r-reachable

introduction

Definition 1(r-reachable~set): For any given r∈Nr\in\mathbb{N}r∈N, a subset of nodes S⊂NS\subset NS⊂N is said to be r-reachable if there exists a node vi∈Vv_i\in\mathcal{V}vi∈V such that ∥Ni\S∥≤r\|\mathcal{N}_i\backslash S\|\le r∥Ni\S∥≤r. rrr-reachable set is a tool to measure the connectivity among the graph, the bigger rrr is, the slighter one node be influenced by one of its neighbor. For example, a complete connected graph with mmm nodes has mmm-reachable set. Hence, the influence of a regular nodes receiving adversary message by a malicious node drops to minimize.

code(Matlab)

function [result] = r_reachable( graph, subset)
temp = 0;
len = length(subset);
gsize = size(graph, 1);
result = 0;
for i = 1:lenfor j = 1:gsizeif(subset(i)~=j && ~ismember(j,subset) && graph(subset(i),j)~=0)temp = temp+1;endcontinueendif result < tempresult = temp;endtemp = 0;
endend

r-robust

introduction

Definition 2(r-robust~graph): For r∈Nr\in\mathbb{N}r∈N, a graph GGG is said to be rrr-robust if for all pairs of disjoint nonempty subsets S1,S2⊂VS_1,S_2\subset\mathcal{V}S1,S2⊂V, at least one of S1S_1S1 or S2S_2S2 is rrr-reachable. The usage of rrr-robust graph is similar to rrr-reachable set. The distinguish between is that rrr -reachable represents local connectivity while rrr-robust represents global connectivity of a graph.Codes is given in index, significantly, it’s really complex to judge a graph is a r-robust with some r. In my opinion, it’s not a good index to measure a rather huge network. For example, we consider a network with 8 nodes, we need to split subset from 8 nodes totally 162 times.(C81+C82+C83+C84=162C_8^1+C_8^2+C_8^3+C_8^4=162C81+C82+C83+C84=162)

code(Matlab)

function [result] = r_robust( graph )
gsize = size(graph, 1);
temp1 = 0;
temp2 = 0;
result = gsize;
for i = 1:floor(gsize/2)combine = nchoosek([1:gsize], i);   for j = 1:size(combine, 1)   temp1 = r_reachable(graph, combine(j,:));corresp = [];for k = 1:gsizeif(~ismember(k, combine(j,:)))corresp(end+1) = k;endendtemp2 = r_reachable(graph, corresp);if(temp1 > temp2)temp2 = temp1;endif(temp2 < result)result = temp2;endend
end
end

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衡量连通图连通性一些指标(r-reachable, r-robust)

衡量连通图连通性的一些指标

r-reachable

introduction

code(Matlab)

r-robust

introduction

code(Matlab)

衡量连通图连通性一些指标(r-reachable, r-robust)相关推荐

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