get k edges to defend based on top edge eigenvector centrality entries :cite:`tong2012gelling`. :param graph: an undirected NetworkX graph :param k: number of edges to add @@ -240,7 +239,7 @@ def add_edge_eig(graph, k=3): def add_edge_degree(graph, k=3): """ - Add k edges to defend based on top edge degree centrality entries + Add k edges to defend based on top edge degree centrality entries :cite:`tong2012gelling`. :param graph: an undirected NetworkX graph :param k: number of edges to add @@ -280,7 +279,7 @@ def add_edge_rnd(graph, k=3): def add_edge_pref(graph, k=3): """ - Adds an edge connecting two nodes with the lowest degrees. + Adds an edge connecting two nodes with the lowest degrees :cite:`beygelzimer2005improving`. :param graph: an undirected NetworkX graph :param k: number of edges to add @@ -311,7 +310,7 @@ def add_edge_pref(graph, k=3): def rewire_edge_rnd(graph, k=3): """ - Removes a random edge and adds one using 'add_edge_rnd()' + Removes a random edge and adds one randomly :cite:`beygelzimer2005improving`. :param graph: an undirected NetworkX graph :param k: number of edges to rewire @@ -333,7 +332,7 @@ def rewire_edge_rnd(graph, k=3): def rewire_edge_rnd_neighbor(graph, k=3): """ - Removes a random edge and adds one using 'add_edge_rnd()' + Randomly selects a neighbor of a node and removes the edge; then adds a random edge :cite:`beygelzimer2005improving`. :param graph: an undirected NetworkX graph :param k: number of edges to rewire @@ -362,7 +361,7 @@ def rewire_edge_rnd_neighbor(graph, k=3): def rewire_edge_pref(graph, k=3): """ - Selects node with highest degree, randomly removes a neighbor; adds edge to random node in graph + Selects node with highest degree, randomly removes a neighbor; adds edge to random node in graph :cite:`beygelzimer2005improving`. :param graph: an undirected NetworkX graph 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attacks.get_edge_ib(graph, k=3, approx=inf)
-

Get k edges to attack based on Initial Betweenness Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf

+

Get k edges to attack based on Initial Betweenness (IB) Removal [13].

Parameters
    @@ -284,7 +284,7 @@
    attacks.get_edge_id(graph, k=3)
    -

    Get k edges to attack based on Initial Degree Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf

    +

    Get k edges to attack based on Initial Degree (ID) Removal [13].

    Parameters
      @@ -301,7 +301,7 @@
      attacks.get_edge_line_deg(graph, k=3)
      -

      Get k edges to attack using degree centrality by transforming the graph into a line graph

      +

      Get k edges to attack using degree centrality by transforming the graph into a line graph [16].

      Parameters
        @@ -318,7 +318,7 @@
        attacks.get_edge_line_eig(graph, k=3)
        -

        Get k edges to attack using eigenvector centrality by transforming the graph into a line graph

        +

        Get k edges to attack using eigenvector centrality by transforming the graph into a line graph [16].

        Parameters
          @@ -335,7 +335,7 @@
          attacks.get_edge_line_ns(graph, k=3)
          -

          Get k edges to attack using Netshield by transforming the graph into a line graph

          +

          Get k edges to attack using Netshield by transforming the graph into a line graph [17,16]

          Parameters
            @@ -352,7 +352,7 @@
            attacks.get_edge_line_pr(graph, k=3)
            -

            Get k edges to attack using PageRank by transforming the graph into a line graph

            +

            Get k edges to attack using PageRank by transforming the graph into a line graph [16].

            Parameters
              @@ -369,7 +369,7 @@
              attacks.get_edge_rb(graph, k=3, approx=inf)
              -

              Get k edges to attack based on Recalculated Betweenness Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf

              +

              Get k edges to attack based on Recalculated Betweenness (RB) Removal [13].

              Parameters
                @@ -387,7 +387,7 @@
                attacks.get_edge_rd(graph, k=3)
                -

                Get k edges to attack based on Recalculated Degree Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf

                +

                Get k edges to attack based on Recalculated Degree (RD) Removal [13].

                Parameters
                  @@ -438,17 +438,20 @@
                  attacks.get_node_ib(graph, k=3, approx=inf)
                  -

                  Get k nodes to attack based on Initial Betweenness Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf

                  +

                  Get k nodes to attack based on Initial Betweenness (IB) Removal [2].

                  Parameters

                  • graph – an undirected NetworkX graph

                  • k – number of nodes to attack

                    • -

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

                    • +

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

                  -
                  Returns
                  -

                  a list of nodes to attack

                  +
                  +

                  is the number of nodes in the graph

                  +
                  +
                  Returns
                  +

                  a list of nodes to attack

                  @@ -456,7 +459,7 @@
                  attacks.get_node_id(graph, k=3)
                  -

                  Get k nodes to attack based on Initial Degree Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf

                  +

                  Get k nodes to attack based on Initial Degree (ID) Removal [2].

                  Parameters
                    @@ -507,17 +510,20 @@
                    attacks.get_node_rb(graph, k=3, approx=inf)
                    -

                    Get k nodes to attack based on Recalculated Betweenness Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf

                    +

                    Get k nodes to attack based on Recalculated Betweenness (RB) Removal [2].

                    Parameters

                    • graph – an undirected NetworkX graph

                    • k – number of nodes to attack

                      • -

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

                      • +

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

                    -
                    Returns
                    -

                    a list of nodes to attack

                    +
                    +

                    is the number of nodes in the graph

                    +
                    +
                    Returns
                    +

                    a list of nodes to attack

                    @@ -525,7 +531,7 @@
                    attacks.get_node_rd(graph, k=3)
                    -

                    Get k nodes to attack based on Recalculated Degree Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf

                    +

                    Get k nodes to attack based on Recalculated Degree (RD) Removal [2].

                    Parameters
                    diff --git a/docs/build/html/defenses.html b/docs/build/html/defenses.html index f751948..68cd823 100644 --- a/docs/build/html/defenses.html +++ b/docs/build/html/defenses.html @@ -241,7 +241,7 @@
                    defenses.add_edge_degree(graph, k=3)
                    -

                    Add k edges to defend based on top edge degree centrality entries

                    +

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

                    Parameters
                      @@ -258,7 +258,7 @@
                      defenses.add_edge_eig(graph, k=3)
                      -

                      Get k edges to defend based on top edge eigenvector centrality entries

                      +

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

                      Parameters
                        @@ -275,7 +275,7 @@
                        defenses.add_edge_pr(graph, k=3)
                        -

                        Get k edges to defend based on top edge PageRank entries

                        +

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

                        Parameters
                          @@ -292,7 +292,7 @@
                          defenses.add_edge_pref(graph, k=3)
                          -

                          Adds an edge connecting two nodes with the lowest degrees.

                          +

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

                          Parameters
                            @@ -326,8 +326,7 @@
                            defenses.get_central_edges(graph, k, method='eig')
                            -

                            Internal function to compute edge PageRank, eigenvector centrality and degree centrality -Based on: http://www.cs.cmu.edu/~htong/pdfs/cikm12_tong.pdf

                            +

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

                            Parameters
                              @@ -345,7 +344,7 @@
                              defenses.get_defense_category(method)
                              -

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

                              +

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

                              Parameters

                              method – a string representing the defense method

                              @@ -359,7 +358,7 @@
                              defenses.get_defense_methods()
                              -

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

                              +

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

                              Returns

                              a list of all defense functions

                              @@ -387,7 +386,7 @@
                              defenses.get_node_ib(graph, k=3, approx=inf)
                              -

                              Get k nodes to defend based on Initial Betweenness Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf

                              +

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

                              Parameters
                                @@ -408,7 +407,7 @@
                                defenses.get_node_id(graph, k=3)
                                -

                                Get k nodes to defend based on Initial Degree Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf

                                +

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

                                Parameters
                                  @@ -425,7 +424,7 @@
                                  defenses.get_node_ns(graph, k=3)
                                  -

                                  Get k nodes to defend based on the Netshield algorithm: http://tonghanghang.org/pdfs/icdm10_netshield.pdf

                                  +

                                  Get k nodes to defend based on the Netshield algorithm [17,5].

                                  Parameters
                                    @@ -442,7 +441,7 @@
                                    defenses.get_node_pr(graph, k=3)
                                    -

                                    Get k nodes to defend based on top PageRank entries

                                    +

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

                                    Parameters
                                      @@ -459,7 +458,7 @@
                                      defenses.get_node_rb(graph, k=3, approx=inf)
                                      -

                                      Get k nodes to defend based on Recalculated Betweenness Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf

                                      +

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

                                      Parameters
                                        @@ -480,7 +479,7 @@
                                        defenses.get_node_rd(graph, k=3)
                                        -

                                        Get k nodes to defend based on Recalculated Degree Removal: https://arxiv.org/pdf/cond-mat/0202410.pdf

                                        +

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

                                        Parameters
                                          @@ -519,7 +518,7 @@
                                          defenses.rewire_edge_pref(graph, k=3)
                                          -

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

                                          +

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

                                          Parameters
                                            @@ -536,7 +535,7 @@
                                            defenses.rewire_edge_pref_rnd(graph, k=3)
                                            -

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

                                            +

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

                                            Parameters
                                              @@ -553,7 +552,7 @@
                                              defenses.rewire_edge_rnd(graph, k=3)
                                              -

                                              Removes a random edge and adds one using ‘add_edge_rnd()’

                                              +

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

                                              Parameters
                                                @@ -570,7 +569,7 @@
                                                defenses.rewire_edge_rnd_neighbor(graph, k=3)
                                                -

                                                Removes a random edge and adds one using ‘add_edge_rnd()’

                                                +

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

                                                Parameters
                                                  @@ -587,7 +586,7 @@
                                                  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

                                                  +

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

                                                  Parameters
                                                    diff --git a/docs/build/html/measures.html b/docs/build/html/measures.html index 6fa5c32..7ee73ae 100644 --- a/docs/build/html/measures.html +++ b/docs/build/html/measures.html @@ -201,7 +201,7 @@

                                                    The larger the algebraic connectivity, the more robust the graph. This is due to it’s close connection to edge connectivity, where it serves as a lower bound: 0 < \(u_2\) < node connectivity < edge connectivity. This means that a network with larger algebraic connectivity -is harder to disconnect [10,5].

                                                    +is harder to disconnect [11,6].

                                                    Parameters

                                                    graph – undirected NetworkX graph

                                                    @@ -218,7 +218,7 @@

                                                    The global clustering coefficient is based on the number of triplets of nodes in the graph, and provides an indication of how well nodes tend to cluster together. The larger the average global clustering coefficient, the more robust the graph i.e., more triangles –> -better connected –> more robust graph [5].

                                                    +better connected –> more robust graph [6].

                                                    Parameters

                                                    graph – undirected NetworkX graph

                                                    @@ -235,7 +235,7 @@

                                                    The average distance between all pairs of nodes in the graph. The smaller the average shortest path distance, the more robust the graph. This can be viewed through the lens of network connectivity i.e., -smaller avg. distance –> better connected graph [5].

                                                    +smaller avg. distance –> better connected graph [6].

                                                    Undefined for disconnected graphs.

                                                    Parameters
                                                    @@ -253,7 +253,7 @@

                                                    Similar to vertex betweenness, edge betweenness is defined as the number of shortest paths that pass through an edge e out of the total possible shortest paths. The smaller the average edge betweenness, the more robust the graph. We can view this as the -load of the network being better distributed and less dependent on a few edges [5].

                                                    +load of the network being better distributed and less dependent on a few edges [6].

                                                    Parameters
                                                      @@ -273,7 +273,7 @@

                                                      The average inverse distance between all pairs of nodes in the graph. The larger the average inverse shortest path distance, the more robust the graph. This can be viewed through the lens of network connectivity i.e., larger average inverse distance -–> better connected graph –> more robust graph [5].

                                                      +–> better connected graph –> more robust graph [6].

                                                      Resolves the issue of not working for disconnected graphs in the avg_distance() function.

                                                      Parameters
                                                      @@ -291,7 +291,7 @@

                                                      The average vertex betweenness of a graph is the summation of vertex betweenness for every node in the graph. The smaller the average vertex betweenness, the more robust the graph. We can view this as the load of the network being better distributed and -less dependent on a few nodes [5].

                                                      +less dependent on a few nodes [6].

                                                      Parameters
                                                        @@ -310,7 +310,7 @@ measures.diameter(graph)

                                                        The diameter of a connected graph is the longest shortest path between all pairs of nodes. The smaller the diameter the more robust the graph i.e., smaller diameter –> -better connected graph –> more robust graph [5].

                                                        +better connected graph –> more robust graph [6].

                                                        Parameters

                                                        graph – undirected NetworkX graph

                                                        @@ -326,7 +326,7 @@ measures.edge_connectivity(graph)

                                                        Measures the minimal number of edges that can be removed to disconnect the graph. Larger edge connectivity –> harder to disconnect graph –> -more robust graph [7].

                                                        +more robust graph [8].

                                                        Parameters

                                                        graph – undirected NetworkX graph

                                                        @@ -343,7 +343,7 @@

                                                        This measure views a graph as an electrical circuit where an edge \((i, j)\) corresponds to a resister of \(r_{ij} = 1\) Ohm and a node i corresponds to a junction. We say the effective graph resistance R is the sum of resistances for all distinct pairs of vertices -The smaller the effective resistance, the more robust the graph [6,11,5].

                                                        +The smaller the effective resistance, the more robust the graph [6,7,12].

                                                        Parameters

                                                        graph – undirected NetworkX graph

                                                        @@ -358,7 +358,7 @@
                                                        measures.generalized_robustness_index(graph, k=30)

                                                        This can be considered a fast approximation of spectral scaling. The smaller the value, the more robust the graph. -Also helps determine if a graph has many bridges (bad for robustness) [12].

                                                        +Also helps determine if a graph has many bridges (bad for robustness) [14].

                                                        Parameters

                                                        graph – undirected NetworkX graph

                                                        @@ -400,7 +400,7 @@ measures.natural_connectivity(graph, k=inf)

                                                        Natural connectivity has a physical and structural interpretation that is tied to the connectivity properties of a network, identifying alternative pathways in a network through the weighted number of closed walks. -The larger the natural connectivity (average eigenvalue of adjacency matrix), the more robust the graph [3].

                                                        +The larger the natural connectivity (average eigenvalue of adjacency matrix), the more robust the graph [4].

                                                        Parameters

                                                        graph – undirected NetworkX graph

                                                        @@ -416,7 +416,7 @@ measures.node_connectivity(graph)

                                                        Measures the minimal number of vertices that can be removed to disconnect the graph. Larger vertex (node) connectivity –> harder to disconnect graph -–> more robust graph [7].

                                                        +–> more robust graph [8].

                                                        Parameters

                                                        graph – undirected NetworkX graph

                                                        @@ -433,7 +433,7 @@

                                                        The number of spanning trees T is the number of unique spanning trees that can be found in a graph. The larger the number of spanning trees, the more robust the graph. This can be viewed from the perspective of network connectivity, where a larger set of -spanning trees means more alternative pathways in the network [1,5].

                                                        +spanning trees means more alternative pathways in the network [1,6].

                                                        Parameters

                                                        graph – undirected NetworkX graph

                                                        @@ -447,7 +447,7 @@
                                                        measures.odd_subgraph_centrality(i, lam, u)
                                                        -

                                                        Calculates the number of odd length closed walks that a node participates in [9]. +

                                                        Calculates the number of odd length closed walks that a node participates in [10]. Used in the calculation of spectral scaling and generalized robustness index.

                                                        Parameters
                                                        @@ -489,7 +489,7 @@ (\(\lambda_1 - \lambda_2\)) is called the spectral gap \(\lambda_d\). The larger the spectral gap, the more robust the graph. Has an advantage over spectral radius since it accounts for -undesirable bridges in the network [2,12].

                                                        +undesirable bridges in the network [3,14].

                                                        Parameters

                                                        graph – undirected NetworkX graph

                                                        @@ -505,7 +505,7 @@ measures.spectral_radius(graph)

                                                        The largest eigenvalue \(\lambda_1\) of an adjacency matrix A is called the spectral radius. The larger the spectral radius, the more robust the graph. This can be viewed from its close relationship to the -“path” or “loop: capacity in a network [13,4].

                                                        +“path” or “loop: capacity in a network [5,17].

                                                        Parameters

                                                        graph – undirected NetworkX graph

                                                        @@ -519,8 +519,8 @@
                                                        measures.spectral_scaling(graph, k=inf)
                                                        -

                                                        Spectral scaling is a combination of spectral gap and subgraph centrality that helps determine if a graph has -many bridges (bad for robustness). The smaller the value, the more robust the graph [8].

                                                        +

                                                        Spectral scaling is a combination of the spectral gap and subgraph centrality. Spectral scaling takes into account +if a graph has many bridges (bad for robustness). The smaller the value, the more robust the graph [9].

                                                        Parameters

                                                        graph – undirected NetworkX graph

                                                        diff --git a/docs/build/html/searchindex.js b/docs/build/html/searchindex.js index 65cbc71..6edab41 100644 --- a/docs/build/html/searchindex.js +++ b/docs/build/html/searchindex.js @@ -1 +1 @@ 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to TIGER\u2019s documentation!","Introduction","Measures","TIGER","Simulation","Tutorial 1: Measuring Vulnerability and Robustness","Tutorial 2: Attacking a Network","Tutorial 3: Defending a Network","Tutorial 4: Cascading Failures","Tutorial 5: Entity Dissemination","Tutorials","Utils"],titleterms:{SIS:7,approxim:[7,11],attack:[0,12],background:7,bibliographi:1,cascad:[2,7,14],compar:11,defend:13,defens:3,diffus:4,dissemin:15,document:6,entiti:15,exampl:7,failur:[7,14],graph:[5,7],indic:6,instal:7,introduct:7,measur:[7,8,11],model:7,motiv:7,network:[7,12,13],non:11,robust:[7,11],simul:[7,10],tabl:6,tiger:[6,9],tutori:[11,12,13,14,15,16],util:17,vaccin:7,vulner:11,welcom:6}}) \ No newline at end of file